Kelly Criterion Calculator
The Kelly criterion is a formula for how much of your account to risk on each trade: f* = W - (1 - W) / R, where W is your win rate and R is your average win divided by your average loss. At a 45% win rate and a payoff of 2, full Kelly is 17.5%, which is why traders who use Kelly usually risk half or a quarter of it.
Enter your win rate and either your payoff ratio or your average win and average loss. You get full Kelly as a percent of your account to risk per trade, the full, half, or quarter Kelly you pick, the dollars that means on your account size, and your expectancy per trade. It is arithmetic on the numbers you type, so it never sees your chart, your account, or your trade history. It works the same for stocks, futures, or forex, because the inputs are a win rate and a payoff.
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Kelly Criterion Calculator
How much of your account the Kelly formula says to risk per trade
Enter your win rate and payoff ratio to see the Kelly size.
The formula
How the Kelly criterion is calculated
Full Kelly f* = W - (1 - W) ÷ R
R = Average win ÷ Average loss
Expectancy (R) = W × R - (1 - W)
Risk per trade = f* × 1, 0.5, or 0.25
Dollar risk = Account size × Risk per trade
J. L. Kelly Jr. published the idea in 1956 in the Bell System Technical Journal, in a paper titled "A New Interpretation of Information Rate". He framed it as a gambler betting on tips from a noisy private wire and showed two things that still matter to traders. Betting everything on every favorable bet maximizes expected wealth, yet kept up long enough it goes broke with probability one. Betting a fixed fraction instead grows capital at the fastest rate over the long run. For an even-money bet that fraction is your chance of winning minus your chance of losing. For a payoff of R to 1, the same maximization gives the formula above.
In trading terms, f* is the share of your account you lose if the stop is hit. It is a risk number, not a position size: the share count comes from dividing that dollar risk by the distance to your stop, which is the job of the position size calculator. The formula also treats every trade as one of two outcomes, a win of R or a loss of 1, so your average win and average loss stand in for the spread of results you really get.
Worked examples, with and without an edge
| Line | From a payoff ratio | From average win and loss | No edge |
|---|---|---|---|
| Win rate | 45% | 50% | 40% |
| Payoff entered as | Ratio 2 | $300 win, $200 loss | Ratio 1.2 |
| Payoff ratio (R) | 2 | 1.5 | 1.2 |
| Expectancy per trade | +0.35R | +0.25R | -0.12R |
| Edge | Positive | Positive | Negative |
| Full Kelly | 17.5% | 16.67% | No edge, size 0 |
| Fraction used | Half Kelly | Quarter Kelly | Half Kelly |
| Risk per trade | 8.75% | 4.17% | 0% |
| Account size | $25,000 | $10,000 | $25,000 |
| Dollar risk per trade | $2,187.50 | $416.67 | $0 |
In the first column, 0.45 - 0.55 ÷ 2 = 0.175, so full Kelly is 17.5% and half Kelly risks 8.75%, or $2,187.50 on $25,000. In the second, $300 ÷ $200 is a payoff of 1.5, full Kelly is 0.5 - 0.5 ÷ 1.5 = 16.67%, and a quarter of that is 4.17%, or $416.67 on $10,000. The third trade wins 40% of the time at a payoff of 1.2, which is 0.4 × 1.2 - 0.6 = -0.12R per trade. Kelly comes out negative, and the calculator reads that for what it is: no edge, don't take it, size 0.
Kelly by the numbers
Full Kelly across win rates and payoff ratios
Read across a row to see what a bigger payoff is worth at the same win rate, and down a column for a better win rate at the same payoff. The "No edge" cells are where the win rate sits at or below the breakeven line for that payoff, 1 ÷ (1 + R), which the breakeven win rate calculator works out. There Kelly says to stay out.
| Win rate | R = 1 | R = 1.5 | R = 2 | R = 3 |
|---|---|---|---|---|
| 30% | No edge | No edge | No edge | 6.67% |
| 40% | No edge | No edge | 10% | 20% |
| 50% | No edge | 16.67% | 25% | 33.33% |
| 60% | 20% | 33.33% | 40% | 46.67% |
| 70% | 40% | 50% | 55% | 60% |
Full Kelly, as a percent of the account to risk per trade, before commissions, spread, or slippage.
Most of these numbers dwarf the 1% or 2% of the account that common risk rules put on a single trade. That gap is the reason for the next section: full Kelly is only right if your win rate and payoff are exactly right, and nobody's are.
