Math and Numerical Method Simulators

Adaptive Filter Lms Simulator

Signal Processing

Explore LMS adaptive-filter convergence and misadjustment from step size, tap count, input power, noise level, and plant drift.

AM/FM Modulation Simulator

Signal Processing

Learn how a message signal such as audio is "carried" by a radio wave through modulation.

Autocorrelation Function Simulator — Period Detection

Signal Processing

The autocorrelation simulator computes the biased autocorrelation R_xx[k] of a noisy sinusoid and visualizes how period detection works by finding the largest peak at lag k.

Bayes' Theorem Visualizer — Conditional Probability & Posterior Update

Statistics & Regression

Adjust prior probability, true positive rate, and false positive rate to calculate posterior probability in real time. Intuitively understand probability updating from e…

Bayesian Calibration via MCMC (Metropolis–Hastings) Simulator

Monte Carlo & Uncertainty

Bayesian Calibration via MCMC (Metropolis–Hastings) Simulator: Calibrate a CAE model parameter the Bayesian way: feed in a prior, a likelihood and observed d…

Bézier Curve Simulator

Geometry & Visualization

Bézier Curve Simulator: An interactive tool for the smooth curves that just a handful of control points can "shape". Move the control points P1 and P2 and wa…

Bifurcation Diagram Simulator — Logistic Map and Chaos

Dynamical Systems & Chaos

Vary the parameter r of the logistic map to visualize the period-doubling route to chaos in real time. Lyapunov exponent displayed simultaneously.

Binomial Distribution Simulator

Statistics & Regression

Binomial distribution B(n,p) simulator. Vary trials n and probability p to visualize PMF, CDF and Poisson/normal approximations in real time.

Bisection Method Simulator — Root Finding by Interval Bracketing

Numerical Analysis

Find roots of f(x)=0 with the bisection method on f(x)=x^3-2x-5. Visualize midpoints, the shrinking bracket and log10 width decay. Tune interval, tolerance, max iter.

Bit Error Rate (BER) Simulator

Signal Processing

Bit Error Rate (BER) Simulator: Compute the bit error rate (BER) that decides the quality of a digital link. Adjust the signal-to-noise ratio Eb/N0, the modu…

Bootstrap Confidence Interval Simulator

Monte Carlo & Uncertainty

Compute 95% bootstrap confidence intervals for the mean and median in real time. Resample with replacement and vary N and B to watch the distribution converge.

Break-Even Analysis Simulator — Fixed Costs, Variable Costs & Profit

Finance & Economics

Break-even analysis simulator. Enter fixed cost, variable cost, price, volume to calculate break-even point, contribution margin and margin of safety in real time.

Brownian Motion & Random Walk Simulator

Monte Carlo & Uncertainty

Brownian motion simulator to verify Einstein's diffusion formula and explore parameters.

Buckingham Pi Theorem Simulator — Dimensional Analysis & Model Similitude

Numerical Analysis

Buckingham Pi Theorem Simulator for dimensional analysis. Visualize Reynolds number and drag coefficient. Learn model similitude and scale-model testing.

Buffon's Needle Simulator — Estimating Pi by Probability

Monte Carlo & Uncertainty

Buffon's needle simulator drops needles at random on a floor of parallel lines and estimates pi from the crossing probability P = 2L/(pi d). Vary needle count, length, line spacing and LCG seed.

Capacity Planning Little Law Simulator

Optimization & OR

Capacity Planning Little Law Simulator: Explore arrival rate, service time, WIP, and utilization with interactive queue modeling for engineers.

Cellular Automata

Dynamical Systems & Chaos

Explore 1D Wolfram rules and Conway's Game of Life. See how simple local rules create extraordinary complexity in cellular automata.

CFL Number Simulator — Stability of Explicit Time Integration

ODEs & PDEs

Real-time Courant number calculator for explicit time integration. Adjust advection speed u, time step dt, grid spacing dx and CFL_max to monitor 1D advection stability.

Chi-Squared Goodness-of-Fit Test Simulator — Pearson's Test

Statistics & Regression

Chi-squared goodness-of-fit test simulator. Vary the four observed counts O_i to compute chi-squared statistic, df, 5% critical value, and the H_0 decision in real time.

Chirp-Z Transform / Zoom-DFT Simulator — High-Resolution Narrow-Band Analysis

Signal Processing

Chirp-Z Transform simulator for high-resolution narrow-band frequency analysis. Zoom into custom frequency ranges, resolve closely spaced tones with flexible bin resolution.

