Kelly criterion calculator for traders and investors. Enter win rate and win/loss ratio to get the optimal bet size, plus half and quarter Kelly stakes.
Kelly Criterion Formula
The Kelly criterion gives the fraction of your bankroll that maximizes long-run growth for a strategy with a known edge:
K% = W - (1 - W) / R
Variables:
- K% is the fraction of your account to risk on each trade or bet
- W is the probability of winning as a decimal (0.55 for a 55% win rate)
- R is the win/loss ratio – the average winning amount divided by the average losing amount
Enter your win rate, then describe your payoff either as a single win/loss ratio or as average win and loss dollar amounts – the calculator derives R for you. If the result is zero or negative, the system has no edge and Kelly says to risk nothing. A positive result is the full Kelly stake, shown alongside half-Kelly and quarter-Kelly sizes and, if you enter an account balance, the dollar amounts each implies. The output also includes the expected value per dollar risked, which is the same edge expressed as a return.
Full Kelly Stakes by Win Rate and Ratio
Full Kelly percentage for common combinations. Negative cells mean no bet.
| Win rate | R = 1.0 | R = 1.5 | R = 2.0 | R = 3.0 |
|---|---|---|---|---|
| 40% | -20% | 0% | 10% | 20% |
| 45% | -10% | 8.3% | 17.5% | 26.7% |
| 50% | 0% | 16.7% | 25% | 33.3% |
| 55% | 10% | 25% | 32.5% | 40% |
| 60% | 20% | 33.3% | 40% | 46.7% |
Even modest edges produce aggressive full-Kelly stakes, which is why most practitioners scale down – the growth penalty for betting half of Kelly is small, but the drawdown reduction is large.
Example Problems
Example 1: Ratio form.
Your system wins 55% of the time and winners average 1.5x losers.
K% = 0.55 – (1 – 0.55) / 1.5 = 0.55 – 0.30 = 0.25, so full Kelly is 25% of the account, half Kelly 12.5%, quarter Kelly 6.25%. On a $25,000 account, quarter Kelly risks $1,562.50 per trade.
Example 2: Dollar averages with no edge.
You win 45% of the time; the average win is $200 and the average loss is $250, so R = 0.8.
K% = 0.45 – 0.55 / 0.8 = 0.45 – 0.6875 = -23.75%. Kelly is negative – this system loses money on average and the correct stake is zero.
Frequently Asked Questions
Why do traders use half or quarter Kelly?
Full Kelly assumes your win rate and payoff ratio are exactly right; in trading they are estimates from limited history. Overestimating the edge makes full Kelly over-bet, and over-betting destroys capital faster than under-betting sacrifices growth. Fractional Kelly buys a margin of safety and much smaller drawdowns.
Can I use Kelly for stock position sizing?
Yes, with care. Treat each trade’s stop-loss distance as the “loss” and your average winner as the “win”, then apply the Kelly fraction to the capital at risk, not the full position value. Many investors cap any single position well below the Kelly figure because market outcomes are not independent coin flips.
What does a negative Kelly mean?
Your expected value is negative – the combination of win rate and payoff loses money over time. No position size fixes a negative edge; the formula is telling you to skip the trade or fix the system.
