Kelly Criterion Calculator
Calculate the Kelly fraction for a given win rate and payoff ratio, with half and quarter Kelly alongside.
A Kelly criterion calculator answers a specific question: given a known edge, what fraction of capital should be committed to each trade to maximise long-run growth? The formula was derived by John Kelly at Bell Labs in 1956 for signal transmission, and taken up afterwards wherever a repeated favourable proposition has to be sized — in trading it is known as Kelly position sizing.
Formula: f* = (payoff x win rate - loss rate) / payoff
Your figures
Percentage of trades that are profitable.
A win returns this multiple of the amount risked.
Optional — converts the fraction into a cash amount.
Results
Full Kelly
25.00%
of capital per trade, at full Kelly
- Half KellyRetains most of the growth for far less volatility.
- 12.50%
- Full Kelly stake
- US$2,500.00
- Half Kelly stake
- US$1,250.00
- Quarter Kelly
- 6.25%
- Edge per trade
- +0.375 R
- Expected growth per trade at full KellyExpected logarithmic growth of capital.
- 4.569%
What this means
Kelly puts the growth-maximising stake at 25.00% of capital per trade. That figure maximises long-run compound growth, but it is deliberately aggressive: it produces severe drawdowns and is highly sensitive to error in the win rate, which is why half Kelly (12.50%) and quarter Kelly are shown alongside. This is the output of a formula, not a suggestion about what to risk.
- Assumes the win rate and payoff ratio are known exactly. Estimated from a small sample, they are not, and overstating either leads Kelly to overstake.
- Assumes every trade is independent and that outcomes are a fixed size. Real results vary around their average.
Full Kelly: 25.00%
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Continue with these figures
About the Kelly Criterion calculation
Its appeal is that it is not a rule of thumb. For a given win rate and payoff ratio there is exactly one fraction that maximises the expected logarithm of wealth, and Kelly finds it — that is what growth-optimal sizing means. Risk less and you grow more slowly; risk more and you grow more slowly again, because the losses compound against you.
This calculator estimates that fraction, along with half and quarter Kelly. Anyone applying the Kelly formula to trading soon finds the fractional versions matter more than the headline number: full Kelly is punishing to sit through, and because it assumes the inputs are known exactly, overstating your edge leads it to oversize by more than you would expect.
Kelly Criterion formula
f* = (b × p − q) ÷ b
where:
p = probability of a win
q = 1 − p
b = payoff ratio — the multiple of the amount risked returned on a win
expected log growth at fraction f:
g = p × ln(1 + f × b) + q × ln(1 − f)- f*
- The fraction of total capital to commit. Negative means there is no edge.
- b
- Payoff ratio. A trade risking 1 to make 2 has b = 2.
- ln
- Natural logarithm. Kelly maximises expected log wealth, not expected wealth.
The numerator of the Kelly formula is the edge: the expected gain per unit risked. Dividing by the payoff ratio scales it into a fraction of capital. When the edge is zero the numerator is zero, so Kelly commits nothing — and when the edge is negative it goes below zero, which has no valid interpretation other than not taking the trade.
Maximising the logarithm of wealth rather than wealth itself is the part that does the work. Expected wealth is maximised by committing everything on any positive-edge trade, which guarantees eventual ruin. Taking logarithms penalises large losses far more heavily than it rewards large gains, which is what produces a finite, survivable fraction.
The growth rate formula shows why over-staking is punished twice. As f rises past f*, the ln(1 − f) term falls away steeply, so growth declines even though the edge has not changed. Staking double the Kelly fraction produces zero long-run growth, and anything beyond that compounds negatively.
Kelly Criterion: a worked example
A strategy that wins 60% of the time at even money — risking 1 to make 1.
- Win probability, p0.60
- Loss probability, q0.40
- Net odds, b1.0
- Numerator(1 × 0.60) − 0.40 = 0.20
- Full Kelly0.20 ÷ 1 = 20% of capital
- Half Kelly10% of capital
- Growth per trade at full Kelly0.6·ln(1.2) + 0.4·ln(0.8) = 2.01%
Full Kelly says risk 20% per trade. That is far more than the figure most traders work with, and the drawdowns at that fraction are severe — which is why half Kelly, at 10%, is the figure usually quoted alongside it.
How to use the Kelly Criterion calculator
- Enter the win rate, ideally measured from a real trade record rather than estimated.
- Enter the payoff ratio — the multiple of the amount risked that a winning trade returns.
- Optionally add your account balance to see the fraction as a cash figure.
- Read half and quarter Kelly alongside the full figure. They give up little growth for much less volatility.
- If the result is zero, the inputs describe a system with no edge. No position size fixes that.
Limitations of the Kelly Criterion calculator
Every calculation makes assumptions. These are the ones that matter here.
- Assumes the win rate and payoff ratio are known exactly. Estimated from a small sample they carry real error, and Kelly is asymmetrically sensitive to overstating either.
- Collapses a distribution of outcomes into two numbers. Kelly is derived for a proposition with one payoff and one loss, so feeding it an average winner and an average loser answers the question for a system nobody actually trades. Dispersion around those averages lowers the growth-optimal fraction, and it does so asymmetrically: an occasional loss several times the average matters far more than an occasional outsized win, because the fraction that survives the worst run is what compounds. The figure this returns is therefore a ceiling on a system with fixed outcomes rather than the optimum for yours.
- Assumes trades are independent. Correlated positions or clustered losing runs break the assumption.
- Full Kelly produces drawdowns that most people will not tolerate — drawdowns exceeding 50% are routine at the optimal fraction.
- Ignores costs, margin limits and the practical minimum position sizes a broker will accept.
Frequently asked questions about Kelly Criterion
Why is half Kelly so widely used instead of full Kelly?
Because the growth curve is flat near its peak but the volatility is not. Half Kelly gives up roughly a quarter of the growth rate while cutting the volatility of returns by about half. It is also far more forgiving of error: if your true edge is smaller than you estimated, half Kelly may still be near optimal while full Kelly is already over-staking.
What happens if I risk more than the Kelly fraction?
Growth falls. At exactly twice the Kelly fraction the long-run growth rate is zero, even with a genuine edge, and beyond that the account declines over time. Over-staking is more damaging than under-staking by a wide margin, which is the practical argument for fractional Kelly.
The calculator returned a negative number. What does that mean?
The edge is negative — the payoff ratio does not compensate for the win rate. Kelly's answer is to commit nothing. There is no position size at which a negative-expectancy system becomes profitable; sizing only changes how quickly the account declines.
Is the Kelly fraction the optimal position size for a trading strategy?
It is the optimal position size only under the Kelly formula's own assumptions — known probabilities, fixed outcome sizes, independent trades — and those rarely hold in trading. This calculator reports the fraction as a mathematical result rather than suggesting you risk it, which is why fractional Kelly and fixed-fractional sizing are more common in practice.
How does Kelly relate to the risk of ruin?
They approach the same problem from opposite ends. Kelly asks what maximises growth; risk of ruin asks what probability of a severe drawdown a given risk fraction implies. Full Kelly usually produces a risk of ruin most traders find unacceptable, which is why the two are worth reading together.
Last reviewed . See our methodology and editorial policy.
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