Cholesky Decomposition Simulator

Linear Algebra & Matrices

Free Cholesky decomposition calculator: enter a symmetric 3×3 matrix and factor it as A=LLᵀ. Check positive-definiteness with Sylvester's criterion and visualise the lower-triangular factor L, the determinant and the operation count versus LU.

Complex Function & Conformal Mapping Visualizer

Geometry & Visualization

Visualize complex functions with domain coloring. Explore conformal mapping, Joukowski transforms, and the residue theorem interactively.

Complex Number Visualizer — Argand Plane, Polar Form & Operations

Geometry & Visualization

Complex Number Visualizer: Manipulate two complex numbers on the complex plane in real time. Explore addition, subtraction, multiplication, division, conjuga…'s formula, and De Moivre's theorem. A free tool to intuitively understand rotation and scaling on the complex plane.

Complex Number & Phasor Calculator

Geometry & Visualization

Complex number and phasor calculator for AC circuit analysis, impedance calculations, and Argand diagram visualization with real-time computation.

Compound Interest Simulator

Finance & Economics

Visualize compound asset growth in real time. Adjust principal, annual rate, contributions and inflation to compare with simple interest and apply the Rule of 72.

Compressive Sensing & L1 Reconstruction Simulator

Signal Processing

A hands-on simulator for compressive sensing: recover a "sparse" N-dimensional signal that has only K non-zero entries from far fewer than Nyquist measurements, using L1…

Matrix Condition Number Simulator

Linear Algebra & Matrices

Matrix Condition Number Simulator: Compute the condition number κ(A) of a 2×2 matrix and visualize its ill-conditioning. As you change the matrix entries, th…

Conic Sections Explorer — Ellipse, Parabola & Hyperbola Visualizer

Geometry & Visualization

Conic Sections Explorer: Interactively adjust parameters for circles, ellipses, parabolas, and hyperbolas in real time. Visualize foci, directrices, eccentri…

Conjugate Gradient Method Simulator — CG vs Steepest Descent

Linear Algebra & Matrices

The conjugate gradient simulator iteratively solves Ax=b for a symmetric positive definite matrix and compares the residual history with steepest descent in real time.

Control Variates Simulator

Monte Carlo & Uncertainty

Control Variates Simulator: Experience the control variates method, which boosts Monte Carlo accuracy almost for free. Using an auxiliary variable strongly c…

Crank Nicolson Simulator

ODEs & PDEs

Crank-Nicolson simulator for analyzing diffusion, stability r-values, and numerical scheme behavior with varying time-space steps.

Derivative & Tangent Line Visualizer

Geometry & Visualization

Interactive derivative and tangent line visualization tool for understanding calculus concepts, slope computation, and function behavior analysis.

Design of Experiments (DOE) Simulator

Optimization & OR

Switch between full factorial, fractional factorial, Central Composite Design (CCD) and Plackett-Burman to compare required runs, statistical power and savings vs OFAT i…

DFT Leakage Window Detail Simulator

Signal Processing

DFT leakage window simulator for analyzing scalloping loss, bin offset, and equivalent noise bandwidth in spectral analysis.

ODE Phase Plane Analysis Tool

ODEs & PDEs

Visualize ODE systems with phase planes, nullclines, and stability analysis. Explore predator-prey and pendulum models with real-time RK4 trajectories.

1D Diffusion Equation Solver

ODEs & PDEs

Solve the 1D diffusion equation using Crank-Nicolson method. Gaussian, step, and sine initial conditions with Dirichlet/Neumann/periodic BCs.

Digital Filter Designer (IIR/FIR)

Signal Processing

Design Butterworth, Chebyshev, and FIR filters. Visualize frequency response, coefficients, and test signals in real-time with this advanced digital filter designer tool.

Design of Experiments (DOE)

Optimization & OR

Optimize designs with factorial & Taguchi L9 DOE. Automatically calculate main effects, ANOVA, F-test, and SN ratios for robust engineering analysis.

Dynamic Time Warping (DTW) Simulator

Signal Processing

Dynamic Time Warping (DTW) Simulator: An interactive tool for Dynamic Time Warping, the classic algorithm that compares two time series whose speed or phase …

SIR Epidemic Model Simulator — Herd Immunity & Outbreak Dynamics

Dynamical Systems & Chaos

Interactive simulator to explore herd immunity and outbreak dynamics. Adjust parameters for COVID-19, flu, and measles to see how R₀ and vaccination stop epidemics.

Euler Method vs RK4 Comparison

ODEs & PDEs

Compare Euler and RK4 methods for solving ODEs. Visualize accuracy differences O(h), O(h²), O(h⁴) by adjusting step size in this interactive numerical analysis tutorial.

