Kelly criterion calculator
The Kelly criterion tells you the bet fraction that maximises long-run account growth — and why almost nobody should trade it in full. Enter your win rate and payoff ratio to get full, half and quarter Kelly instantly, with your per-trade edge.
By Mustafa Bilgic · Published 2026-06-27 · Last updated 2026-06-27
Kelly Criterion Calculator
Optimal bet fraction from your win rate and payoff ratio
How the Kelly criterion is calculated
The Kelly criterion, introduced by Bell Labs researcher John L. Kelly Jr. in a 1956 paper in the Bell System Technical Journal, answers one precise question: what fraction of your capital should you stake to maximise the long-run growth rate of your account? For a bet that wins with probability p and a payoff ratio b (your average win divided by your average loss), the optimal fraction is:
f* = p − (1 − p) / b
Equivalently, f* = (b·p − q) / b where q = 1 − p is the loss probability. The numerator b·p − q is your edge per trade measured in units of R (one R = the amount you risk per trade). If that number is zero or negative you have no positive expectancy, Kelly returns zero, and no bet size is "safe" — the only winning move is not to trade that setup.
A worked example
Suppose your backtest shows a 55% win rate and your average winner is 1.5× your average loser, so p = 0.55 and b = 1.5. Then f* = 0.55 − 0.45/1.5 = 0.55 − 0.30 = 0.25, or 25% of equity per trade. That is an enormous bet — and that is exactly the problem with full Kelly.
Full Kelly maximises theoretical growth but produces brutal drawdowns and is hypersensitive to estimation error. Your real win rate and payoff are estimates from noisy history, and traders almost always overestimate their edge. Overstate it a little and full Kelly over-bets a lot. The standard practice is half-Kelly or quarter-Kelly — it keeps most of the growth while roughly halving the volatility and buying a large margin of safety. That is why this calculator shows all three.
From Kelly fraction to a real position
The Kelly fraction is a ceiling on how much of your account to risk, not the notional position itself. In practice you cap your fixed-fractional risk at a conservative slice of Kelly, then convert that risk into a number of units with the position-size calculator using your actual stop distance. Kelly sets the speed limit; the position-size formula tells you how many units that speed limit allows for a given stop. For the full theory and why fractional Kelly dominates, see position sizing for trading bots, and test any chosen fraction in the risk-of-ruin simulator.
Frequently asked questions
What is the Kelly criterion in trading?
The Kelly criterion is a formula for the bet fraction that maximises the long-run growth rate of an account. For a win probability p and payoff ratio b it is f* = p minus (1 minus p)/b. In trading it is used as a ceiling on how much of your capital to risk per trade.
Why use half-Kelly or quarter-Kelly instead of full Kelly?
Full Kelly maximises growth in theory but produces violent drawdowns and is extremely sensitive to overestimating your edge. Because real win rates and payoffs are only estimates, most practitioners bet a half or a quarter of the Kelly fraction to keep most of the growth with far less volatility.
What does a negative Kelly fraction mean?
A zero or negative Kelly fraction means the setup has no positive expectancy at the win rate and payoff you entered — the math says do not bet at all. You would need a higher win rate, a better payoff ratio, or both before any position size is justified.
Is the Kelly calculator free and private?
Yes. It runs entirely in your browser as client-side JavaScript. Nothing you type is sent to a server or stored, and there is no signup.