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Math / Monte Carlo

Monte Carlo and Uncertainty Analysis Simulators

A probability and simulation hub for Monte Carlo methods, importance sampling, rejection sampling, Bayesian estimation, bootstrap intervals, and uncertainty propagation.

8 related simulators

This hub groups closely related tools with static links. Individual simulator URLs stay unchanged while users can move quickly to the right calculation.

Core simulators
Monte Carlo Pi Estimator
Keeps variation, sample size, and uncertainty evaluation inside the same specialist cluster for easier navigation.
Monte Carlo Statistics Simulator — π, Integration, CLT
Explore Monte Carlo methods: estimate π, test the Central Limit Theorem, perform integration, and simulate random processes with this interactive statis...
2D Random Walk Simulator — MSD & Diffusion Coefficient
Simulate 2D random walks in real time.
Importance Sampling Simulator
Importance sampling simulator: estimate the standard normal tail probability P(X>t).
Rejection Sampling Simulator
Rejection sampling simulator: cover a hard target p(x) with a proposal q(x) and envelope M, accept with probability p(x)/(M·q(x)).
Bootstrap Confidence Interval Simulator
Compute 95% bootstrap confidence intervals for the mean and median in real time.
Uncertainty Propagation & Monte Carlo Analysis Tool
Calculate measurement uncertainty with our free Monte Carlo analysis tool.
Probability Distributions Calculator — Normal, Poisson, Binomial, Exponential
Interactive probability distributions calculator.

Explore by task

Monte Carlo basics

Monte Carlo Pi Estimator Monte Carlo Statistics Simulator — π, Integration, CLT 2D Random Walk Simulator — MSD & Diffusion Coefficient

Sampling methods

Importance Sampling Simulator Rejection Sampling Simulator

Estimation and intervals

Bootstrap Confidence Interval Simulator

Uncertainty and distributions

Uncertainty Propagation & Monte Carlo Analysis Tool Probability Distributions Calculator — Normal, Poisson, Binomial, Exponential

Related categories

Math & Numerical Analysis Frequency Response, Bode, and Stability Simulators Beam and Flexural Analysis Simulators

FAQ

What is Monte Carlo simulation good for?
It is useful for approximating probabilities, expectations, intervals, risk, and sensitivity when closed-form analysis is hard.
Does increasing sample count always help?
Random error usually falls with the square root of sample size, but random quality, tail behavior, and model error also matter. Importance sampling can be more efficient.
How do uncertainty propagation and sensitivity analysis differ?
Uncertainty propagation maps input variability into output distributions. Sensitivity analysis compares which inputs drive the output most.