Kelly Criterion Calculator

f* = W − (1 − W) ÷ R, where W is your win probability (as a decimal) and R is your win/loss ratio — the average win size divided by the average loss size. f* is the fraction of your bankroll that maximizes the expected long-run geometric growth rate, derived by John Kelly in 1956 and popularized for trading and gambling by Ed Thorp.

The growth-rate curve is asymmetric around the full-Kelly point: it rises steeply on the way up to f*, then falls off faster past it. Two effects follow. First, overestimating your win rate or win/loss ratio — which real traders do, because both are estimated from a limited sample — pushes the true optimum lower than the one calculated, so full Kelly calculated from noisy inputs tends to over-bet in practice. Second, full Kelly still carries large peak-to-trough drawdowns even when the inputs are exactly right, because it maximizes growth rate, not smoothness. Half Kelly gives roughly three-quarters of the growth rate of full Kelly with roughly half the variance, which is why it is the most commonly cited compromise.

Kelly sizing requires a positive edge — W×R must exceed (1−W), i.e. your expected value per dollar staked must be positive. If it isn't, f* is negative, and this calculator shows a stake of $0 rather than a negative position, because the Kelly criterion has no interpretation for betting against your own edge. The break-even win probability shown is 1 ÷ (1 + R): at your win/loss ratio, that is the win rate at which f* crosses zero.

No — they answer different questions. The position size calculator fixes a risk percentage you choose and computes shares from your entry and stop. The risk/reward calculator checks a single trade's reward-to-risk ratio. This calculator instead asks what risk percentage is edge-optimal in the first place, given your historical win rate and win/loss ratio — its output (the Kelly fraction) is a reasonable input to feed into the position size calculator's risk-per-trade field.

It assumes every trade is a fixed win of R units or a fixed loss of 1 unit at a stable probability W — a two-outcome simplification of what is really a continuous distribution of trade outcomes. It also assumes W and R are known exactly, when in practice both are estimates from a finite trade history and drift over time as market conditions change. It does not account for correlated trades (multiple open positions that win or lose together), commissions, slippage, or taxes. Treat the output as a starting point for a risk framework, not a guarantee.