Physics Simulators

3D Projectile Motion Simulator (Drag & Magnus Effect)

3D Projectile Motion

Simulate 3D projectile trajectory with air resistance and Magnus effect. Ballistic analysis for artillery shells and sports balls.

ProjectileMagnus Effect3DAir Resistance

Simple Pendulum Simulator

Simple Pendulum

Real-time simulation of period, amplitude, and angular velocity of a simple pendulum. Compare small-angle approximation with exact solution; supports damped pendulum.

Simple PendulumPeriodAmplitudeDamping

Uniform Circular Motion Simulator

Circular Motion

Real-time calculation of centripetal acceleration, centrifugal force, period, and angular velocity of uniform circular motion. Applied to planetary orbits and vehicle cornering.

Circular MotionCentripetal AccelerationCentrifugal ForceAngular Velocity

Doppler Effect Calculator

Doppler Effect

Calculate apparent frequency change due to the Doppler effect from source and observer velocities. Includes visualizations for ambulances and the sound barrier.

Doppler EffectFrequencySource VelocitySpeed of Sound

Ideal Gas Law Calculator

Gas Laws

Calculate Boyle's, Charles', Gay-Lussac's laws and the ideal gas equation PV=nRT. Visualize P-V-T changes with graphs.

Ideal GasEquation of StateP-V-TBoyle's Law

Diffraction & Young's Double-Slit Interference Calculator

Diffraction & Interference

Calculate fringe spacing and positions for Young's double-slit experiment. Also supports single-slit diffraction and multi-slit diffraction gratings.

DiffractionInterferenceDouble SlitDiffraction Grating

Thin Lens Formula & Image Formation Simulator

Lens Optics

Calculate object distance, image distance, and magnification using the thin lens formula. Real-time ray diagram visualization for convex and concave lenses.

LensThin Lens FormulaImage FormationMagnification

Snell's Law & Light Refraction Simulator

Snell's Law

Calculate refraction angle and total internal reflection critical angle from incident angle and refractive indices using Snell's Law. Interactive visualization at the interface.

Snell's LawRefractionTotal Internal ReflectionRefractive Index

Inclined Plane Motion Simulator

Inclined Plane

Calculate acceleration, friction force, and normal force for objects on a frictional inclined plane. Conditional branching by static/kinetic friction coefficient with animation.

Inclined PlaneFrictionNormal ForceAcceleration

Wave Fundamentals Visualizer (Frequency, Wavelength & Speed)

Wave Basics

Visualize the fundamental relationships among wave frequency, wavelength, speed, and amplitude. Display transverse/longitudinal wave propagation animations and superposition principle.

WaveFrequencyWavelengthWave Speed

String Standing Wave & Resonance Simulator (Harmonics)

Standing Wave String

Calculate standing wave modes and natural frequencies of a string fixed at both ends. Animate nth harmonic waveforms and learn the fundamentals of musical instrument strings.

Standing WaveString VibrationHarmonicsNatural Frequency

Double Pendulum (Chaos) Simulator

Double Pendulum

Real-time simulation of the chaotic behavior of a double pendulum. Visualize how small differences in initial conditions strongly affect the trajectory.

Double PendulumChaosNonlinearLyapunov Exponent

Lissajous Figures & Vibration Synthesis Simulator

Lissajous

Real-time drawing of Lissajous figures from two vibrations with different frequency ratios and phase differences. Experience the principles of an oscilloscope.

LissajousVibration SynthesisPhase DifferenceFrequency Ratio

Photoelectric Effect & Planck Constant Calculator

Photoelectric Effect

Calculate the maximum kinetic energy of emitted electrons and stopping voltage from the photoelectric effect. Visualize the relationship between Planck's constant and work function.

Photoelectric EffectPlanck ConstantWork FunctionQuantum

Hydrogen Atom Spectrum & Bohr Model Calculator

Hydrogen Atom

Calculate hydrogen atom energy levels and absorption/emission spectrum wavelengths using the Bohr model. Visualize Lyman and Balmer series.

Hydrogen AtomBohr ModelEnergy LevelSpectrum

Particle in a Box (Infinite Potential Well)

Particle in Box

Calculate the quantum mechanical solution for an infinite potential well. Visualize energy eigenvalues and wave functions psi(x) by principal quantum number n.

