Monte Carlo Simulator

Run seeded Monte Carlo simulations over a linear formula using up to three random variables.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

This calculator runs a seeded Monte Carlo experiment over up to three random inputs and a linear result formula, then summarizes the sampled output distribution. The seeded generator keeps scenarios reproducible so changes in assumptions are easy to compare.

It combines Simulation Count, Seed, Constant Term, Variable X Distribution to estimate Mean Output, Std Dev, 5th Percentile.

Formula & Method

Core equations: This simulator evaluates

Y=c+aX+bY+dZ

over repeated random draws, then estimates empirical moments and percentiles from the sampled output distribution.

Notation used in the formulas: $R$ = Mean Output; $x_{1}$ = Simulation Count; $x_{2}$ = Seed; $x_{3}$ = Constant Term; $x_{4}$ = Variable X Distribution; $x_{5}$ = Variable X Coefficient; $x_{6}$ = Variable X Param A.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when a result depends on uncertain inputs and you want a distribution of outcomes, confidence bands, and downside or upside percentiles instead of a single deterministic point estimate.

Reference Book

Introduction to Probability

Second Edition

Joseph K. Blitzstein and Jessica Hwang · Chapman and Hall/CRC

A widely used probability text for counting, conditioning, expected value, core distributions, and simulation.

View Book

Inputs Used

Simulation Count: Used directly in the calculation.
Seed: Used directly in the calculation.
Constant Term: Used directly in the calculation.
Variable X Distribution: Used directly in the calculation.
Variable X Coefficient: Used directly in the calculation.
Variable X Param A: Used directly in the calculation.
Variable X Param B: Used directly in the calculation.
Variable X Param C: Used directly in the calculation.
Variable Y Distribution: Used directly in the calculation.
Variable Y Coefficient: Used directly in the calculation.
Variable Y Param A: Used directly in the calculation.
Variable Y Param B: Used directly in the calculation.
Variable Y Param C: Used directly in the calculation.
Variable Z Distribution: Used directly in the calculation.
Variable Z Coefficient: Used directly in the calculation.
Variable Z Param A: Used directly in the calculation.
Variable Z Param B: Used directly in the calculation.
Variable Z Param C: Used directly in the calculation.

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