Kelly Criterion Calculator
Parameters
Kelly Criterion Results
Capital Growth Simulation
Simulation Results
| Kelly Fraction | Final Capital | Total Return | Annualized Growth Rate |
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Understanding Kelly Criterion
The Kelly Criterion helps traders determine the optimal fraction of their capital to risk on each trade, based on their edge (win rate and risk/reward ratio).
Full Kelly is mathematically optimal for maximizing long-term capital growth, but it comes with high volatility.
Half Kelly (50% of the Kelly percentage) is often preferred by professional traders because it captures ~75% of the optimal growth rate while significantly reducing drawdown risk.
Quarter Kelly is extremely conservative, capturing ~50% of the optimal growth rate but with much lower volatility.
The formula used: Kelly % = Win Rate - [(1 - Win Rate) / Risk:Reward Ratio]
Note on the simulation: This calculator includes market friction factors like slippage and transaction costs that increase with position size, as well as position size limits. In real markets, larger positions typically face greater execution challenges and costs. The simulation caps position sizes at 25% of capital regardless of the Kelly calculation, reflecting real-world constraints.
Kelly Position Sizing in Trading
The Kelly criterion turns your strategy's statistics into a position sizing rule: the fraction of capital to risk on each trade that maximizes long-term compound growth. For trading, the formula takes your win rate W and your risk/reward ratio R (average win ÷ average loss):
Kelly % = W − (1 − W) / R
The output is the share of capital to risk — not the notional position size. If the calculator returns 8% on a $10,000 account, you size the position so the stop-loss costs $800 if hit; with a 2% stop distance, that means a $40,000 notional position (or $800 risked with tighter sizing). Both inputs should come from a statistically meaningful sample — a backtest of hundreds of trades, not a feeling. If your W and R come from a small sample, the true Kelly fraction may be far lower than the calculated one, which is one more reason professionals size below full Kelly.
A negative Kelly result means the strategy has no edge — no position size fixes that. Pair this tool with the risk of ruin calculator to see the survival probability of your chosen fraction, and the trading profit calculator to project the resulting P&L trade by trade.
Half Kelly and Quarter Kelly: Why Fractional Sizing Wins
Full Kelly is optimal only in the mathematical limit — it assumes your win rate and risk/reward are known exactly and never change. In live trading both are estimates, and betting the full fraction on an overestimated edge is how accounts blow up. That is why the standard practice is fractional Kelly: betting a fixed fraction c of the Kelly number.
The trade-off is quantifiable. Under the standard growth-rate approximation, betting c × Kelly delivers about (2c − c²) of the maximum growth rate: half Kelly captures ~75% of the growth with half the position size, and quarter Kelly ~44% of the growth at a quarter of the size — while drawdown volatility shrinks roughly in proportion to c. Use the fraction multiplier slider above to see this on the simulated capital curves: the aggressive multiples (1.5x, 2x Kelly) frequently end below the conservative ones despite the identical edge, because oversized losses compound against you.
Kelly Criterion for Betting Odds
The original Kelly formula was written for wagers quoted in odds, and the Betting Odds mode above accepts them directly. With decimal odds o, the net odds are b = o − 1 (profit per 1 staked), p your win probability and q = 1 − p:
f* = (b·p − q) / b
Worked example: decimal odds of 2.50 (b = 1.5) and a 45% win probability give f* = (1.5 × 0.45 − 0.55) / 1.5 ≈ 8.3% of bankroll per bet. This is the same equation as the trading form — the risk/reward ratio simply plays the role of the net odds — so the fractional-Kelly guidance above applies unchanged: if the true probability is uncertain, bet a fraction of the calculated stake.