Quantum MechanicsInfinite WellEnergy EigenvalueWave Function

Radioactive Decay & Half-Life Calculator

Radioactive Decay

Calculate the exponential decay curve and half-life of radioactive materials. Display nuclide composition time evolution for chain decay (parent to daughter) using the Bateman equation.

Radioactive DecayHalf-LifeBateman EquationNuclide

Orbital Mechanics & Kepler Orbit Simulator

Orbital Mechanics

Simulate elliptical orbits of planets and satellites based on Kepler's laws. Calculate period, velocity, and periapsis/apoapsis from orbital elements.

KeplerElliptical OrbitOrbital MechanicsPeriod

Rocket Equation & Delta-V Calculator

Rocket Equation

Calculate delta-V and final velocity using the Tsiolkovsky rocket equation. Compare multi-stage rocket staging optimization and delta-V required for orbital insertion.

Rocket EquationDelta-VTsiolkovskyMulti-Stage Rocket

Lorentz Force & Charged Particle Motion Simulator

Magnetic Force

Simulate circular motion of a charged particle in a uniform magnetic field using the Lorentz force. Real-time calculation of cyclotron radius and rotation period.

Lorentz ForceCharged ParticleMagnetic FieldCyclotron

Energy Conservation Law — Mechanical Energy Simulator

Energy Conservation

Animate the conversion between potential and kinetic energy. Experience conservation of mechanical energy on slopes, pendulums, and roller coasters.

Energy ConservationPotential EnergyKinetic EnergyMechanical Energy

Conservation of Momentum & Collision Simulator

Momentum Conservation

Calculate conservation of momentum in 1D and 2D collisions. Animate changes in momentum and energy for elastic and inelastic collisions.

Momentum ConservationCollisionElastic CollisionInelastic Collision

Work-Energy Theorem & Power Calculator

Work-Energy Theorem

Calculate work from force and displacement, and visualize the relationship with changes in kinetic energy. Also supports calculation of power and efficiency.

WorkEnergy TheoremPowerEfficiency

Room Acoustics & Reverberation Time Calculator (Sabine)

Room Acoustics

Calculate room reverberation time RT60 using the Sabine and Eyring formulas. Support optimal acoustic design from room geometry and absorbing material placement.

Reverberation TimeSabineRoom AcousticsSound Absorption

Sound Pressure Level & Noise Calculation (dB Combination)

Sound Level

Calculate combined sound pressure levels from multiple sources using decibel addition. Real-time display of distance attenuation, directivity, and comparison with noise regulations.

Sound Pressure LevelDecibelNoiseDistance Attenuation

Acoustic Impedance — Reflection & Transmission Coefficient Calculator

Acoustic Impedance

Calculate reflection and transmission coefficients for sound waves at a two-medium interface from acoustic impedance. Fundamentals of ultrasonic testing and soundproofing design.

Acoustic ImpedanceReflection CoefficientTransmission CoefficientUltrasonic

Air Quality Dispersion (Gaussian)

Calculate chimney plume concentration distribution using the Gaussian atmospheric dispersion model. Visualize ground-level concentration as isopleths as a function of wind speed, atmospheric stability, and effective stack height.

Atmospheric DispersionGaussian DispersionChimneyGround Concentration

Blood Flow Hemodynamics

Calculate pressure loss and velocity profile of pulsatile blood flow using Hagen-Poiseuille flow and Womersley number. Biofluid mechanics analysis of the circulatory system.

Blood FlowHagen-PoiseuilleWomersleyBiofluid

Bone Fracture Risk Assessment

Calculate bone strength from bone density and shape indices to evaluate fracture risk. Display risk index based on FRAX-equivalent age and weight correction factors.

Fracture RiskBone DensityBone StrengthFRAX

Cell Potential (Electrochemistry)

Calculate EMF, activity, and equilibrium potential of electrochemical cells using the Nernst equation. Visualize temperature, concentration, and pH dependence on Pourbaix diagrams.

EMFNernst EquationPourbaix DiagramElectrochemistry

CO₂ Emissions & Carbon Footprint

Calculate CO₂ emissions from fuel consumption, electricity use, and transportation using IPCC emission factors. Visualize carbon footprint and reduction potential.

CO2 EmissionsCarbon FootprintEmission FactorCarbon Neutral

Offshore Platform Load Analysis

Calculate wave and current forces on offshore structures using Morrison's equation. Compute design loads from significant wave height, current velocity, and structural geometry.

