Monte Carlo Simulator and Retirement Calculator
Run your portfolio or retirement plan through 1,000 random markets and see your success rate and the range from bad to good outcomes, free and without signup.
By Cédric Mauquoi · Last updated: October 2026
1The market
$
% / yr
%
years
2Contributions
$
Added at the end of each month
Median outcome after 25 years1,000 simulations
872,781
Half of the 1,000 simulated markets ended above this, half below. Your total contributed was 325,000.
Worst case - 5th336,439
Poor - 10th382,793
Strong - 90th2,024,833
Best case - 95th2,676,389
Range of outcomes over time
5th-95thMedianNaive projection
$2.78M
$2.09M
$1.39M
$696k
$0
Now4y8y12y16y20y24y25y
Volatility drag
A standard calculator, with no volatility, would project 1,087,765 (the dashed line). Once the swings of a real market are included, the median outcome is 872,781, about 20% lower. That gap is the cost of risk a single-line projection hides.
Total contributed325,000
The method
What is a Monte Carlo simulation?
A Monte Carlo simulation runs the same plan through 1,000 randomly generated markets instead of one average return, so you see the range of possible outcomes and how often a goal is reached. Each path draws a new return every month from your expected return and volatility, and the simulator then reads the percentiles of all paths at every year.
Every month, on every path: balance × e^(m − s²/2 + s × Z), then add the contribution or take out the withdrawal. Here m = ln(1 + expected return) ÷ 12, s = volatility ÷ √12 and Z is a random draw from a standard normal distribution.
How a Monte Carlo simulation works, step by step
1
Describe the market
An expected annual return and a volatility (how far yearly returns swing around it) define the market every path is drawn from.
2
Draw 1,000 paths
Each path gets a fresh random return for every month of the horizon, so no two paths are alike and a crash can come early or late.
3
Apply your cash flows
Monthly contributions are added and, in Retirement mode, the monthly withdrawal is taken out. A path that reaches zero stays at zero: on that path the plan failed.
4
Read the distribution
The ending balances are sorted: the 10th, 50th and 90th percentiles give a bad, a typical and a good outcome, and the share of paths that reach the goal or never run dry is the success rate.
Worked example: the default plan
Start with 85,000, add 800 a month for 25 years and expect 7% a year with 16% volatility. A steady 7% every year would end at 1,087,765. The median of the 1,000 random paths ends at 872,781, 19.8% lower, because volatility drags compound growth: a 20% loss needs a 25% gain to recover. One market in ten ends below 382,793, one in ten above 2,024,833.
| Percentile | Ending balance | How to read it |
|---|---|---|
| P10 | 382,793 | 1 market in 10 ends below this |
| P25 | 576,502 | 1 market in 4 ends below this |
| P50 | 872,781 | The middle outcome |
| P75 | 1,350,798 | 1 market in 4 ends above this |
| P90 | 2,024,833 | 1 market in 10 ends above this |
What is a good success rate?
There is no universal pass mark, but the trade-off is easy to see. The table withdraws a fixed amount every month from 1,000,000 for 30 years, at the default 7% return and 16% volatility. This simulator colours a result green from 85%; below about 75% a plan is leaning on luck.
| Withdrawal rate | Withdrawn per month | Success rate |
|---|---|---|
| 3% | 2,500 | 95.6% |
| 3.5% | 2,917 | 92.1% |
| 4% | 3,333 | 86.8% |
| 4.5% | 3,750 | 80.7% |
| 5% | 4,167 | 72.6% |
The classic 4% rule, from William Bengen's 1994 study of historical US returns, raises the withdrawal with inflation every year. This simulation keeps it flat, so its success rates read slightly better than the rule's own test.
Run the 4% rule: 1,000,000, 3,333 a month, 30 years
Using it for a withdrawal plan
Switch to Retirement mode, enter the portfolio at the start of the plan and the monthly amount you want to take out, and set the year withdrawals begin; until then your contributions are added. The headline then shows the share of the 1,000 markets in which the money lasts the whole horizon, and the year the failing paths typically run dry.
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How to use this calculator
How to use this Monte Carlo simulator
1
Pick a question
Choose a mode at the top: project growth, test a retirement withdrawal, or find the odds of hitting a target. The mode decides which extra inputs appear and what the headline answer means.
2
Set the market
In card 1, enter your starting portfolio, the expected annual return, the annual volatility, and your time horizon. Volatility is the dial that widens or narrows the cone of outcomes.
3
Add the cashflows
In card 2, set the contributions, withdrawals or target for your chosen mode. We prefill these from your accounts when you are signed in.
4
Read the range
The fan chart shows the spread of 1,000 simulated markets. Read the headline probability or median, scan the best and worst case percentiles, and hover the chart for any year.
Key concepts
How to read Monte Carlo percentiles
Why a range, not a number
A normal calculator assumes your return arrives smoothly every year. Real markets do not: the same average can produce wildly different paths. A Monte Carlo simulation runs thousands of those paths so you see the spread of what could actually happen, not one tidy line.