Generalized Extreme Value (GEV) Distribution Simulator

Statistics & Regression

Generalized Extreme Value (GEV) Distribution Simulator: Use the Generalized Extreme Value distribution to compute the "100-year event" and the probability th…

Eye Diagram Simulator

Signal Processing

Eye Diagram Simulator: Reproduce the "eye diagram" that shows the quality of a high-speed digital signal at a glance. Adjust the bit rate, rise time, jitter …

FFT Spectrum Analyzer — Time-Domain Signal to Frequency Spectrum

Monte Carlo & Uncertainty

Analyze time-series signals with the Fast Fourier Transform. Tweak window functions, sampling frequency and signal components to feel aliasing and leakage.

FFT Spectrum Analyzer Simulator

Signal Processing

Simulate FFT spectrum analysis with up to 5 sine waves. Explore windowing, spectral leakage, THD, and DFT parameters like frequency resolution in real time.

1D Finite Volume Method Simulator — Steady Diffusion

ODEs & PDEs

1D Finite Volume Method Simulator — Steady Diffusion: Solve the 1D steady diffusion equation with the finite volume method (FVM). The domain is split into co…

FIR Filter Design Simulator — Window Method

Signal Processing

Design linear-phase FIR low-pass filters by the window method. Impulse, dB magnitude, transition width, stopband attenuation and group delay update live.

Fourier Epicycles Simulator — Draw Any Curve with Rotating Circles

Signal Processing

Draw a curve with your mouse and watch it decomposed by DFT into rotating circles (epicycles). Adjust the number of circles in real time to see how Fourier approximation works.

Fourier Series Visualizer — Rotating Phasors & Wave Synthesis

Signal Processing

Explore Fourier series synthesis: simulate square, triangle, and sawtooth waves with 1-50 harmonics. Watch Gibbs phenomenon and harmonic spectrum evolve in real-time.

Fourier Transform Visualizer — FFT Spectrum Analyzer

Signal Processing

Explore Fourier transforms interactively. Adjust signals, windows and frequencies with sliders to visualize real-time waveform and spectrum changes.

Mandelbrot Set Viewer

Dynamical Systems & Chaos

Explore the infinite complexity of the Mandelbrot fractal. Zoom, navigate, and discover Julia sets in this interactive mathematical visualization.

Fractal Tree & Snowflake Generator — Self-Similarity & Fractal Dimension

Dynamical Systems & Chaos

Explore fractal geometry. Generate self-similar trees, Koch snowflakes, Sierpinski triangles, and Dragon curves by tuning parameters. Discover infinite patterns.

Conway's Game of Life — Cellular Automaton Simulator

Dynamical Systems & Chaos

Conway's Game of Life. Draw cells, create patterns, and discover emergent complexity driven by three simple rules.

Game Theory Simulator — Nash Equilibrium, Prisoner's Dilemma & Evolutionary Games

Optimization & OR

Edit game theory matrices and simulate outcomes. Automatically find Nash equilibria and watch cooperation evolve in real-time.

Gauss Quadrature Simulator

Numerical Analysis

Gauss Quadrature Simulator: Experience Gauss-Legendre quadrature, the rule the finite element method uses to integrate element stiffness matrices. Change the…

Gauss Quadrature Simulator — Convergence of Gauss-Legendre Integration

Numerical Analysis

The Gauss quadrature simulator visualizes the sample points and weights of Gauss-Legendre integration and computes the numerical integration error and convergence in real time.

Gauss-Seidel Simulator — Iterative Solution of Linear Systems

Linear Algebra & Matrices

Gauss-Seidel iteration simulator for Ax=b. Sweep SOR omega from 0.5 to 1.9 to visualize convergence trajectories and log10 residual decay in real time.

Gershgorin Circle Theorem Simulator

Linear Algebra & Matrices

The Gershgorin circle theorem lets you bound where the eigenvalues of a matrix must be from its entries alone, without ever computing them.

Gibbs Sampling Simulator

Monte Carlo & Uncertainty

Gibbs Sampling Simulator: Draw samples from a bivariate normal distribution with Gibbs sampling, the classic MCMC (Markov chain Monte Carlo) method. Adjust t…

Gini Coefficient Simulator — Income Inequality & Lorenz Curve

Finance & Economics

Interactively visualize the Gini coefficient and Lorenz curve. Adjust the shape of the income distribution and see changes in inequality in real time.

Goertzel Algorithm Simulator — DTMF Single Frequency Detection

Signal Processing

Detect DTMF tones with the Goertzel algorithm. A second-order IIR filter extracts 8 DFT bins in O(N), ideal for embedded single-tone detection without an FFT.

