# Monte Carlo Simulation Builder

Define input distributions (normal/uniform/lognormal/triangular), write a formula, run thousands of trials, and get the output distribution histogram with confidence intervals.

> Canonical page: https://elysiatools.com/en/tools/monte-carlo-simulation-builder

- **Category:** Data Analysis

- **Keywords:** monte carlo, simulation, probability, distribution, normal, uniform, lognormal, triangular, confidence interval, risk, forecast, random

## Overview

Build custom Monte Carlo simulations by combining random inputs (normal/uniform/lognormal/triangular), a formula over variable names, and N trials. Returns histogram, mean/median/std, confidence intervals and P(outcome>0).

## Inputs

- **Distributions (one per line: name = type \[params\])** (textarea): Declare each random input. Types: normal \[mean, sigma\], uniform \[min, max\], lognormal \[mu, sigma\], triangular \[a, b, c\].
- **Output formula** (text): Arithmetic expression over the variable names. Supports + - * / % ^, parentheses, abs/sqrt/exp/log/min/max/pow, PI, E.
- **Number of trials** (number): How many samples to draw. More trials → smoother histogram (100 – 200000).
- **Random seed (optional, for reproducibility)** (text): A fixed seed makes results reproducible run-to-run. Leave blank for a fresh random draw.
- **Confidence level (%)** (number): Confidence interval percentile band (50–99.9%). Default 90% → P5–P95.

## When to use

- When forecasting business revenue, project costs, or investment returns that involve uncertain variables.
- When you need to calculate the probability of a specific outcome, such as a project exceeding its budget or falling below a target profit.
- When analyzing physical or engineering systems where inputs have known measurement tolerances or noise distributions.

## How it works

- Define your input variables by specifying their probability distribution types (normal, uniform, lognormal, or triangular) and parameters.
- Enter an arithmetic formula using your defined variables, supporting standard operators, parentheses, and mathematical constants like PI and E.
- Set the number of simulation trials and optionally provide a random seed to ensure reproducible results.
- Run the simulation to generate a detailed histogram, statistical metrics (mean, median, standard deviation), confidence intervals, and the probability of a positive outcome.

## Use cases

- Estimating project profit margins by modeling uncertain revenues and variable operational costs.
- Calculating the area of geometric shapes or physical outputs when dimensions have measurement tolerances.
- Assessing financial risk by simulating portfolio returns with lognormal asset price distributions.

## Frequently asked questions

### What probability distributions are supported?

You can use normal, uniform, lognormal, and triangular distributions to model your input variables.

### How do I write the output formula?

Use standard arithmetic operators (+, -, *, /, %, ^), parentheses, and functions like abs, sqrt, exp, log, min, max, or pow, along with constants like PI and E.

### Can I make my simulation results reproducible?

Yes, by entering a value in the optional random seed field, the generator will produce the exact same sequence of random trials every time.

### What is the maximum number of trials I can run?

You can run up to 200,000 trials per simulation for highly accurate and smooth distribution curves.

### What statistics does the tool calculate?

The tool outputs the mean, median, standard deviation, a custom confidence interval range, and the probability of the outcome being greater than zero.

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