OffshoreMorison EquationWave ForceMarine Structure

Pharmacokinetics PK/PD Model

Calculate drug plasma concentration-time profiles using one-compartment and two-compartment models. Visualize AUC, half-life, and clearance.

PharmacokineticsPK/PDPlasma ConcentrationAUC

Quantum Tunneling Effect

Calculate transmission probability through rectangular potential barriers using WKB approximation and exact solutions. Real-time visualization of transmission probability changes with energy, barrier height, and width.

Quantum TunnelingWKB ApproximationTransmission ProbabilityPotential Barrier

Radiation Shielding Calculator

Calculate gamma ray and X-ray transmission, half-value layer, and tenth-value layer from attenuation coefficients. Supports composite shielding design with build-up factor correction.

Radiation ShieldingHalf-Value LayerAttenuation CoefficientBuild-up Factor

Special Relativity Calculator

Real-time calculation of Lorentz transformation, time dilation, length contraction, relativistic momentum, and E=mc². Visualize relationships between velocity parameter β and Lorentz factor γ.

Special RelativityLorentz TransformationTime DilationE=mc2

Traffic Flow Theory & LOS

Calculate relationships between traffic flow, density, and speed using Greenshields and Greenberg models. Evaluate traffic capacity and Level of Service (LOS).

Traffic FlowLOSTraffic CapacityGreenshields

Vector Field Visualization

Real-time calculation and visualization of streamlines, contours, divergence, and curl of 2D vector fields. Useful for learning fundamentals of vortex flow, potential flow, and electromagnetic fields.

Vector FieldStreamlinesDivergenceCurl

Aircraft Performance Calculator

Calculate lift coefficient, drag coefficient, and lift-to-drag ratio using Prandtl lifting line theory. Real-time computation of cruise speed, stall speed, and maximum climb rate.

AircraftLiftDragLift-to-Drag Ratio

Lorenz Attractor Simulator

Lorenz Attractor

Visualize chaotic solutions of the Lorenz equations as a 3D attractor. Vary σ, ρ, β parameters to experience the butterfly effect. Verify initial-value sensitivity and Lyapunov exponents.

Lorenz AttractorChaosButterfly EffectSensitivityNonlinear Dynamics

Three-Body Problem Simulator

Three-Body Problem

Real-time simulation of the three-body gravitational problem. Choose figure-8 periodic orbits, Lagrange triangles, or random initial conditions. Experience chaotic trajectories with no general analytic solution.

Three-Body ProblemGravityChaosFigure-8N-body

Charged Particle in E×B Fields

Charged Particle E×B

Simulate charged particle motion in electric and magnetic fields using Boris integration. Visualize E×B drift, Larmor radius, and cyclotron motion. Select electrons, protons, or alpha particles.

Charged ParticleLorentz ForceE×B DriftLarmor RadiusPlasma Physics

Ball Physics Simulator

Simulate ball motion in real time by adjusting gravity, coefficient of restitution, and friction. An intuitive tool for high-school physics.

MechanicsRestitutionFrictionMotion

Glider Simulation & Polar Curve

Glider Simulation

Calculate glider polar curves, best glide speed, MacCready speed, and cross-country speed considering thermals in real time.

GliderGlide RatioPolar CurveAerodynamics

Orbital Transfer Calculator (Hohmann)

Orbital Transfer (Hohmann)

Calculate Hohmann transfer two-impulse ΔV, transfer time, bi-elliptic comparison, and fuel mass ratio in real time. Canvas orbital diagram included.

Hohmann TransferΔVOrbital MechanicsRocket Equation

Multi-Stage Rocket Design Calculator

Multi-Stage Rocket Design

Calculate total ΔV and payload ratio for 1–3 stage rockets using the Tsiolkovsky equation. Includes Saturn V and Falcon 9 presets.

RocketΔVTsiolkovskyMulti-StagePayload

Satellite Power Budget Simulator

Satellite Power Budget

Calculate solar array size, battery capacity, eclipse time, orbital period, depth of discharge (DoD), and EOL power for satellites in real time.

SatellitePower BudgetSolar ArrayBatteryDoD

Wave Superposition (Beats & Interference)

Visualize superposition of two sinusoidal waves in real time. Experience beats and constructive/destructive interference through animation.

WaveSuperpositionBeatsInterferenceSine Wave

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