Hilbert Transform & Analytic Signal — Envelope Detection

Signal Processing

The Hilbert envelope simulator applies a DFT-based Hilbert transform to an AM signal and extracts instantaneous amplitude, phase and frequency to visualize envelope detection.

Huber Regression Robust Simulator

Statistics & Regression

Explore the Huber M-estimator for robust regression.

Hypothesis Test Calculator (z-test & t-test)

Statistics & Regression

Run interactive z-tests and t-tests. Get real-time p-values, see critical regions on a chart, and calculate effect size instantly.

Bilinear Transform Simulator — Analog to Digital IIR

Signal Processing

Bilinear Transform Simulator — Analog to Digital IIR: Convert an analog first-order lowpass filter H(s)=ωc/(s+ωc) into a digital IIR filter with the bilinear…

IIR Filter Designer — Butterworth Low-Pass Magnitude Response

Signal Processing

IIR Butterworth low-pass filter designer. Visualize gain |H(jω)| on a Bode plot in real time and compute the minimum order needed for given f_c, f_s and A_s.

Importance Sampling — Efficient Tail Probability Estimation

Monte Carlo & Uncertainty

Importance Sampling for tail probability estimation: reduce Monte Carlo variance by tuning proposal distributions. Interactive simulator for engineers.

Inflation & Purchasing Power Simulator — CPI, Real Value & Time Value

Finance & Economics

Inflation & Purchasing Power Calculator: Adjust inflation rate, time period, and initial amount to calculate purchasing power change, real interest rate, and…

Interpolation Methods Comparison

Numerical Analysis

Compare Lagrange, Newton, cubic spline, PCHIP, and linear interpolation methods. Understand Runge's phenomenon and choose optimal interpolation techniques for CAE applications.'s phenomenon and understand continuity conditions for piecewise cubic functions.

Inventory Management EOQ & Reorder Point Calculator

Optimization & OR

Calculate your optimal order quantity and reorder point with this free EOQ calculator. Visualize cost tradeoffs and inventory patterns.

Isotonic Regression Simulator

Statistics & Regression

Isotonic Regression Simulator: An interactive tool for monotone nonparametric regression. Adjust sample size, noise level and constraint direction to see PAV…

Jacobi Eigenvalue Method Simulator

Linear Algebra & Matrices

Jacobi Eigenvalue Method Simulator: Find the eigenvalues of a symmetric 3×3 matrix with the Jacobi method — a sequence of plane rotations. Change the diagona…

Jacobi Iteration Simulator — Linear Systems

Linear Algebra & Matrices

Solve a 2x2 linear system A·x=b by the Jacobi iterative method.

Kaplan-Meier Survival Analysis Simulator

Statistics & Regression

Kaplan-Meier Survival Analysis Simulator: Estimate a survival curve from censored time-to-event data with the Kaplan-Meier method. Adjust the sample size, tr…

Lagrange Multiplier Optimization Simulator

Optimization & OR

Lagrange Multiplier Optimization Simulator: A tool that visualizes the Lagrange multiplier method for optimizing an objective function under an equality cons…

Lambert Conformal Conic (LCC) Projection Simulator

Geometry & Visualization

Lambert Conformal Conic (LCC) Projection Simulator: Wrap a cone around the Earth so that it intersects along two standard parallels, then project geodetic po…

Laplace Transform Calculator & Visualizer

Signal Processing

Master Laplace transforms with our interactive calculator. Visualize f(t) and F(s), compute partial fractions, and explore pole-zero maps in real time.

Latin Hypercube Sampling — LHS vs Plain Monte Carlo

Monte Carlo & Uncertainty

Latin Hypercube Sampling vs Monte Carlo: stratified design sampling technique for improved integration accuracy and uncertainty quantification in CAE.

Linear Algebra Matrix Transformation Visualizer

Linear Algebra & Matrices

Visualize 2D matrix transformations in real time. Control a 2x2 matrix, animate rotations, scaling, shear, and see eigenvectors and eigenvalues.

Linear Programming

Optimization & OR

Learn to solve 2-variable linear programming problems visually. See the feasible region, optimal vertex, and objective lines in real-time with graphical method steps.

Linear Regression Simulator

Statistics & Regression

Visualize least-squares linear regression interactively. Add data points and see how the regression line updates in real time.

Loan Amortization Calculator

Finance & Economics

Simulate monthly payments, total interest and balance for fixed-rate loans. Adjust principal, rate and term interactively.

Logistic Population Growth Model

Dynamical Systems & Chaos

Simulate population growth, stabilization and overshoot using the logistic equation. Adjust carrying capacity and growth rate.

