Kelly Criterion Calculator
Kelly gives the fraction of capital that maximises long-run growth for a known edge. Enter your win rate and payoff ratio to get full Kelly, plus the half and quarter fractions almost everyone actually uses.
The formula
f* = W − (1 − W) ÷ R, where W is the win probability and R the payoff ratio. The default — 55% at 1.5:1 — gives 25%, meaning full Kelly would put a quarter of the account at risk on every trade.
That number should provoke suspicion, and it should. Kelly maximises the long-run growth rate of capital, and it does so by accepting drawdowns that no human tolerates. At full Kelly, a 50% drawdown is an ordinary event, not a disaster.
Why nobody trades full Kelly
Three reasons, and they compound.
The inputs are estimates. Kelly assumes W and R are known. Yours are measured from a finite sample and are uncertain. Overestimating the edge causes overbetting, and the penalty is asymmetric — betting double the optimal fraction produces a negative growth rate even with a genuine edge.
The drawdowns are brutal. Full Kelly's expected maximum drawdown is roughly 50%, and it recurs. Almost nobody keeps trading a system through that, and abandoning it at the bottom converts a theoretical optimum into a realised disaster.
Edges decay. Kelly assumes a stationary edge. Real edges erode as conditions change, and by the time the decay is visible in your statistics you have been overbetting for months.
Half Kelly captures about 75% of the growth rate with roughly half the drawdown. Quarter Kelly is the common professional choice. Both are in the results above.
Compare against your risk rule
Even quarter Kelly here is 6.25% of the account per trade — well above the 1–2% most risk frameworks use, and the gap is instructive. Kelly answers "what maximises growth if my numbers are exactly right"; the 1–2% rule answers "what survives my numbers being wrong". The second question is the more important one, which is why fixed-fractional sizing remains the default in practice. Use the position size calculator for the size you actually trade.
Negative Kelly is a real answer
If the formula returns zero or below, the strategy has no edge and the optimal size is nothing. No amount of position sizing fixes negative expectancy — it only changes how fast the account declines.
Where the formula comes from
Kelly derived it in the Bell System Technical Journal in 1956, not as a betting tip but as the growth-optimal fraction of a bankroll given an edge[1] — the result being that there is a finite optimum and that betting above it lowers long-run growth even when the edge is real.
The number is the easy part
Everything above is arithmetic, and anyone opening this page gets the same answer. What no calculator can settle is whether you took the trade on these terms, or are describing — afterwards — the version of it that worked out.
That is what a trade recorder is for: the trade committed before it resolves, timestamped and sealed on the spot, on a Merkle-anchored log a stranger can check without kappi's cooperation. The plan you typed here stops being a plan you remember having. $15/month, no free tier.
Sources
Frequently asked questions
What is the Kelly criterion formula?
f* = W − (1 − W)/R, where W is win probability and R is the payoff ratio. It gives the fraction of capital that maximises long-run growth.
Why do traders use half Kelly?
It captures roughly 75% of the growth rate with about half the drawdown, and it is far more forgiving when your estimated win rate turns out to be optimistic.
What happens if I overestimate my edge?
You overbet, and the penalty is asymmetric. Betting twice the optimal fraction can turn a genuine edge into a negative growth rate.
Why is Kelly so much larger than the 1–2% rule?
They answer different questions. Kelly maximises growth assuming your numbers are exactly right; the 1–2% rule is built to survive them being wrong.