Kelly Criterion Calculator
Your win rate, your payoff, your balance — and the share of it the Kelly formula says to put at risk, at full Kelly or at whatever fraction of it you choose.
At a glance
- f = p − (1 − p) ÷ b. At a 55% win rate with a payoff ratio of 2 that is 0.55 − 0.45 ÷ 2 = 0.325, so 32.50% of the balance at risk.
- On a 10,000.00 balance that is 3,250.00 at full Kelly, 1,625.00 at half, and the expected growth per trade falls from 10.36% to 7.79% — half the risk for about three quarters of the growth.
- Break-even win rate = 1 ÷ (1 + R). At 2:1 that is 33.33%, so 55% sits 21.67 points of edge above it.
- Full Kelly assumes your inputs are exact. A 55% win rate measured over 100 trades carries a standard error of about 5 points, which is why this page also shows the answer five points lower.
- Full Kelly is an average, not a worst case. At 32.50% per trade, two losers take the balance below half; at 0.50% per trade — one sixty-fifth of full Kelly here — twenty losers still leave 90.46%.
- Kelly sizes the risk, not the trade. Turn the money figure into units with the forex position size calculator.
A label on the figures, nothing more. Nothing is converted and no exchange rate is fetched, stored or estimated on this page.
Read as: — A multiplier of 1 is full Kelly; a percentage of 100 is full Kelly. Pick the unit, and the page reads your number in it.
How the number is worked out
Two inputs carry the whole calculation: how often you win, and how much you make when you do compared with what you lose when you do not. Everything else on the page is those two numbers rearranged.
The one thing to read before you use any of it: f is the amount you stand to lose, expressed as a share of the balance. It is not the notional size of the trade. If a losing trade costs you the whole amount you put up, the two are the same number; if a losing trade costs you 10% of the position, the position is ten times this figure. That distinction is where most misreadings of Kelly come from, and it is the one this page states rather than leaves for you to guess.
The break-even win rate is worth reading alongside the answer, because it is the number that does not depend on your estimate. At a payoff ratio of 2, break-even is 1 ÷ 3 = 33.33%: below that win rate the formula returns a negative share, which is its way of saying the trade is not worth taking. The gap between your win rate and the break-even rate is your edge, and everything else is that gap multiplied out.
What the Kelly fraction field reads as
A kelly calculator that takes a fraction of Kelly has to say what unit that field is in, and most do not. A field labelled "Kelly fraction" can mean either of two numbers that differ by a factor of a hundred: type 50 meaning "half" into a field read as a multiplier and you have asked for fifty times full Kelly — 5,000% of your balance.
This page makes you choose, and then echoes your number back in both units so there is no ambiguity left in the result:
- Multiplier — 1 is full Kelly, 0.5 is half, 0.25 is a quarter. Type 50 here and you are asking for fifty times full Kelly; the page will say so in words before you act on it.
- Percent of full — 100 is full Kelly, 50 is half, 25 is a quarter.
Half Kelly and quarter Kelly are printed alongside the full figure so the three can be compared side by side. The page does not choose between them for you: full Kelly is the fraction that maximises the growth rate and nothing else, and it maximises it under the assumption that you know your win rate exactly. Sizing below it buys a smoother ride at a lower growth rate, and how much that trade is worth is a judgement about you, not about arithmetic.
Worked example: 55% at 2:1 on a 10,000 balance
You win 55% of the time and make 2 for every 1 you risk. The balance is 10,000.00 USD and the fraction is set to 0.5 — half Kelly.
- q = 1 − 0.55 = 0.45.
- Full Kelly: f = 0.55 − 0.45 ÷ 2 = 0.55 − 0.225 = 0.325, so 32.50% of the balance, or 3,250.00 USD at risk.
- Half Kelly: 0.5 × 32.50% = 16.25%, or 1,625.00 USD at risk. Quarter Kelly is 8.13%, or 812.50 USD.