Lorenz Attractor Simulator — Butterfly Effect & Chaos

Dynamical Systems & Chaos

Explore chaos theory with a real-time Lorenz Attractor simulator. Adjust parameters, launch trajectories, and witness the butterfly effect in 3D.

LU Decomposition Simulator — Direct Solver for Ax=b

Linear Algebra & Matrices

The LU decomposition simulator factors a 3x3 matrix into L and U and solves Ax=b with forward and back substitution in real time, with partial pivoting.

Mandelbrot Set Explorer

Dynamical Systems & Chaos

Explore the infinite Mandelbrot set fractal in real time. Zoom, pan, and switch to Julia mode to discover its self-similar geometry.

Markov Chain Simulator — Two-State Stationary Distribution and Mixing Time

Monte Carlo & Uncertainty

Two-state Markov chain simulator. Vary p, q to see the stationary distribution π=(q/(p+q), p/(p+q)), the t-step probability P_1(t), and 99% mixing time t_mix.

Matched Filter Simulator — Pulse Detection in Noise

Signal Processing

Matched filter simulator: detect a known pulse in white noise via convolution. Compute input/output SNR and processing gain in real time, visualize gain = L.

Matrix Operations & Eigenvalue Calculator

Linear Algebra & Matrices

Compute matrix operations instantly: addition, multiplication, determinant, inverse, eigenvalues, eigenvectors, and solve linear systems. Free online calculator.

Matrix Transformation Visualizer — Geometric Meaning of Linear Algebra

Linear Algebra & Matrices

Visualize 2x2 matrix transformations with animation. See the grid, basis vectors, and shapes change while computing determinant and eigenvalues.

MCMC Metropolis-Hastings Sampler — Acceptance & Autocorrelation

Monte Carlo & Uncertainty

MCMC Metropolis-Hastings sampler for arbitrary 1D distributions. Tune proposal variance, analyze chain mixing, trace plots, and autocorrelation. Bayesian inference sampling.

MFCC Feature Simulator — Mel-Frequency Cepstral Coefficients

Signal Processing

The MFCC simulator applies pre-emphasis, a Hamming window, FFT, a mel filter bank, log and DCT to extract Mel-Frequency Cepstral Coefficients from a speech signal in real time.

Monte Carlo Pi Estimator

Monte Carlo & Uncertainty

Estimate π using random numbers! This Monte Carlo simulation drops points into a square to reveal the value of Pi through probability and error analysis.

Monte Carlo Statistics Simulator — π, Integration, CLT

Monte Carlo & Uncertainty

Explore Monte Carlo methods: estimate π, test the Central Limit Theorem, perform integration, and simulate random processes with this interactive statistics simulator.

Morris Elementary Effects Method Simulator

Monte Carlo & Uncertainty

Morris Elementary Effects Method Simulator: Run the cheapest global sensitivity method — the Morris Elementary Effects (EE) screening — directly in your brow…

Multigrid Simulator — V-cycle for 1D Poisson

Linear Algebra & Matrices

Multigrid V-cycle solver for 1D Poisson equation. Accelerate convergence orders of magnitude faster than Gauss-Seidel. Residual reduction, numerical methods.

Mutual Information (MI) Estimation Simulator

Signal Processing

An interactive playground for I(X;Y), the information-theoretic measure of dependence that captures both linear and non-linear relations.

Newton-Raphson Simulator — Roots of Nonlinear Equations

Numerical Analysis

Find roots of f(x)=0 with the Newton-Raphson method. Visualize tangent steps and the log10 error curve for f(x)=x^3-2x-5. Tune initial guess, tolerance, and relaxation.

Normal Distribution Calculator & Visualizer

Statistics & Regression

Interactive normal distribution tool. Set μ and σ to visualize PDF/CDF, compute probabilities, Z-scores, and percentiles instantly.

Numerical Integration Methods Comparator (Trapezoidal, Simpson, Gauss)

Numerical Analysis

Compare Trapezoidal, Simpson's, Gauss-Legendre & Romberg integration methods. View error convergence rates and accuracy orders in a detailed log-log chart.

ODE Numerical Methods Comparison

ODEs & PDEs

Compare Euler, Heun (RK2), and RK4 ODE solvers. Adjust step size to see global error update in real time. Visualize the accuracy difference: O(h), O(h²), O(h⁴).

Nyquist Sampling Theorem Simulator — Aliasing of Sampled Signals

Signal Processing

Nyquist sampling simulator: signal frequency f, sampling rate f_s, duration and bit depth N to compute Nyquist f_s/2, alias frequency f_alias and quantisation SNR=6.02N+1.76 dB.

