Your model gives one number. What are the odds it is right?

What Monte Carlo simulation is

The method is older than the spreadsheet and simpler than its name. For each uncertain input you say which values are plausible and which are most likely. The computer then plays the model out thousands of times. Each pass draws one value for every uncertain input, recalculates, and records the answer. Sort those answers and you have a picture of what can happen, and how often.

The point is not a better single number. The point is the shape: how wide the spread is, which way it leans, and the probability of the outcomes you actually care about, like going over budget or running out of cash before the next raise.

The questions it answers

• What is the realistic range, rather than the best guess?
• What are the odds we come in under the number we already promised?
• Which of my assumptions is driving the spread?
• What number should I plan around if I want to be right eight times out of ten?

When you do not need Monte Carlo

Skip it when the inputs are known. A fixed-rate loan repayment has one right answer, and simulating it only decorates arithmetic. Skip it when nothing you would do changes with the spread: if you would make the same decision at the pessimistic end as at the optimistic one, the distribution is trivia.

And it does not rescue guesses. The output range is only as honest as the input ranges, so ten thousand trials on numbers you invented gives you an invented distribution, drawn very precisely. The right response to a wide result is usually to go and narrow one input, not to run more trials.

And you may not need an add-on for it. On a model that fits in one row, with two or three uncertain inputs and shapes you can write down, the whole method goes into five columns of ordinary formulas. That build is here in full, with the numbers it produces and the five things it cannot give you.

A worked example

A renovation quoted at $30,000. Two things are genuinely unknown: how far the job runs over the quote, and what the walls hide.

What you get back in the sheet

• 36 distribution shapes. Including the three-point minimum, likely and maximum estimate people actually have, plus normal, lognormal, Weibull, Pareto, Student-t, chi-square, Laplace, Rayleigh, log-uniform for a number that could be ten times bigger or smaller, inverse Gaussian for a wait that ends when a target is reached, a compound events-times-cost shape for claims and outages, and the discrete ones, with optional truncation on the continuous shapes.
• Rank correlations between inputs, so price and volume can move together: enter them pair by pair, or point the panel at a correlation matrix already sitting on your sheet. Drawing inputs independently makes the tail look thinner than it really is.
• Percentile entry for any continuous shape. People know the P10 and the P90 of a quantity more readily than a distribution's own parameters, so type those and the panel solves for the parameters that honor them, for every continuous family.
• Per-input stress sampling. Pin one input to the slice of its distribution that worries you, like its worst tenth, run again, and read the difference. The report discloses the stressed input, so the run cannot pass as a plain simulation.
• Latin hypercube sampling, on by default, which reaches the same answer with fewer trials.
• A percentile ladder at 1, 5, 10, 25, 50, 75, 90, 95 and 99 percent, alongside mean, median, standard deviation, variance, skewness and kurtosis.
• A tornado chart ranking every input by its rank correlation with the output. That is sensitivity analysis on the model you already have, and the biggest bar is where your next hour of estimating goes.
• A seed box. The same model with the same seed reproduces the same numbers, which is what makes a run reviewable by someone else.
• A SIPmath 3.0 export. Every output of a run, or the model's whole input set with its correlation matrix, saves as a .SIPmath library, the open standard from probabilitymanagement.org for passing uncertain quantities between tools. Risk Analysis also reads a .SIPmath library as inputs, and a coherent run option draws each SIPmath input from the file's own seeds, so its trials are the ones any other SIPmath tool reads from the same file (an input correlated through the file's copula, or truncated or correlated in Sortia, shares the shape rather than the trial order).
• Up to 100,000,000 trials in a single run, and ten thousand come back in well under a second, because the run happens in your browser rather than through the sheet. A model that uses a function the browser cannot evaluate falls back to recalculating the sheet itself for every trial, and that path stops at 300 trials. The panel warns you before it starts, and says whether it ran in your browser or on the sheet.
• A written reading of the result. Every run ends with a card titled “What this means”: the probability that matters, the biggest driver, and what to tighten first. On the free tier the tool writes it from its own figures. On Pro you also get an AI reading of the same figures, written by a language model, and See what was sent shows the whole payload: “Ratios, shares, counts and cell references only. No cell values, no labels, no names, no formulas.”

Free or Pro

Try it in your own sheet

1. Open Sortia in Google Sheets and choose Start from a template.
2. Pick one of the models above, and it loads with the inputs filled in.
3. Change the assumptions to fit your situation and press Run.

Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.

Other methods: Decision trees · Schedule risk · Critical chain · Optimization under uncertainty · Statistics · Machine learning · Forecasting · Optimization · What-if analysis