- Expected value: 0.55 × 2 − 0.45 = 0.65 per 1 risked.
- Break-even win rate: 1 ÷ (1 + 2) = 33.33%. Your 55% sits 21.67 points above it.
- Growth at half Kelly: g = 0.55 × ln(1 + 0.1625 × 2) + 0.45 × ln(1 − 0.1625) = 0.55 × ln(1.325) + 0.45 × ln(0.8375) = 0.1548 − 0.0798 = 0.0749, and e0.0749 − 1 = 7.79% per trade. At full Kelly the same inputs give 10.36%.
Step 6 is the honest argument for sizing below full Kelly, and it is visible rather than asserted: halving the fraction here costs about a quarter of the growth rate. What it buys is not printed, because it is not arithmetic — it is the difference between a drawdown you can sit through and one you cannot.
| Fraction | Share at risk | In money | Growth per trade |
|---|---|---|---|
| Full Kelly (1.00) | 32.50% | 3,250.00 USD | 10.36% |
| Half Kelly (0.50) | 16.25% | 1,625.00 USD | 7.79% |
| Quarter Kelly (0.25) | 8.13% | 812.50 USD | 4.57% |
| Tenth Kelly (0.10) | 3.25% | 325.00 USD | 2.00% |
This row is one example. Across five win rates at the same 2:1 payoff the answer runs from 2.50% to 40.00%, and the break-even win rate underneath it never moves: the Kelly criterion write-up prints the whole bracket in one table, so you can see where your own win rate lands before you type anything in here.
Full Kelly against half Kelly, when the losers arrive in a row
The comparison above is one trade at a time: full Kelly grows the example balance 10.36% per trade, half Kelly grows it 7.79%, and the price of halving the fraction is roughly a quarter of the growth rate. That is the number the formula is optimising, and it is the right number if your next trade is drawn from the same distribution as your last one and you never have to explain the path in between.
The other end of the same decision is arithmetic the formula does not print: what is left of the balance after a run of losers, if every loser costs exactly the share Kelly named. Run the example's four fractions through it — a 55% win rate at 2:1 on 10,000.00 — and the fractions separate far more sharply than they did on growth:
| Fraction | At risk per trade | After 3 losers | After 5 | After 10 | Losers to halve it |
|---|---|---|---|---|---|
| Full Kelly | 32.50% | 30.75% | 14.01% | 1.96% | 2 |
| Half Kelly | 16.25% | 58.74% | 41.20% | 16.98% | 4 |
| Quarter Kelly | 8.13% | 77.54% | 65.44% | 42.83% | 9 |
| Tenth Kelly | 3.25% | 90.56% | 84.77% | 71.86% | 21 |
| One sixty-fifth | 0.50% | 98.51% | 97.52% | 95.11% | 139 |
Two losers at full Kelly put the balance below half; ten leave 1.96% of it, which is a 98% hole that needs a 5,000% recovery to fill. Half Kelly takes four to halve the account and leaves 16.98% after ten. The growth rate moved by a quarter between those two fractions; the surviving balance moved by a factor of eight. That asymmetry is the whole argument for the fraction field, and it is why the field exists rather than the page simply printing full Kelly and wishing you well.
The bottom row is there for scale. A risk of 0.50% per trade is 50.00 on this balance, which is one sixty-fifth of full Kelly at these inputs — 0.50 ÷ 32.50, about 0.0154 in the multiplier field. Nobody arrives at that number by believing their edge is tiny; they arrive at it by deciding how deep a hole they intend to sit in. How likely a run of that length actually is belongs to a different calculation, and the risk of ruin calculator is where that side lives — this page fixes the size of the hole at a chosen risk and stops there.