Numerical ODE Solver Comparison

ODEs & PDEs

Compare Euler, Heun, RK2, RK4, and RK45 ODE solvers. Visualize accuracy and stability on problems like logistic growth and Van der Pol.

Option Pricing Calculator — Black-Scholes Model & Greeks

Finance & Economics

Calculate call/put option prices, Greeks, and implied volatility in real time. Visualize payoff diagrams and delta curves with our Black-Scholes calculator.

Parseval's Theorem — Energy Conservation in Time and Frequency

Signal Processing

Parseval's theorem for the DFT: time-domain energy of a discrete signal equals frequency-domain energy. Test with sinusoid, rectangular pulse and Gaussian signals in real time.

Particle Size Distribution (Rosin-Rammler Analysis)

Statistics & Regression

Analyze particle size with Rosin-Rammler, Log-Normal, or GGS models. Compute d10/d50/d90, cumulative curves, and histograms instantly. Perfect for CAE simulation.

PERT/CPM Network Project Schedule Calculator

Optimization & OR

Calculate project critical path and on-time probability with this PERT/CPM network scheduler. Automates forward/backward pass for up to 12 activities.

Phase Space Portrait — Nonlinear Dynamics & Chaos Visualizer

Dynamical Systems & Chaos

Visualize nonlinear dynamics and chaos. Simulate Lorenz, Duffing, Van der Pol systems, explore attractors and limit cycles with this interactive RK4 integrator.

Picard Iteration (Fixed-Point) Simulator

Numerical Analysis

Visualize fixed-point iteration — rewrite an equation as x = g(x) and repeat x_{n+1} = g(x_n). Change the map g(x), the starting value and the step count to watch the co…

Polynomial Chaos Expansion (PCE) Simulator

Monte Carlo & Uncertainty

Polynomial Chaos Expansion (PCE) Simulator: For a Gaussian input X ~ N(μ, σ²) and the model Y = a₁X + a₂X², this tool builds a Hermite Polynomial Chaos Expan…

Predator-Prey (Lotka-Volterra) Simulator — Population Dynamics

Dynamical Systems & Chaos

Explore predator-prey dynamics with an interactive Lotka-Volterra simulator. Adjust key parameters and visualize population oscillations and phase portraits.

Population Pyramid Simulator — Age-Sex Structure & Demographic Transition

Statistics & Regression

Population pyramid simulator. Adjust fertility rate, life expectancy and migration to visualize age structure changes in real time, with aging and dependency ratio.

Power Iteration Simulator — Dominant Eigenvalue by Iteration

Linear Algebra & Matrices

The power iteration simulator estimates the dominant eigenvalue and eigenvector of a 3x3 symmetric matrix by iterating v ← Av/||Av|| and reading the Rayleigh quotient.

Predictor-Corrector Method Simulator — Heun's Method

ODEs & PDEs

A tool that visualizes Heun's method, the two-stage predictor-corrector integrator for ordinary differential equations.

Birthday Paradox Probability Calculator

Statistics & Regression

Calculate and animate the probability that at least two people share a birthday in a group of n people.

Probability Distributions Calculator — Normal, Poisson, Binomial, Exponential

Statistics & Regression

Interactive probability distributions calculator. Plot PDF/PMF and CDF curves, compute percentiles, mean, and variance in real time.

QR Decomposition Simulator — Gram-Schmidt & Least Squares

Linear Algebra & Matrices

QR decomposition using Gram-Schmidt for least-squares problems. Learn orthogonal matrix factorization and back substitution techniques for engineers.

Quadratic Function Explorer

Geometry & Visualization

Explore the graph of y = ax² + bx + c interactively. Drag a, b and c sliders to see vertex, axis of symmetry, discriminant and roots plotted live in three tabs.

Quantile Regression Simulator

Statistics & Regression

Quantile Regression Simulator: Place quantile regression (QR) side by side with ordinary least squares. Move the sample size, the quantile tau, the noise dis…

Quasi-Monte Carlo Simulator — Sobol Sequence

Monte Carlo & Uncertainty

Quasi-Monte Carlo Simulator — Sobol Sequence: Integrate numerically with low-discrepancy sequences such as the Sobol and Halton sequences. Change the sample …

Queuing Theory Simulator — M/M/1 & M/M/c Queue Analysis

Optimization & OR

Queuing Theory (M/M/c) Calculator: Adjust arrival rate λ, service rate μ, and number of servers c to visualize average wait time, queue length, and probabili…

2D Random Walk Simulator — MSD & Diffusion Coefficient

Monte Carlo & Uncertainty

Simulate 2D random walks in real time. Visualize diffusion laws with MSD plots and switch between lattice, Gaussian, and Lévy flight modes.

