Risk of Ruin Calculator

Two ways an account reaches its floor

There are only two routes from a healthy balance to a ruined one, and they call for two different answers. The first is the slow bleed: the method has no edge, or its edge has stopped working, and every trade takes a small amount that nothing puts back. That route is close to certain over a long enough sequence, which is why the calculator above returns a flat 100% the moment expectancy goes to zero or below — there is no probability left to estimate.

The second is the unlucky sequence: the method does have an edge, and the drawdown still arrives before compounding has carried equity far enough above the line. This is the figure worth estimating, because it is the one sizing controls. Halving the stake does not halve this probability; it pulls it down along a curve steep enough that a quarter of the stake can move the answer by a factor of thousands.

Notice what the estimate is not. It is not the chance of a bad month, and it is not the worst drawdown you should plan for. It answers a narrow question with a narrow number: given this edge and this stake, how often does an account starting at this balance touch this level before the walk drifts upward for good. Anything outside that sentence is not what the output means.

The arithmetic, printed out

Everything below runs in your browser from the five fields above, and every step can be redone on a hand calculator. The first line is plain expectancy in units of risk, R. The next three convert a per-trade result into a drift and a spread in log terms, because percentages gained and lost multiply rather than add — losing 1% then gaining 1% leaves less than you started with, and logs keep that honest. The last line is the classic barrier-crossing formula.

Run it on the defaults — 10,000.00, 1% per trade, 45% winners, 1.5 payoff, floor at 50% — and the numbers come out like this:

Check the last row by multiplying instead of logging: 0.99⁶⁹ = 0.4996, just under half, and 0.99⁶⁸ = 0.5046, just over. Sixty-nine consecutive losers is therefore the count, and it is that number rather than any probability that most people find easy to picture. At 0.5% per trade the count is 139; at 2% it is 35. A losing sequence that long arrives about once per 1.8 x 10¹⁸ trades at a 45% hit rate, which is another way of saying the slow bleed, not the monster streak, is what actually has to be guarded against.

The streak nobody sizes for

Fifteen losses in a row reads like a catastrophe while it is happening, and it is the run most traders quit during. It is also, at ordinary stake sizes, a long way short of ruining anything. The rows below are cut straight from the losing-streak file behind this site: equity remaining after eleven to fifteen consecutive losses, at each of the three reference stakes. Read the 2% column and then read the 0.5% column, and the whole argument for small stakes is visible without any probability at all.

Reproduce any cell with (1 - risk)ⁿ. At 1% and fifteen losses that is 0.99¹⁵ = 0.86014, or 86.01% — six points of each diagonal step, and nothing like the fifty the floor sits at. The distance between "the worst run I have ever had" and "account closed" is usually much wider than it feels in the middle of one.

What the chart hides is worth saying out loud. Each line assumes the next loser costs the same percentage of a shrinking balance, which is what fixed-fraction sizing does — so the deeper it gets, the flatter the fall. A trader who switches to a fixed money amount when confidence drops, or who widens stops after a bad week, is not on any of these lines.

What the estimate leaves out

This is an estimate built on a simplified model, and you should know which simplifications before you let it pick your stake. The formula treats every trade as an independent draw from one fixed distribution. Real results are none of those things: losses cluster, volatility clusters, and the edge itself drifts as regimes change. Cluster a few losses together and the same average performance produces a deeper trough than this page predicts.

The model also has no tail. A gap, a news spike or a stop that slips two distances instead of one lands outside a distribution made of wins and losses only, and each of those is worth several ordinary losers. Spread and commission are absent too, which means the effective expectancy is lower than the one you typed unless you already deducted them.

Use it for the one thing it is good at: choosing a stake you can hold through the bad patch, rather than tuning inputs until the probability looks acceptable. Move the risk field from 2% to 1% and watch the answer fall by a factor you could not get from any improvement in entries. That comparison is the whole value of the page.

Whatever number comes back, it is not a position. Sizing still runs through account size, risk percentage and stop distance, which is what the calculator below does — this page only says how much room the account has before any of it stops mattering.

Open the position size calculator

What people call this

A risk of ruin formula search usually lands on the barrier-crossing expression printed above, offered without the inputs filled in. Supplying the inputs is the entire job: the same expression returns 0.0026% and 100% depending on whether the drift term is positive, and which side of zero it falls on is decided long before anyone opens a spreadsheet.

Someone asking for a probability of ruin calculator or a ruin probability calculator wants the same figure with the threshold already chosen for them — often a prop firm's maximum drawdown, which is why the floor field above is editable rather than fixed at zero. Set it to the evaluation limits and this becomes the funded-account version of the question; the mechanics of those limits are set out in prop firm position sizing.

A drawdown probability calculator is asking about a shallower floor, typically 20% rather than 50%. Put that in the field and read the output — the shallower the floor, the closer it sits to where the account already is, and the less any model of long-run drift can tell you about reaching it.

Questions traders ask

The chance your account falls to a level you name before anything else happens to it. It is not the chance of going to exactly zero — most traders want the probability of losing half, or of hitting a drawdown limit a firm set. Set that level in the floor field, because the answer moves sharply with it: a floor at 50% is far away, a floor at 80% of the starting balance is not.

Work out expectancy first, then convert each trade into a log return and take its drift and variance. On the defaults here: expectancy is 0.45 x 1.5 - 0.55 = 0.125R, drift is 0.45 x ln(1.015) + 0.55 x ln(0.99) = 0.0011722, and variance is 0.45 x 0.55 x (0.0148886 + 0.0100503)^2 = 0.00015393. With the floor at half the account, the distance is 0.6931472 and the probability is exp(-2 x 0.0011722 x 0.6931472 / 0.00015393) = 0.0026%.

You can, and this page prices it rather than forbidding it. Holding the 45% hit rate and 1.5 payoff: 1% gives 69 losses to the floor and a 0.0026% chance, while 2% gives 35 losses and 0.71% — about 270 times the odds for twice the stake. The trade has twice the profit potential and roughly 270 times the chance of never getting paid for it.

Because the drift term is zero or negative, meaning the method has no edge over its own costs at this win rate and payoff. A 45% hit rate at even money has an expectancy of -0.10R per trade, and nothing about the stake size rescues that — reaching any floor below the current balance becomes certain eventually. The only variables that move this answer are the hit rate, the payoff and the costs.

More than feels plausible. From the table above, fifteen in a row at 1% still leaves 86.01% of the balance, which means the run that breaks an account is far longer than the run that breaks a trader's nerve. Size so that the count which would actually hurt is longer than anything your history suggests is realistic, then check the arithmetic on the risk per trade percentage page against the smallest account you trade.

No, and deliberately so. This page takes the stake as a percentage and reports what it costs in survival probability; converting a risk budget into units needs a balance, a stop distance and a contract size. Use the position size calculator for that, or the forex position size calculator if you want the pair-level version.

Related guides

• Risk per trade percentage — how much of the balance to stake, and what consecutive losses do to it.
• Drawdown calculator — once equity has fallen, the larger gain the reduced balance needs to climb back.
• Kelly criterion calculator — the stake that maximises growth, and the fractions of it people actually use.
• Risk reward calculator — the hit rate a given payoff demands before it earns anything.
• Reference data — the four files every figure on this site is cut from.