A half-percent risk, twenty losers deep
Set the fraction to that one sixty-fifth and the losing run stops being a cliff. Each loser costs 0.50% of whatever is left, so the balance does not fall by a fixed amount each time — it falls by a slightly smaller amount each time, because there is slightly less to take 0.50% of. The compounding runs in your favour on the way down as well as on the way up, and the table below is that arithmetic carried out twenty trades, straight from this site's losing-streak data.
| Consecutive losses | Equity remaining | Consecutive losses | Equity remaining |
|---|---|---|---|
| 1 | 99.50% | 11 | 94.64% |
| 2 | 99.00% | 12 | 94.16% |
| 3 | 98.51% | 13 | 93.69% |
| 4 | 98.01% | 14 | 93.22% |
| 5 | 97.52% | 15 | 92.76% |
| 6 | 97.04% | 16 | 92.29% |
| 7 | 96.55% | 17 | 91.83% |
| 8 | 96.07% | 18 | 91.37% |
| 9 | 95.59% | 19 | 90.92% |
| 10 | 95.11% | 20 | 90.46% |
On the 10,000.00 balance the first loser costs 50.00 and the twentieth leaves 9,046.00 — a 9.54% hole, which needs a 10.55% gain to fill. That is the part worth carrying into the fraction field: at one sixty-fifth of Kelly, the worst ordinary run costs single digits and the recovery is a matter of weeks. At full Kelly the same twenty losers would leave 0.04% of the balance, and there is no fraction of anything that climbs back from that.
None of this is a forecast, and the table does not say a twenty-loss run is coming. It says what the hole looks like if it does, at the risk you chose, so the choice is made before the streak rather than during it. Kelly's percentage is the starting point for that choice, not the end of it: it assumes the win rate and the payoff you typed are exact, and the drawdown it can hand you is the price of being wrong about them.
The same formula on decimal odds
Decimal odds and a payoff ratio are the same number wearing different clothes. Decimal odds of 2.50 mean you get 2.50 back for every 1 staked, including your stake, so the net payoff is 1.50 for every 1 at risk — and b in the formula is 1.50, not 2.50.
A 45% chance at odds of 2.50 on a 1,000.00 balance:
- b = 2.50 − 1 = 1.50; q = 0.55.
- Full Kelly: f = 0.45 − 0.55 ÷ 1.50 = 0.45 − 0.3667 = 8.33%, or 83.33 at risk.
- Break-even win rate: 1 ÷ (1 + 1.50) = 40.00%. Your 45% is five points of edge.
- Expected value: 0.45 × 1.50 − 0.55 = 0.13 per 1 risked; growth 0.52% per event.
Notice what five points of edge buys: 8.33% of the balance. That is the shape of the whole formula near break-even — the share is small, and it stays small until the edge is large. It is also why the five-points-lower row exists on the results panel: at this input it takes the answer from 8.33% to 0.00%, because 40% is exactly break-even.
When the answer is larger than your whole balance
It can be, and this page will print it rather than quietly trimming it. A 90% win rate at a payoff ratio of 5 gives f = 0.90 − 0.10 ÷ 5 = 0.88, so 88.00% of the balance at risk, with a break-even win rate of 16.67%.
Take that same setup and say a losing trade costs you only 10% of the position — a wide, soft stop — and the position itself is 0.88 ÷ 0.10 = 880% of the balance. Both figures are the same formula. The first is what you risk, the second is what you hold, and confusing them is how a plausible-looking percentage turns into a margin call.
Nothing here caps the answer, on purpose. A cap is a second opinion wearing the costume of a calculation, and this page would rather hand you the arithmetic and say plainly what it means: at or above 100% of the balance, the figure is leverage you would have to borrow, the per-trade growth rate stops being defined because the formula would be taking the logarithm of a non-positive number, and the honest reading is that the inputs describe an opportunity you almost certainly do not have.
Rounding, precision and what is not capped
The rules, stated rather than left to be discovered from the display:
- Shares are shown to two decimal places — 8.13%, not 8.125%.
- Money is shown to two decimal places, rounded half away from zero, the way a bank statement rounds.
- Growth is shown to two decimal places, as eg − 1, with g in natural logarithms.
