Monte Carlo Simulator Online
This Monte Carlo simulator runs hundreds or thousands of random trials from a starting value and shows the range of places it can end up. Enter a starting value, a number of periods, an expected change per period and a volatility, and it draws a fan chart: a median line, a 5th percentile line and a 95th percentile line over a cloud of faint sample trials. The numbers are worked out in your browser and nothing is uploaded.
How to Run a Monte Carlo Simulation
- On the setup screen, type a Starting value. It can be any number from 0 up to 1,000,000,000,000. The default is 1000.
- Set Periods, the number of steps to simulate, as a whole number from 1 to 1000. The default is 30.
- Enter the Expected return per period (%), the average change each period. Use the ± button beside the box to flip it between positive and negative. The default is 7, and the range is -100 to 1000.
- Enter the Volatility per period (%), how widely each period's change varies. The default is 15, and the range is 0 to 1000. A volatility of 0 removes the randomness.
- Press Advanced if you want to change the Number of trials or the Progression.
- Press Run simulation. A percentage shows while it runs, and Cancel stops it.
- Read the result screen. Press Run again to draw a fresh set of trials with the same settings, or Change parameters to go back and edit them.
What Each Setting Does
| Setting | Meaning | Allowed range |
|---|---|---|
| Starting value | The amount or baseline every trial begins with | 0 to 1,000,000,000,000 |
| Periods | How many steps each trial takes | Whole number, 1 to 1000 |
| Expected return per period (%) | The average change each period; it can be negative | -100 to 1000 |
| Volatility per period (%) | The standard deviation of each period's change | 0 to 1000 |
| Number of trials | How many random runs are made | 100 to 10,000 in steps of 100 (default 1,000) |
The numbers are neutral. The starting value can be a sales figure, a population, a score or a balance, and a period can be a day, a month or a round of a game. A value never goes below 0: once a trial reaches zero it stays there.
Geometric or Arithmetic Progression
Progression under Advanced decides how each period's random change is applied. Geometric, the default, compounds: each period the new value is the current value times (1 + return + volatility × Z), where Z is a random draw from a standard normal distribution. Growth builds on itself, so the spread widens quickly and the highest outcomes pull far ahead of the lowest. Arithmetic adds the same size of step each period: the current value plus the starting value times (return + volatility × Z). The value drifts in a more even band around a straight line.
How to Read the Fan Chart and Percentiles
The heading After 30 periods (with your own number) sits above the chart and three cards. The chart legend lists 100 sample trials as thin grey lines, a 5th percentile line, a Median line and a 95th percentile line. The percentiles are worked out at every period from all of your trials, not just the sample you can see, by sorting the values and interpolating between neighbouring ranks. The sample is limited to 100 lines so the picture stays readable.
- 5th percentile: 5% of trials ended at or below this value. A low-end outcome.
- Median (50th): half of the trials ended below this value and half above. The middle outcome.
- 95th percentile: 95% of trials ended at or below this value. A high-end outcome.
The gap between the 5th and 95th percentile cards is the range that holds the middle 90% of trials. A wide gap means the outcome is very uncertain on your settings, and a narrow one means it is tightly bunched.
Check It with a Volatility of 0
Set Volatility per period (%) to 0 and the randomness disappears, so every trial is the same and the three percentile cards show one number. That makes a handy check. With the defaults of 1000, 30 periods and 7%, Geometric gives 1000 × 1.0730, about 7,612.26, while Arithmetic gives 1000 + 30 × 1000 × 0.07, exactly 3,100. Raise the volatility again and the 5th and 95th percentile spread out on either side of the median.
How Many Trials Should You Run?
The default is 1,000. Each percentile is estimated from the trials, so with fewer trials the cards jump around from run to run, and with more they settle. Under Advanced the slider reads Number of trials: 1,000 and goes from 100 to 10,000. 10,000 trials with 1000 periods is the heaviest run and takes longest, but it runs in a background thread, so the page stays responsive and you can press Cancel. Every run is random and there is no seed, so two runs with the same settings never match exactly.
This is a plain simulator with one rule: independent bell-curve changes each period. It has no withdrawals, contributions, taxes or real market data, and it is not a financial planner or a forecast. Treat the fan chart as a picture of what the numbers you typed imply.
Your Numbers Stay on Your Device
The random numbers are generated and the percentiles calculated in your browser, in a background thread. Your inputs and results are not sent to a server or saved, and there is no account to create.
Other Tools for Growth and Chance
For steady growth with no randomness, use the Compound Interest Calculator. To see chance on a smaller scale, the Bulk Coin Flipper flips many coins at once and counts the heads and tails.
Frequently Asked Questions
How does a Monte Carlo simulation work?
It repeats the same random experiment many times and looks at the spread of the results. Here, every trial starts at your starting value and, for each period, applies a change drawn from a bell curve centred on your expected return with the width you set as volatility. After all trials finish, the simulator sorts the final values and reads off the 5th percentile, the median and the 95th percentile.
How many trials do I need in a Monte Carlo simulation?
More trials give steadier percentiles but take longer to run. The default of 1,000 is enough to see the shape of the range. Press Advanced and drag the slider anywhere from 100 to 10,000 in steps of 100. If the 5th and 95th percentile cards move a lot between runs, raise the number of trials.
Is a Monte Carlo simulation accurate?
It is exactly as accurate as its assumptions. The arithmetic is exact for the model you enter, but the model is simple: every period's change is drawn independently from the same bell curve, and nothing else happens. Real situations with trends, shocks or outside events will not follow it, so read the fan chart as a range of what the numbers you typed imply, not a forecast.
Why do the results change every time I run it?
Each run draws fresh random numbers, and there is no seed to set, so two runs with the same settings differ slightly. The difference shrinks as you raise the number of trials under Advanced. Press Run again to see how much the 5th percentile, median and 95th percentile move on your settings.
What do the 5th and 95th percentile mean in a Monte Carlo simulation?
They mark the edges of the range that covers most trials. The 5th percentile is the final value that 5% of trials ended at or below, the median (50th) splits the trials in half, and the 95th percentile is the value that 95% of trials ended at or below. Together the 5th and 95th bound the middle 90% of outcomes.
What is the difference between geometric and arithmetic progression?
Geometric compounds: each period's change applies to the current value, so growth builds on itself. Arithmetic takes a fixed-size step each period, a share of the starting value, so the value moves in a straight line plus noise. Geometric is the default and suits growth that compounds; arithmetic suits a steady, additive drift.
Does Monte Carlo simulation assume a normal distribution?
This one does. The random change in each period comes from a standard normal draw using the Box-Muller method, scaled by your volatility and shifted by your expected return. You cannot choose another distribution. With compounding, that usually leaves a longer tail above the median than below it.
Is there a free Monte Carlo simulation calculator online?
Yes. This page runs a Monte Carlo simulation online with no account, no sign-up and no limit on how many runs you do. The calculation happens in your browser in a background thread, so nothing you enter is uploaded.
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