Geometric Brownian motion
Each simulated month applies a random return drawn from your expected return and volatility, compounding on the last balance. Run it 1,000 times and the outcomes fan out into a distribution. It is the standard model for how asset prices wander.
Volatility drag
Because losses hurt more than equal gains help when compounding, the median outcome sits below the naive projection at the same average return. The dashed line on the chart is that naive projection; the gap to the median band is the drag your calculator never showed you.
Percentiles, best to worst
The 95th percentile is a top-5% market; the 5th is a bottom-5% one. The bands show where the middle 50% and 80% of outcomes land. Planning to the median alone ignores how bad the unlucky paths get, which is exactly what the percentiles reveal.
Sequence-of-returns risk
In retirement, the ORDER of returns matters as much as the average. A crash early in withdrawals can drain a portfolio that an identical-average but better-ordered market would have sustained. Survival probability captures this; a single projection cannot.
Survival vs success probability
In retirement, survival probability is the share of markets where your money lasts the full horizon without hitting zero. In goal mode, success probability is the share where you finish at or above your target. Both turn a vague hope into a concrete number.
Why 1,000 simulations
More paths sharpen the estimate, but with fast-diminishing returns: sampling error shrinks with the square root of the count. At 1,000 paths, a success or survival probability is accurate to within about one to two percentage points, tight enough for any planning decision, and the result appears instantly. This calculator also uses a fixed random seed, so identical inputs always replay the same 1,000 markets. Tools that draw fresh random numbers on every run show results that wiggle by a point or two even when nothing changed; that wiggle is sampling noise, not information.
Fat tails: what the model misses
The simulation draws monthly returns from a lognormal distribution in which extreme moves are rare and each month is independent. Real markets are messier: crashes arrive more often than the bell curve implies, bad months cluster into bad years (2008, 2020), and volatility itself shifts over time. So read the 5th percentile as a plausible unlucky decade, not the true worst case, and keep defences the model cannot see, like a cash buffer and the willingness to cut spending, for the events no distribution predicts.
Tips for using the odds
Turning a success rate into a plan
Plan to a low percentile
Building a plan that works at the 10th or 25th percentile, not the median, is what keeps it intact when markets disappoint. The median is a coin-flip; the lower bands are your margin of safety.
Mind the volatility input
Volatility moves the answer more than people expect. A 60/40 portfolio (about 11%) gives a far tighter cone than an all-stock one (about 17%) at the same average return. Set it to match what you actually hold.
Stress-test retirement early
Run retirement mode with a withdrawal that starts in year one and watch survival probability. If it is below about 85%, a lower withdrawal or a later start usually buys a large jump in safety.
Contributions beat timing
Raising the monthly contribution lifts the entire fan, including the worst-case bands. It is a far more reliable lever than hoping for a higher return, which simply widens the cone.
Re-run as life changes
A simulation is a snapshot of today's assumptions. Re-run it when your portfolio, horizon or spending shifts, rather than trusting a number you generated years ago.
De-risk as the goal nears
Volatility you can ride out over 25 years can sink a goal due in three. Re-run the simulation with the lower return and volatility of a bond-heavier mix to preview a glide path: the cone tightens exactly when you need certainty most.
Monte Carlo simulator FAQ
How is this different from the Investment Return Calculator?+
The Investment Return Calculator answers how much: one smooth projection at a fixed return. This one answers how likely: it runs 1,000 random markets at your return and volatility and shows the full range of outcomes. Same inputs, a fundamentally different question. The dashed line here is exactly what that calculator would draw.
How many simulations does a Monte Carlo calculator need?+
This one runs 1,000. Each path is one possible future, built month by month from random returns centred on your expected return with your volatility. At a success rate near 87%, 1,000 paths carry a sampling error of about one percentage point, so a fresh set of random numbers would land within about two points. The random numbers are seeded, so the same inputs always give the same result. More paths would smooth the estimate without changing the answer; the return, volatility and withdrawal you enter matter far more.
Why is the median below the dashed line?+
That gap is volatility drag. Compounding punishes a down year more than an equal up year rewards you, so once randomness is included the typical (median) outcome falls below the naive constant-return projection. The more volatile the portfolio, the wider that gap. It is the single most useful thing this tool shows.
What counts as survival in retirement mode?+
A simulated market survives if the portfolio never hits zero before your horizon ends, after taking the monthly withdrawal you set. Survival probability is the share of the 1,000 markets that last the distance. We also show the year the portfolio runs out in the unlucky paths, so you can see how early failure tends to strike.
Are these returns guaranteed or predictions?+
Neither. The simulation explores the consequences of your assumptions; it does not predict the future. Real markets can fall outside any model, returns are not perfectly random, and crises cluster in ways a simple model misses. Treat the probabilities as a structured way to compare plans, not a forecast.