- No intermediate value is rounded before it is used. The full-precision share is what goes into the money figure, the growth figure and the copy text; only the number you see is rounded.
- Nothing is capped. There is no hidden maximum, no clamp at 25% or at 100%, and no floor that turns a negative Kelly into a small positive one. If the arithmetic says 880%, it prints 880% and flags it.
- Anything within a ten-trillionth of zero is treated as zero, so the page never prints −0.00% where the answer is exactly nothing.
One thing this number is not: a lot size. Kelly returns money at risk. Turning that into units requires the instrument, the distance to your stop, the spread and the commission, and that is a different calculation with different inputs — the position size calculator does it from a risk budget, and the forex version does it from a stop distance in pips.
Where each number comes from
| Input | Where it comes from |
|---|---|
| Win rate | You. From your own records. Nothing is fetched, nothing is typical, nothing is assumed. |
| Payoff ratio | You. Average win ÷ average loss, measured over your own closed trades. |
| Decimal odds | You, typed as quoted. The page takes 1 off it to get the net payoff b. |
| Account balance | You. Kelly is a share of balance, so the balance only scales the money column, never the percentage. |
| Account currency | You, as a label only. No conversion happens anywhere on this page. |
| Kelly fraction | You, in the unit you picked. Stated back to you in words under the field. |
| Net payoff b | Arithmetic: the payoff ratio as typed, or decimal odds − 1. |
| Full Kelly f | Arithmetic: p − q ÷ b. |
| Break-even win rate | Arithmetic: 1 ÷ (1 + b). |
| Expected growth | Arithmetic: p·ln(1+f·b) + q·ln(1−f), reported as eg − 1. |
Two of the inputs above — the win rate and the payoff ratio — can only be measured over your own closed trades, and the reliable way to measure them is a trade journal that pulls the fills in and works the statistics out. TraderSync is one of them: it connects to a broker, groups your trades by setup and reports the win rate and the average win ÷ average loss this page asks for, so the numbers typed here are measured rather than remembered.
The win rate is the input most likely to be wrong, and the page says so with a number rather than a warning. The standard error of a win rate measured over n trades is √(p(1−p) ÷ n): at 55% over 100 trades that is about 5 percentage points, which is why the results panel carries a row showing the answer five points lower. Everything else — the payoff ratio, and whether the future resembles the past at all — is held constant in that row, and stated as such.
What this page will not tell you
- Whether your win rate is real. The formula treats the number you type as a fact. It is an estimate, and the estimate has error in it.
- Whether your trades are independent. Kelly assumes each one is. Ten positions opened on the same view are not ten independent events, and the formula has no way to know.
- Whether the payoff ratio holds. An average win ÷ average loss from a hundred trades is not a distribution. Fat tails on either side move the answer.
- Anything about margin, leverage or financing. Kelly knows nothing about margin requirements, borrow costs or overnight charges. At large fractions those dominate.
- A lot size, a stop distance or a take-profit level. Those come from the instrument and the chart, not from this formula.
- What to do. It prints the arithmetic and the meaning of each figure. The fraction is yours to choose.
What people call this
A kelly formula calculator, a kelly calculator, a kelly criterion position sizing tool and a half kelly calculator are all the same question: given how often I win and how much I make when I do, what share of the balance goes on the next one. This page answers all four in the same place, and prints full, half and quarter Kelly together so the fraction is a comparison rather than a hunt.
The two halves of the question come from two different worlds, which is why both are accepted here. Traders think in a payoff ratio — average win over average loss — and get it from their own closed trades. Bettors think in decimal odds, and get it from a price. Subtract 1 from the odds and the two become the same number, so one formula covers both.
Kelly is one answer to "how much", and it is the answer that starts from your edge. The other starts from what you can afford to lose: the risk-per-trade percentage page works that one through, and the position size calculator turns either into units.
FAQ
How do I calculate the Kelly criterion?
