The math-optimal bet size for a repeatable edge. Enter your win rate and average win/loss ratio to get the full Kelly fraction — plus the half- and quarter-Kelly stakes real traders actually use, in percent and dollars.
Answer first: the Kelly criterion says the growth-optimal fraction of your bankroll to risk is f = W − (1 − W) ÷ R, where W is your win probability and R is your average win divided by average loss. This Kelly criterion calculator solves that formula and immediately shows the fractional stakes — half and quarter Kelly — that practitioners prefer once real-world uncertainty enters the picture.
f = W − (1 − W) ÷ R
Example: 55% win rate, winners average 1.5× the size of losers → f = 0.55 − 0.45 ÷ 1.5 = 25% of bankroll. Half-Kelly = 12.5%, quarter-Kelly = 6.25%. On a $10,000 account, that's $2,500 / $1,250 / $625 at risk per trade.
The formula was published in 1956 by Bell Labs physicist John L. Kelly Jr., and famously used by Edward Thorp — first to size bets at blackjack tables, then in his hedge fund. Its promise is precise: among all fixed-fraction betting rules, Kelly maximizes the long-run compound growth rate of capital. Bet more than Kelly and volatility actively destroys growth; bet double-Kelly and your expected growth rate drops to zero. The formula is a ceiling, not a target.
Full Kelly is optimal only if W and R are your true long-run numbers. In markets you only ever have estimates from a limited sample, and edges decay. Overestimate your win rate by a few points while betting full Kelly and you're unknowingly betting past the optimum — the zone where drawdowns deepen and growth shrinks. Betting half-Kelly costs surprisingly little (roughly 3/4 of the theoretical growth rate) while cutting the swings dramatically, and it's forgiving of estimation error in a way full Kelly is not. Quarter-Kelly is common where the inputs are shakiest. Even full Kelly, done right, produces gut-wrenching drawdowns — a 50% loss of bankroll is entirely within its normal behavior.
Plug in a 45% win rate with even-sized wins and losses and the formula returns a negative number. That's not an error — it's the whole point. A negative Kelly fraction means the system has no edge: the expected value per trade is below zero, and the growth-maximizing allocation is exactly nothing. The calculator flags this case explicitly. Position sizing multiplies an edge; it cannot create one. If your numbers come back negative, the fix is a better strategy, not a cleverer stake.
W and R must come from data — a trading journal or a back-test — never from optimism. Count your last 50+ trades: the fraction profitable is W; average dollar gain on winners divided by average dollar loss on losers is R. Two warnings: small samples lie (10 trades tell you almost nothing), and the two inputs interact — tightening a stop-loss raises R but usually lowers W. Practice generating a genuine sample in the stock market simulator before risking anything real.
Reality check: Kelly assumes known, stable probabilities and independent, repeatable bets — markets offer none of these guarantees, and most traders' estimated edge is smaller than they think. This is an educational calculator, not financial advice or a betting recommendation. Risk-management basics from the U.S. SEC: investor.gov.
Compare with the simpler fixed-risk approach in the position size calculator, understand the R multiple in the risk/reward ratio calculator, see what drawdowns do to compounding in the maximum drawdown calculator, and build the discipline side with risk management basics and trading psychology basics.
Last updated July 2, 2026 · Written by Mustafa Bilgic. Educational only — not financial advice.
f = W − (1 − W) ÷ R, where W is your win probability and R is the ratio of average win to average loss. With a 55% win rate and wins 1.5× the size of losses, f = 0.55 − 0.45 ÷ 1.5 = 25% of bankroll. The formula maximizes long-run compound growth of capital.
It means the strategy has a negative edge — over many repetitions it loses money, so the growth-optimal stake is zero. No position sizing can rescue a system that loses on average; the Kelly answer is simply: don't take the bet.
Full Kelly assumes you know your true win rate and payoff ratio exactly — in markets you never do, and overestimating your edge with full Kelly leads to brutal drawdowns. Betting half the Kelly fraction keeps roughly three-quarters of the theoretical growth rate with about half the volatility, which is why half-Kelly (or less) is the practical standard.
From your own records: the percentage of past trades that were profitable, average profit on winners and average loss on losers. You need a meaningful sample — a few dozen trades at minimum — and even then the numbers are estimates that drift as markets change.