Regression Analysis & Curve Fitting

Statistics & Regression

Interactive regression analysis tool: add data points, choose models, and instantly view R², RMSE, fitted equations, and residuals.

Rejection Sampling Simulator — Monte Carlo Sample Generation

Monte Carlo & Uncertainty

Rejection sampling simulator for Monte Carlo methods. Visualize envelope-based sample generation from complex distributions. Learn proposal functions and acceptance rates.

Response Surface Methodology (RSM) Simulator

Optimization & OR

Response Surface Methodology (RSM) Simulator: A hands-on simulator for Response Surface Methodology — the workhorse technique for optimizing process conditio…

Richardson Extrapolation & Order of Accuracy Simulator

Numerical Analysis

From three step sizes and three numerical solutions, get the observed order of accuracy p and the Richardson-extrapolated true value u_ext in real time.

Ridge Regression (Tikhonov) Shrinkage Simulator

Statistics & Regression

Ridge Regression (Tikhonov) Shrinkage Simulator: Change the L2 penalty λ of ridge regression (Tikhonov regularisation) and watch the effective degrees of fre…

Riemann Sum Numerical Integration Visualizer

Numerical Analysis

Compare five numerical integration methods — left, right, midpoint, trapezoidal, and Simpson's rule — intuitively. Increase partition count n and observe how errors conv…

Runge-Kutta Stability Simulator

ODEs & PDEs

Free Runge-Kutta stability simulator: visualize the absolute stability of forward Euler, RK2 and RK4. Compute the amplification factor R(z) of the test equation y'=λy and the complex-plane stability region to see how large a step size h you can use without the numerical solution blowing up.

Runge-Kutta Simulator — RK4 vs Euler Accuracy Comparison

ODEs & PDEs

Runge-Kutta RK4 vs Euler accuracy simulator: integrate dy/dx = -k*y in real time, compare against the exact solution y0*exp(-k*x), and visualise cumulative error on a log10 scale.

Secant Method Simulator — Derivative-Free Root Finding

Numerical Analysis

Find roots of f(x)=0 with the secant method, a derivative-free root finder. Visualize secant lines, log10 error decay on f(x)=x^3-2x-5. Tune the two initial points and tolerance.

Shannon Channel Capacity Simulator — Information Theory Limit

Signal Processing

Compute Shannon-Hartley capacity C=B·log2(1+S/N) in real time from bandwidth, signal and noise power. Visualises SNR, spectral efficiency and required bandwidth for a target rate.

Shooting Method Simulator

ODEs & PDEs

Shooting Method Simulator: Solve boundary value problems by iteratively guessing initial slopes and adjusting aims. Numerical methods, BVP solver.''=c·y into an initial value problem, integrates with 4th-order Runge-Kutta, and iterates the unknown initial slope until the trajectory hits the boundary target.

Digital Filter Design — Frequency Response Simulator

Signal Processing

Design digital low-pass, high-pass and band-pass filters and inspect their frequency response in real time.

Digital Filter Frequency Response Design Tool

Signal Processing

Design and visualize Butterworth, Chebyshev & Bessel IIR filter responses in real time. Adjust type, order, and cutoff frequency instantly.

Signal Modulation Simulator

Signal Processing

Visualize AM, FM, and PM modulation in real time. Adjust parameters like carrier frequency and modulation index to see waveforms and spectra.

Signal & Noise SNR Analyzer

Signal Processing

Analyze signal integrity in real time. Add noise types, compute SNR/ENOB, and visualize results with this interactive CAE tool.

Sampling Theorem & Aliasing Visualizer

Signal Processing

Visualize the Nyquist-Shannon sampling theorem interactively. See real-time aliasing when sampling is too slow and understand the Nyquist frequency.

Significant Figures, Rounding & Measurement Uncertainty Calculator

Numerical Analysis

Calculate significant figures, apply rounding rules, and determine measurement uncertainty for addition, subtraction, multiplication, division, and more.

Sobol Sensitivity Indices Simulator

Monte Carlo & Uncertainty

A hands-on global sensitivity analysis tool that decomposes how input uncertainty drives output variance into main effects and interactions.

Successive Over-Relaxation (SOR) Simulator

Linear Algebra & Matrices

Solve the 1D Laplace equation with an iterative solver.

Natural Cubic Spline Interpolation Simulator

Numerical Analysis

Natural cubic spline interpolation simulator for engineers. Visualize smooth curves through data points, compare with linear interpolation, and understand tridiagonal system solving in real time.

Spread Spectrum Processing Gain Simulator

Signal Processing

Design a direct-sequence spread spectrum (DSSS) communication link.

