Kelly Criterion Calculator — Optimal Position Sizing Formula

The Kelly Criterion is a mathematical formula that solves the most fundamental question in trading and gambling: how much of your bankroll should you risk on each bet or trade to maximize your long-term growth rate? Developed by John Kelly Jr. at Bell Labs in 1956, the formula was originally intended for problems in information theory, but it was quickly adopted by professional gamblers, fund managers, and traders because it provides a precise, mathematically optimal answer to the position sizing question that every risk-taker faces.

The formula works by balancing two competing forces: the desire to bet aggressively when you have an edge (to maximize growth) and the need to preserve capital (to avoid ruin). If you bet too little, you grow too slowly and your edge is wasted. If you bet too much, you expose yourself to ruin before your edge can manifest. The Kelly Criterion finds the exact middle ground — the bet size that maximizes the expected logarithm of your wealth, which is mathematically equivalent to maximizing the long-term compound growth rate of your bankroll.

What makes the Kelly Criterion unique among position sizing methods is its theoretical optimality. No other bet sizing strategy produces a higher expected growth rate over an infinite number of bets. A Kelly-sized bankroll will, with probability approaching 1, exceed the bankroll produced by any other sizing strategy over the long run. This does not mean Kelly produces the highest returns in any given month or year — it means that over the longest time horizon, Kelly is mathematically unbeatable. The catch is that "long run" can be very long, and the short-term volatility of Kelly betting is extreme, which is why most practitioners use a fractional version of the formula.

This Kelly Criterion calculator takes two inputs and outputs both the full Kelly percentage and a recommended fractional Kelly percentage for practical use.

Win Rate (%)

Enter the percentage of your trades that are winners. This is your historical win rate, calculated from a meaningful sample of at least 50 to 100 trades. A higher win rate increases the Kelly percentage because it means you should bet more aggressively when wins are more frequent. If you are evaluating a new strategy, use conservative estimates — the downside of underestimating your win rate is modest (you bet slightly too little), while the downside of overestimating it (you bet too much and risk ruin) is severe.

Reward-to-Risk Ratio

Enter the ratio of your average winning trade to your average losing trade. If your average win is $600 and your average loss is $400, your reward-to-risk ratio is 1.5. A higher ratio means each win is larger relative to each loss, which increases the Kelly percentage because each bet is more favorable. A ratio of 1.0 means wins and losses are the same size; below 1.0 means losses are larger than wins, which decreases the Kelly percentage and may push it to zero if the edge is negative.

Reading the Output

The calculator outputs two numbers: the full Kelly percentage (the mathematically optimal bet size) and a fractional Kelly recommendation (typically 25% to 50% of full Kelly). The fractional recommendation is what most practitioners actually use because it captures the majority of the growth rate while dramatically reducing volatility and drawdowns. A full Kelly of 8% would display a fractional Kelly of approximately 2% to 4% depending on the fraction chosen.

The Kelly Criterion formula is: Kelly % = W − (1 − W) / R, where W is the win rate (as a decimal) and R is the reward-to-risk ratio.

Let us derive it step by step. The expected value of a bet with probability W of winning R units and probability (1 − W) of losing 1 unit is: E = W × R − (1 − W). If E is positive, you have an edge. The Kelly formula finds the fraction f of your bankroll that maximizes the expected logarithm of wealth after the bet. The optimization yields f = W − (1 − W) / R.

Using a concrete example: a 55% win rate (W = 0.55) and a 1.5 reward-to-risk ratio (R = 1.5) produces Kelly = 0.55 − (0.45 / 1.5) = 0.55 − 0.30 = 0.25, or 25%. This means you should risk 25% of your bankroll per trade to maximize long-term growth. At 50% fractional Kelly, you would risk 12.5% instead — capturing most of the growth with far less volatility.

The formula can also be expressed as: Kelly % = (W × R − L) / R, where L = 1 − W. This is algebraically identical and sometimes easier to compute. For the same example: (0.55 × 1.5 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.375 / 1.5 = 0.25, or 25%.

Example 1: A Strong Edge

A trend-following strategy has a 45% win rate and a 2.5 reward-to-risk ratio. Full Kelly = 0.45 − (0.55 / 2.5) = 0.45 − 0.22 = 0.23, or 23%. Despite winning fewer than half the trades, the Kelly Criterion recommends risking 23% of the bankroll per trade because the winners are so much larger than the losses. At half-Kelly (11.5%), the strategy would still compound aggressively while keeping drawdowns manageable. This example illustrates why win rate alone is misleading — a below-50% win rate with a high reward-to-risk ratio can produce a large Kelly percentage.

Example 2: A Marginal Edge

A scalping strategy has a 53% win rate and a 1.1 reward-to-risk ratio. Full Kelly = 0.53 − (0.47 / 1.1) = 0.53 − 0.427 = 0.103, or about 10.3%. The edge is real but small, so Kelly recommends a modest position size. At quarter-Kelly (2.6%), the growth rate is lower but the strategy is far more resilient to variance. This is the profile of a strategy where full Kelly is too aggressive relative to the thin edge — the margin for error is small, and a few bad streaks at full Kelly could produce devastating drawdowns.

Example 3: No Edge

A random strategy has a 50% win rate and a 1.0 reward-to-risk ratio. Full Kelly = 0.50 − (0.50 / 1.0) = 0.50 − 0.50 = 0. The Kelly Criterion says risk nothing — there is no edge, so the optimal bet size is zero. This is one of the most valuable outputs of the formula: it tells you when not to trade. A strategy with zero or negative expectancy should not be traded at any size, and Kelly makes this explicit.

Use Half-Kelly or Less in Practice

The full Kelly Criterion is mathematically optimal under perfect conditions — known edge, independent outcomes, no correlation between positions. Real trading violates all of these assumptions. Your edge is estimated with error, outcomes are not perfectly independent, and positions may be correlated. Using 25% to 50% of the Kelly recommendation (quarter-Kelly to half-Kelly) captures 75% to 94% of the growth rate while reducing volatility by 50% to 75%. For most traders, half-Kelly is the practical sweet spot between growth and safety.

Kelly Requires Accurate Inputs

The Kelly formula is only as good as the win rate and reward-to-risk ratio you feed it. If your edge is declining because market conditions have changed, but you are still using historical inputs, Kelly will recommend a bet size that is too large for your current edge. Recalculate regularly, and when in doubt, err on the side of lower win rates and lower reward-to-risk ratios — underestimating your edge produces smaller, safer bets, while overestimating produces dangerously large ones.

Kelly Does Not Maximize Dollar Returns

Kelly maximizes the expected logarithm of wealth (compound growth rate), not the expected dollar return. In any given period, a more aggressive or more conservative strategy might produce higher dollar returns. Kelly is the long-game strategy — it produces the highest wealth over an infinite time horizon, but at the cost of significant short-term volatility. If you cannot tolerate large drawdowns, use fractional Kelly even if it means slightly lower long-term growth.

Pair with Drawdown Expectations

The Kelly Criterion does not tell you what drawdown to expect — it only tells you the optimal bet size for maximum growth. In practice, full Kelly in the stock market can produce maximum drawdowns of 50% or more. Use our drawdown calculator to estimate the drawdown your chosen fractional Kelly level is likely to produce, and adjust the fraction downward if the expected drawdown exceeds your tolerance.

All content on this page is educational and does not constitute financial advice. The Kelly Criterion is a mathematical model and does not guarantee future returns. Past performance does not predict future results. For personalized guidance, consult a certified financial planner.