Take your win rate as a decimal (p), take your net payoff per 1 risked (b — the payoff ratio, or decimal odds minus 1), and compute f = p − (1 − p) ÷ b. At a 55% win rate with a payoff ratio of 2 that is 0.55 − 0.45 ÷ 2 = 0.325, so 32.50% of the balance at risk. Multiply by your balance for the money figure, and by your chosen Kelly fraction to size below full Kelly.
Is the Kelly fraction field a multiplier or a percentage?
Whichever you select next to it, and the page reads your number in that unit and repeats it back in words. As a multiplier, 1 is full Kelly, 0.5 is half and 0.25 is a quarter; as a percentage, 100 is full, 50 is half and 25 is a quarter. The two differ by a factor of a hundred, which is why the unit is chosen explicitly rather than left to the label.
Is the result the size of the position or the amount I risk?
The amount you risk — the money you lose if the trade goes against you. If a losing trade costs you the entire amount you put up, that is also the position size. If a losing trade costs you only 10% of the position, the position is ten times the figure shown.
Why is my Kelly percentage negative?
Because at that win rate and that payoff there is no edge: the break-even win rate is above the one you entered. The formula's answer is to stake nothing, and the page shows 0.00% as the recommendation while still printing the raw negative number in the Full Kelly row so you can see where it came from.
Can Kelly be more than 100% of my balance?
Yes, and this page will print it rather than cap it. It happens when the edge is large: a 90% win rate at a payoff ratio of 5 returns 88% of the balance at risk. Read it as leverage you would have to borrow. The per-trade growth rate is not defined at or above 100%, because the formula would be taking the logarithm of a non-positive number, so that cell stays blank.
What is half Kelly, and why is it printed?
Half Kelly is half of the full-Kelly share: 16.25% where full Kelly is 32.50%. It is printed next to quarter Kelly so the three can be compared rather than hunted for. Full Kelly maximises the growth rate and nothing else; the lower fractions grow more slowly, and whether the difference is worth it is a judgement about the drawdown you can sit through, not about arithmetic.
What does expected growth per trade mean?
It is the compounded growth rate of the balance per trade at the fraction shown: g = p·ln(1 + f·b) + q·ln(1 − f), reported here as eg − 1 so it reads as a percentage. It assumes every trade is independent, the same size, and drawn from the same distribution — which is the strongest assumption on the page.
Does the currency do anything?
No. It is a label on the money figures. Nothing is converted, and no exchange rate is fetched, cached or estimated — there is no rate feed anywhere on this site.
Do I need an account, and is anything uploaded?
No and no. There is no sign-up, no login and no pop-up. The page is one HTML file, one shared stylesheet and one script, and every calculation runs in your browser.
How many losing trades in a row can I survive at full Kelly?
At the 32.50% full-Kelly share from the example, three losers leave 30.75% of the balance and five leave 14.01% — it takes two to put the account below half, and ten to leave 1.96%. Half Kelly takes four losers to halve it and leaves 16.98% after ten. The fraction field is what moves you along that scale; the formula itself has no view on it.
Why does half Kelly give up less growth than it gives up risk?
Because growth is flat near its maximum while the drawdown is not. Halving the share from 32.50% to 16.25% in the example takes the growth rate from 10.36% to 7.79% — about three quarters of the growth for half the risk — while the balance left after ten straight losers goes from 1.96% to 16.98%, an eightfold difference. Near its peak the growth curve barely slopes; the hole left by a losing run scales with the size you chose.
Can I use the Kelly percentage as my risk per trade?
It is the share that maximises growth for a single bet with a known edge, and most trading accounts run far below it. At the example's inputs, a risk of 0.50% per trade is one sixty-fifth of full Kelly — 50.00 on a 10,000.00 balance — and twenty straight losers at that size leave 90.46%, a 9.54% hole needing a 10.55% gain to fill. Kelly tells you where the growth peak is; the per-trade risk you actually take is a separate decision about the hole you can sit through.