Fractional Kelly
Why traders who use Kelly risk half or a quarter of it
Full Kelly maximizes long-run growth only if your inputs are exact. Edward O. Thorp, whose 2006 chapter on the Kelly criterion in blackjack, sports betting, and the stock market is one of the standard references, worked out what smaller and larger fractions do in a continuous-time model. Two of its results are worth knowing before you pick a fraction: how much growth each fraction keeps, and how likely the account is to fall to half its starting value at some point.
| Bet size | Long-run growth kept | Chance the account ever halves |
|---|---|---|
| Twice Kelly | 0% | 100% |
| Full Kelly | 100% | 50% |
| Half Kelly | 75% | 12.5% |
| Quarter Kelly | 43.75% | 0.78% |
From Thorp's formulas: growth kept = c × (2 - c) and chance of ever falling to half = 0.5 ^ (2 ÷ c - 1), where c is the multiple of full Kelly. Both assume the edge is known exactly.
Half Kelly gives up a quarter of the growth rate and cuts the chance of ever losing half the account from 1 in 2 to 1 in 8, a trade Thorp writes that most people strongly prefer. Overbetting is the expensive mistake: at twice Kelly, growth falls to zero in this model, and past that the account shrinks. These figures assume a perfectly known edge, so they flatter full Kelly. For what a deep drawdown costs to climb back from, see what drawdown is and why getting back costs more.
What an optimistic win rate does to each fraction
Win-rate estimates are where Kelly breaks. Say you believe you win 55% of the time at a payoff of 1.5, so full Kelly says 25%, but your real win rate is 45%. The table runs each fraction through the growth Kelly maximizes, W × ln(1 + R × f) + (1 - W) × ln(1 - f) per trade, at the real win rate.
| Fraction | Risk per trade, sized for 55% | Long-run result at 45% |
|---|---|---|
| Full Kelly | 25% | Shrinks the account |
| Half Kelly | 12.5% | Grows at 76% of the best possible rate |
| Quarter Kelly | 6.25% | Grows at 94% of the best possible rate |
At 45% the right full Kelly is 8.33%. Sizing full Kelly off the optimistic estimate risks 3 times that, and the account shrinks over time even though the trades still have an edge. Half Kelly keeps most of the growth, and quarter Kelly barely notices the error. That forgiveness is the real case for a fraction.
Common mistakes
Common Kelly criterion mistakes
- Using a win rate from too few trades. 12 wins in 20 trades is 60%, and at a payoff of 1.5 full Kelly says 33.33%. Flip 2 of those wins to losses and it is 50% and 16.67%. In a 20-trade sample every trade moves the win rate by 5 percentage points, so one hot streak can double the size Kelly hands you.
- Reading Kelly as a position size. Kelly is the share of the account you lose if the stop is hit. Putting 17.5% of your account into a stock with a stop 2% away risks 0.35% of it. Risking 17.5% means a position many times bigger. Size the shares from the dollar risk, never from the Kelly percent.
- Running full Kelly and expecting a smooth ride. Even with an edge known exactly, Thorp's model gives full Kelly a 1 in 2 chance of halving the account at some point. Ask yourself whether you would keep following the method through that, because the growth only shows up if you do.
- Blending setups into one win rate. Kelly sizes one bet with one edge. A win rate mixed from your best setups and your impulse trades describes neither, so measure each setup you size on its own record.
- Using numbers before costs. Commissions, spread, and slippage come out of every win and add to every loss. If they trim a payoff of 2 to 1.8 at a 45% win rate, full Kelly drops from 17.5% to 14.44%. Use your averages after costs.
- Treating the answer as fixed. Your win rate moves with the market and with you. Rerun the numbers as the record grows, and size down when recent results fall below the inputs you used.
Kelly sits on top of the basics. The breakeven win rate calculator shows the win rate a payoff needs before there is any edge to size, the risk reward calculator gives the payoff of a single planned trade, and position sizing from risk per trade walks through turning a risk percent into a position. For why a measured edge has to come before any sizing formula, see what a trading edge is, and for scaling size with setup quality instead of one flat number, see why traders stall at breakeven.
Grade the setup before you size it
Kelly takes your win rate and payoff on trust. It can't tell whether the next setup looks anything like the ones that earned that record. Upload a chart screenshot and SnapPChart grades the setup A+ to F in seconds. If you log the entry and exit of the trades you take on graded setups, the SnapPChart analytics page shows the win rate and the average win and loss of those logged trades, the same inputs this calculator asks for. They are only as good as what you log, and you still type them in here yourself.