Central Limit Theorem Simulator — Sampling Distribution Visualization

Monte Carlo & Uncertainty

Central Limit Theorem Simulator: Repeatedly sample from uniform, exponential, bimodal, or skewed distributions. Vary sample size n and observe how sample mea…

Normal Distribution Simulator

Statistics & Regression

Normal Distribution Simulator: Adjust mean and standard deviation to explore probability distributions and statistical analysis for engineering applications.

Stratified Sampling Simulator

Monte Carlo & Uncertainty

Stratified Sampling Simulator: A tool for experiencing stratified sampling, a way to boost the accuracy of Monte Carlo integration for free. Split the interv…

Supply & Demand Curve Simulator

Finance & Economics

Manipulate shifts in the demand and supply curves in real time to visualize changes in equilibrium price and quantity. A free tool to learn price elasticity and surplus analysis.

Higher-Order Taylor Error Propagation Simulator — Mean Shift, Skewness & Kurtosis to 4th Order

Numerical Analysis

Higher-Order Taylor Error Propagation Simulator — Mean Shift, Skewness & Kurtosis to 4th Order focuses on nearby design assumptions and key metrics, giving a compact rea…

Taylor Series Approximation Visualizer

Numerical Analysis

Use this page to relate representative assumptions to nearby design assumptions and key metrics before moving into the adjacent engineering checks.

Taylor Series Approximation Visualizer

Numerical Analysis

Visualize Taylor series approximations for sin, cos, eˣ, and more. Adjust order and expansion point to explore convergence, error, and applications in FEM and Newton's method.

Thomas Algorithm (Tridiagonal Solver) Simulator

Linear Algebra & Matrices

Thomas Algorithm (Tridiagonal Solver) Simulator: Experience the Thomas algorithm (TDMA) solving a tridiagonal linear system in O(n). It discretises and solve…

Topology Optimization Map Viewer — SIMP Density Distribution

Geometry & Visualization

Generate virtual terrain from mathematical functions and visualize contour maps, gradient heat maps, and cross-section profiles in real time.

Traffic Flow Simulator — LWR Model Speed-Density-Flow Diagram

Dynamical Systems & Chaos

Plot the traffic-flow fundamental diagram with Greenshields, Greenberg and Underwood models. See how congestion emerges as density crosses the critical value.

Unit Circle Trigonometry Animator

Geometry & Visualization

Unit Circle Trigonometry Animator: Adjust angle θ to confirm how point P on the unit circle and sin, cos, tan values change in real time. Waveform graph and …

Truncation Error & Order of Accuracy Visualization Tool

Numerical Analysis

Visualize truncation error and order of accuracy with our free online calculator. Understand numerical methods through interactive graphs and examples.

Uncertainty Propagation & Monte Carlo Analysis Tool

Monte Carlo & Uncertainty

Calculate measurement uncertainty with our free Monte Carlo analysis tool. Simulate error propagation and analyze results online instantly.

Engineering Unit Converter

Convert 100+ engineering units across 16 categories. Supports SI and mm-tonne-s systems for Abaqus and LS-DYNA, highlighting CAE-critical units at a glance.

2D Vector Addition Simulator

Linear Algebra & Matrices

Add up to five vectors and calculate the resultant in real time.

2D Vector Field Visualizer

Linear Algebra & Matrices

Visualize 2D vector fields with arrows and streamlines. Switch between uniform flow, source, vortex, dipole and saddle and adjust strength and grid density.

Waveform Generator & Synthesizer — RMS, FFT Spectrum, THD Calculator

Signal Processing

Design complex waveforms by combining up to 4 signal components. Instantly analyze key metrics like RMS, THD, and crest factor while visualizing the composite result.

Daubechies-4 Wavelet Simulator — db4 Multiresolution Analysis

Signal Processing

Interactive Daubechies-4 (db4) wavelet simulator: multi-level DWT of 1D signals, thresholding of detail coefficients, and reconstruction MSE. Smoother basis than Haar.

Haar Wavelet Transform Simulator — Multiresolution Analysis and Compression

Signal Processing

Haar wavelet decomposition for step signal analysis with real-time coefficient visualization, compression, and reconstruction error thresholding.

Window Function Spectral Comparison — Mainlobe Width and Sidelobe Suppression

Signal Processing

Window Function Spectral Comparison tool for analyzing mainlobe width and sidelobe suppression in rectangular, Hann, Hamming, Blackman windows. Spectral leakage analysis.

Z-Transform & Digital Signal System Analyzer

Signal Processing

Visualize and analyze digital filters in real-time. Enter H(z) coefficients to get pole-zero plots, frequency & impulse responses, and stability checks.