Kelly Criterion Calculator

How to calculate the Kelly fraction

Kelly fraction = W - (1 - W) / R

• W = your win rate, as a decimal (55% becomes 0.55).
• R = your average win divided by your average loss.
• The result, when positive, is the fraction of the account this edge supports for maximum long-run growth. A negative result is floored at 0: no fraction has a positive expected growth rate.

Worked example

With a win rate of 55% and a win/loss ratio of 1.5:

• W = 0.55, R = 1.5
• Kelly fraction = 0.55 - (0.45 / 1.5) = 0.55 - 0.30 = 25%
• Half Kelly = 12.5%
• Quarter Kelly = 6.25%

The growth table confirms the math: expected log growth per trade rises as the sizing multiple approaches 1x full Kelly, peaks exactly there, and falls again past it, including going negative for multiples large enough to risk the whole edge on variance. That shape is why sizing beyond full Kelly is never worth it, and why sizing below it costs only a little growth for a lot less volatility.

The growth curve and fractional Kelly

Expected log growth as a function of sizing multiple is not a straight line down from the peak, it is a curve that falls off slowly at first and only steeply near the edges. That asymmetry is the entire case for fractional Kelly: moving from 1x to 0.5x full Kelly gives up a modest slice of the theoretical growth rate, while the swings in account value shrink far faster than that. Quarter Kelly gives up more growth again, but the resulting curve is gentle enough that an inaccurate win rate or ratio estimate is unlikely to push the real, unknown edge past zero.

This is also why the calculator marks the peak explicitly in the table rather than just stating a single number: seeing the neighboring rows shows how much room there is around 1x before growth drops meaningfully, and how sharply it turns negative once a mistaken multiple approaches or passes 1 (a single fraction that size risks the account on one loss). Full Kelly is mathematically optimal for growth here and practically aggressive to hold through; most traders who use Kelly at all use a fraction of it, and only once they trust the win rate and ratio behind it. For the wider set of sizing approaches this sits inside, see position sizing strategies compared.

When it misleads you

The Kelly fraction is only as good as the win rate and win/loss ratio you feed it, and both are estimates from a finite sample, not certainties. A small or recent sample can overstate an edge that will not hold going forward, and an overstated edge makes Kelly suggest a fraction that is too large for the account's real, unknown edge. The formula also treats each trade in isolation: it says nothing about correlated positions held at the same time, where the combined risk can run well past any single Kelly fraction. Use a fraction below full Kelly, keep a hard cap regardless of what the formula returns, and revisit the inputs as your sample of trades grows.

How to use this tool

1. Enter your win rate. The percentage of trades that close as winners, from a real sample of trades.
2. Enter your win/loss ratio. Your average winning trade divided by your average losing trade, in R or in money.
3. Read the Kelly fraction. The full, half, and quarter Kelly fractions of the account this edge supports.
4. Check the growth table. See how expected growth changes as you scale from 0 to 1.5x full Kelly, with the peak marked.
5. Choose a fraction below full Kelly. Most traders use half or quarter Kelly to keep most of the growth with far less volatility.

Frequently asked questions

Related tools and guides

• Risk/Reward Ratio Calculator
• Kelly criterion explained
• Position sizing strategies