Upload a Chart ScreenshotYour first grade is free and shows the setup's grade and the general read. Entry, stop, targets and the trade plan come with a paid plan.
Keep going
Related free tools and guides
- GuidePosition sizing from risk per tradeThe 1% rule math, a worked table across account sizes, and why a fixed share count quietly randomizes your losses.
- Free toolPosition Size CalculatorFree position size calculator: enter account size, risk percent, entry, and stop loss to get your share size instantly. No signup, no AI, pure risk math.
- Free toolBreakeven Win Rate CalculatorFree breakeven win rate calculator: enter your reward:risk ratio (or entry, stop, target) to see the minimum win rate to break even, plus expectancy.
- Free toolFutures Position Size CalculatorFree futures position size calculator: pick ES, NQ, MES, MNQ, CL or GC, enter your risk and stop, and get the contract count with tick and point values.
- Free toolProp Firm Drawdown CalculatorFree prop firm drawdown calculator: enter your balance, peak, and max loss limit to see your liquidation level, buffer left, and losses until you fail.
- Free toolRisk Reward Ratio CalculatorFree risk reward ratio calculator: enter entry, stop and target for a long or short trade to get the R:R as 1 : X, the R-multiple, and your breakeven win rate.
FAQ
Kelly criterion questions
What is the Kelly criterion formula for trading?
f* = W - (1 - W) / R. W is your win rate as a decimal, and R is your average win divided by your average loss. The answer is the share of your account to risk per trade. At a 45% win rate and a payoff of 2: 0.45 - 0.55 ÷ 2 = 0.175, so full Kelly is 17.5%.
What does a negative Kelly percentage mean?
That the trade has no edge at your numbers. It loses money on average, so Kelly's answer is to skip it, a size of 0. Kelly is zero or negative whenever your win rate is at or below 1 ÷ (1 + R). At a payoff of 1.2 that line is 45.5%, so a 40% win rate comes out negative.
Should I use full Kelly or half Kelly?
Traders who use Kelly usually take a fraction. In Thorp's model, half Kelly keeps 75% of full Kelly's long-run growth while cutting the chance of ever losing half the account from 50% to 12.5%, and it is far more forgiving when your win rate is overestimated. Quarter Kelly gives up more growth for a smoother ride still. Full Kelly only makes sense if you are sure your numbers are right, and with trading results you rarely are.
Is the Kelly percentage my position size?
No. It is the share of your account you lose if the stop is hit. Multiply it by your account size for the dollar risk, then divide that by the distance from entry to stop to get the share count, which is what the position size calculator does.
Why is the Kelly number so much bigger than the 1% rule?
Kelly assumes the win rate and payoff you enter are exact and stable, and it only cares about long-run growth, not how deep the drawdowns get on the way. A fixed rule like risking 1% per trade builds in room for wrong estimates and losing streaks. If your fractional Kelly comes out below the risk you already take, take that seriously: your edge may be thinner than your sizing assumes.
How many trades do I need before I trust my win rate?
There is no exact number, but small samples swing hard. In 20 trades, each trade is 5 percentage points of win rate, and two results going the other way can halve the Kelly size. Use as many trades of the same setup as you have, and stay on a fraction of Kelly until the record is long.
What happens with a 0% or 100% win rate?
At 0% every trade loses, so Kelly says size 0. At 100% the formula says to risk the whole account, because it assumes you can never lose. A record with no losses is a sample that is too short, so the calculator asks for a win rate that includes your losing trades instead of printing 100%.
Does this calculator read my trades or my account?
No. It does arithmetic on the numbers you type and nothing else. It does not see your chart, your broker account, or your trade history, and it leaves out commissions and slippage unless you have already taken them out of your averages.
Benjamin Loh
Founder & Developer at SnapPChart
I build AI-powered tools for traders. I created SnapPChart to help day traders analyze chart patterns faster using computer vision and machine learning. Learn more · Follow on X
This calculator is for planning purposes only and is not financial advice. The Kelly criterion assumes your win rate and payoff are accurate and will stay the same, which real results rarely do, and most traders who use it risk a fraction of full Kelly. It does not know your broker's fees, slippage, or your other open positions. Trading involves risk of loss.