Kelly Criterion Calculator
Calculate kelly criterion with our free Kelly criterion Calculator. Compare rates, see projections, and make informed financial decisions.
Kelly Criterion Calculator
Calculator
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Formula: Kelly % = (b × p − q) / b | where b = Avg Win / Avg Loss, p = Win Rate, q = 1 − p
Worked example — Full Kelly: 32.5% | Half Kelly: 16.25% | Quarter Kelly: 8.13%
Formula
Kelly % = (b × p − q) / b | where b = Avg Win / Avg Loss, p = Win Rate, q = 1 − p
The Kelly Criterion calculates the fraction of your account to risk per trade that maximizes long-term geometric growth. b is the win/loss ratio (average win divided by average loss), p is the probability of winning, and q is the probability of losing. Half Kelly and Quarter Kelly are fractional versions recommended for real-world trading to reduce volatility.
Worked Examples
Example 1: Profitable Day Trading Strategy
Problem:Win rate: 55%, Average win: $200, Average loss: $100. What is the optimal position size?
Solution:Win/Loss Ratio (b) = $200 / $100 = 2.0 Kelly % = (2.0 × 0.55 - 0.45) / 2.0 = (1.10 - 0.45) / 2.0 = 0.325 = 32.5% Half Kelly = 16.25% Quarter Kelly = 8.13%
Result:Full Kelly: 32.5% | Half Kelly: 16.25% | Quarter Kelly: 8.13%
Example 2: Scalping Strategy Assessment
Problem:Win rate: 70%, Average win: $50, Average loss: $80. Should you trade this?
Solution:Win/Loss Ratio (b) = $50 / $80 = 0.625 Kelly % = (0.625 × 0.70 - 0.30) / 0.625 = (0.4375 - 0.30) / 0.625 = 0.22 = 22% Half Kelly = 11% Expectancy = (0.70 × $50) - (0.30 × $80) = $35 - $24 = $11 per trade
Result:Full Kelly: 22% | Half Kelly: 11% | Profitable with $11 expectancy per trade
Frequently Asked Questions
What is the Kelly Criterion in trading?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. at Bell Labs in 1956. It calculates the optimal percentage of your bankroll to risk on each bet or trade to maximize long-term geometric growth. The formula considers your win rate and win/loss ratio to determine the ideal position size. In trading, it helps determine what percentage of your account to risk per trade. However, most traders use a fractional Kelly (half or quarter) because full Kelly can lead to large drawdowns despite being mathematically optimal for long-term growth.
Why should I use Half Kelly instead of Full Kelly?
Full Kelly maximizes long-term growth rate but comes with extremely high volatility and large drawdowns. In practice, half Kelly provides about 75% of the growth rate of full Kelly but with significantly less risk and smaller drawdowns. The estimates for win rate and average win/loss are never perfectly accurate in trading, and even small estimation errors can make full Kelly dangerously aggressive. Most professional traders and fund managers recommend half Kelly or less. Quarter Kelly is even more conservative and suitable for traders who prioritize capital preservation.
How do I calculate my win rate and average win/loss for Kelly?
To calculate your inputs: 1) Win Rate = Number of winning trades / Total trades × 100. 2) Average Win = Total profit from winners / Number of winning trades. 3) Average Loss = Total loss from losers / Number of losing trades (use absolute value). You need a statistically significant sample size — at least 30-50 trades minimum, ideally 100+. These metrics should come from actual trading results or thorough backtesting. Remember that market conditions change, so periodically recalculate these values.
What does a negative Kelly percentage mean?
A negative Kelly percentage means your trading strategy does not have a positive expected value — you are expected to lose money over time. The formula is telling you not to bet at all. This can happen when your win rate is too low relative to your win/loss ratio. For example, if you win 40% of the time but your average win equals your average loss, Kelly will be negative. In this case, you need to either improve your win rate, increase your average win, decrease your average loss, or find a different strategy before risking real money.
Can the Kelly Criterion be used for forex trading?
Yes, the Kelly Criterion can be applied to forex trading, but with important caveats. Forex markets are not simple win/lose bets — outcomes are continuous, and the distribution of returns matters. The basic Kelly formula assumes binary outcomes, so it is an approximation when applied to trading. Best practices include: using fractional Kelly (half or quarter), recalculating regularly as your statistics change, accounting for correlation between trades, and never using Kelly as your sole position sizing method. Combine it with maximum risk limits (such as never risking more than 2% per trade regardless of what Kelly suggests).
What is the expected geometric growth rate, and why does it use logarithms?
Kelly maximises the expected logarithm of wealth, because trading returns compound multiplicatively rather than adding up — a 50 percent loss needs a 100 percent gain to undo. The growth figure shown is p times the natural log of one plus f times b, plus q times the natural log of one minus f. With a 55 percent win rate and a 2:1 win/loss ratio, committing the full 32.5 percent yields roughly 9.9 percent expected log growth per trade, and no other fraction beats it.
What is the difference between expectancy and the Kelly fraction?
Expectancy is arithmetic and denominated in currency: win rate times average win minus loss rate times average loss. At a 55 percent win rate with a 200 dollar winner and a 100 dollar loser that is 65 dollars per trade. It tells you an edge exists but says nothing about stake size. The Kelly fraction is geometric and dimensionless, converting the same edge into a share of equity to commit. A strategy can carry healthy expectancy and still be ruinous at the wrong bet size.
What happens if I risk more than the full Kelly fraction?
Growth as a function of bet size is a curve, not a line: it climbs to a peak at the Kelly fraction and then falls away steeply. Past the peak you accept more variance for less growth, and far enough past it the expected growth turns negative even while expectancy stays positive. With the default 55 percent win rate and 2:1 payoff, doubling from 32.5 to 65 percent per trade pushes expected log growth just below zero. That is the risk-of-ruin region.
Why is Kelly expressed as a percentage of current equity rather than a fixed stake?
Kelly is defined as a fraction of equity, recalculated before each trade, not a fixed cash amount. That is what makes it self-correcting: after a losing run the absolute amount risked shrinks automatically, so a strict fractional bettor cannot mathematically reach zero. Fixed-dollar staking loses that property — a 3,000 dollar risk that was 3 percent of a 100,000 dollar account becomes 6 percent once the account halves, quietly converting a conservative plan into an over-bet one.
How sensitive is the Kelly fraction to an error in my estimated win rate?
Very sensitive, and the sensitivity scales with the payoff ratio. Rearranged, the formula is f equals p times one plus one over b, minus one over b. At a 2:1 win/loss ratio that reduces to 1.5 times the win rate minus 0.5, so every percentage point of win rate you over-estimate inflates the recommended fraction by one and a half points. That same 2:1 ratio breaks even at a 33.3 percent win rate. Fractional Kelly exists largely to absorb this estimation error.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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