Monte Carlo Simulation simply explained

A Monte Carlo simulation is a way to answer the question: what could happen if the important inputs are uncertain? Instead of calculating only one result, the simulation calculates the same model many times with randomly selected input values.

The result is not a single number. It is a range of possible outcomes, together with an estimate of how likely each outcome is. This makes Monte Carlo simulation useful for risk analysis, forecasts, process capability, tolerance studies, and business planning.

You can try it directly with the Monte Carlo simulation calculator.

What is a Monte Carlo simulation?

In a normal calculation you enter fixed values. For example, you might calculate revenue with this equation:

But in real life, these values are rarely known exactly. The number of visitors changes from week to week, the conversion rate can be higher or lower, and the average order value also varies. A Monte Carlo simulation describes each uncertain input with a probability distribution and then calculates many possible revenues.

How does it work?

1. Define the uncertain input variables.
2. Choose a probability distribution for each input.
3. Write the formula that connects the inputs to the output.
4. Let the computer repeat the calculation thousands of times.
5. Look at the distribution of all simulated results.

Each run is one possible version of reality. After many runs, the pattern of the results shows which outcomes are common, which outcomes are rare, and where the biggest risks are.

A simple example

Imagine an online shop wants to estimate next month's revenue. The team does not know the exact values, but it can make realistic assumptions:

• Visitors are usually around 12,000, but can vary.
• The conversion rate is likely between 2.5% and 6%.
• The average order value is likely between 42 and 68.

A single average-case calculation hides this uncertainty. A Monte Carlo simulation instead combines many possible visitor counts, conversion rates, and order values. The output can show the expected revenue, the low and high ends, and the probability of missing a target such as 18,000.

Common probability distributions

The distribution tells the simulation which values are possible and which values are more likely. The right choice depends on what the input represents.

How to interpret the results

The most important output is the distribution of the simulated results. A histogram shows where most results are located and how wide the possible range is.

The mean is the average simulated result. The standard deviation shows how strongly the result varies. The minimum and maximum show the extreme simulated values, but they should not be interpreted as guaranteed limits.

If specification limits or target limits are added, the simulation can estimate how often the result falls below or above the limit. This is useful when the question is not only "what is the expected result?" but also "how likely is it that we miss the target?"

What is sensitivity analysis?

Sensitivity analysis shows which input variables have the strongest influence on the output. This helps you decide where better data would be most valuable.

For example, if revenue is much more sensitive to the conversion rate than to order value, then improving the conversion-rate estimate will improve the simulation more than refining the order-value estimate.

When should you use Monte Carlo simulation?

• When several uncertain inputs influence one result.
• When a simple average-case calculation is too optimistic or too limited.
• When you need to estimate the probability of missing a target.
• When you want to compare best-case, typical, and worst-case outcomes.
• When you want to find the input variables that drive most of the risk.

Calculate a Monte Carlo simulation online

With numiqo, you can define input distributions, enter output equations, add specification limits, and run the simulation online. Open the Monte Carlo simulation calculator to create your own model.