Can a Monte Carlo simulation account for inflation?+
This one is nominal and before tax: returns, balances and withdrawals are in money of the day, and withdrawals stay flat rather than rising with prices. To think in today's money, enter a real return (after inflation, roughly 4 to 5% a year for stocks) and read every figure as inflation-adjusted. For after-fee and after-tax figures on a single path, pair it with the Investment Return Calculator.
What is a good success rate in a Monte Carlo simulation?+
100% is not on offer; chasing it just means oversaving and retiring later than needed. If you can trim spending in bad years, 85 to 90% is a sound target, and this tool colours results green from 85%. With a rigid budget or a very long horizon, aim for 90 to 95%. Below about 75% the plan is leaning on luck: lower the withdrawal, add contributions or extend the horizon. A failed simulation path is a plan adjustment in real life, not ruin.
Why does the fan get wider every year?+
Because randomness compounds: each year's surprise multiplies everything that came before, so uncertainty stacks instead of averaging out. The spread grows roughly with the square root of time, so ten years out it is about three times the one-year spread, not ten times. That is also why long horizons remain plannable at all: the range of final amounts widens in dollars, while the range of annualised returns narrows.
Can I test the 4% rule with this calculator?+
Yes. In retirement mode, enter $1,000,000, a $3,333 monthly withdrawal (4% a year), 30 years and a 7% return. At 12% volatility, roughly a 60/40 portfolio, survival probability comes out around 96%; at 16% volatility (all stocks) about 87%. Raising the withdrawal to 5% ($4,167) at 12% volatility drops it to about 86%. One caveat: the classic rule raises withdrawals with inflation, while this simulation holds them flat, so it flatters the result slightly. For the reasoning behind the rule rather than the simulation of it, The Simple Path to Wealth covers it in about two hours of reading.
What expected return should I enter?+
For a broad stock portfolio, long-run nominal returns have averaged around 7 to 10% a year; the 7% default with 16% volatility is a reasonable planning stance. A 60/40 mix sits nearer 5 to 6% with 10 to 12% volatility. Always subtract your fund fees. If you would rather think in today's purchasing power, enter a real return instead, roughly 4 to 5% for stocks, and read every dollar on screen as inflation-adjusted.
How do I run a Monte Carlo retirement simulation?+
Switch to Retirement mode, then enter your starting portfolio, expected return and volatility, the monthly withdrawal you plan to take, and the year it begins. The tool runs 1,000 markets and reports survival probability: the share in which the money lasts your full horizon without ever hitting zero. Because it draws a fresh return every month rather than a smooth average, a Monte Carlo retirement simulation captures sequence-of-returns risk, the danger that a slump in the first few years of withdrawals drains a portfolio that a calmer-ordered but identical-average market would have sustained. Watch the median depletion year on the failing paths to see how early trouble tends to strike, and if survival sits below about 85%, test a smaller withdrawal or a later start.
Is this Monte Carlo simulation free, and does it run online?+
Yes to both. The simulator is completely free, needs no signup or download, and runs entirely online in your browser, so your figures never leave your device. Every mode, all 1,000 paths, the percentile fan chart and the probability read-outs are available with no paywall, trial or usage cap. Signing in is optional: it only prefills the inputs from your own accounts and is never required to run a simulation.
How accurate is a Monte Carlo simulation, and how should I read the percentiles?+
Treat it as a disciplined way to compare plans, not a forecast. Each percentile describes this model's assumptions, not a promise: the 5th is a bottom-5% run of the 1,000 simulated markets, the median a coin-flip outcome, the 95th a top-5% run. The results are only as trustworthy as the return and volatility you enter, and the model assumes both stay fixed and that each month is independent. Real crises cluster and arrive more often than a bell curve implies, so a genuinely bad decade can fall outside even the 5th percentile. Read the low percentiles as your planning margin, plan to the 10th or 25th rather than the median, and keep defences the model cannot see, such as a cash buffer and the willingness to trim spending in a downturn.
Why is Monte Carlo better than a regular retirement calculator?+
A regular calculator grows your savings at one fixed return, so the order of good and bad years never matters. In retirement it does: a slump in the first years of withdrawals can drain a portfolio that the same average return would have sustained. Monte Carlo draws a different sequence of returns on every path and reports how often the money lasts, which a single projection cannot tell you.
What is a safe withdrawal rate?+
It is the share of a portfolio you can take out in the first year, and keep taking, without running out over your horizon. The 4% rule comes from William Bengen's 1994 study of historical US returns: a 4% first-year withdrawal, raised with inflation each year, lasted at least 30 years in every period he tested. The table above shows how the success rate falls as the rate rises in this simulator; run your own portfolio and horizon in Retirement mode to find the rate that meets your target.
Each of the 1,000 paths applies monthly returns drawn from your expected return and volatility (geometric Brownian motion), compounding on the running balance, with contributions or withdrawals applied monthly. Results are nominal and before tax, use a fixed seed for reproducibility, and assume returns are independent month to month. Markets are not perfectly random and the future may differ; treat the probabilities as illustrative, not financial advice.
1,000-path geometric Brownian motion at your return and volatility - nominal, pre-tax, illustrative, not advice
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