Kelly Criterion Calculator
Calculate the mathematically optimal position size for long-run capital growth.
Please note: Trading carries substantial risk of loss. These calculators are planning tools, not trading advice, and no position sizing method prevents losses.
What the Kelly Criterion Calculator does
The Kelly criterion finds the bet size that maximises the long-run growth rate of capital. It is mathematically optimal but assumes perfect knowledge of your edge, so practitioners almost always trade a fraction of it to survive estimation error.
Formula
Kelly % = (b × p − q) ÷ bwhere b = payoff ratio, p = win probability, q = 1 − p
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Win probability | % | Yes | — |
| Win/loss payoff ratio | number | Yes | Average win divided by average loss. Accepts more than 0. |
| Account balance | selected currency | Optional | Accepts 0 or more. |
| Currency | one of 10 options | Optional | — |
How to use it
- Choose Currency.
- Enter Win probability and Win/loss payoff ratio.
- Optionally add Account balance.
- Select Calculate.
Worked example
A 55% win rate with average wins twice the size of average losses.
- Win probability
- 55
- Payoff ratio
- 2
(2 × 0.55 − 0.45) ÷ 2 = 32.5% full Kelly. Half Kelly is 16.25%, which is still aggressive.
Frequently asked questions
Why do people use half Kelly?
It captures about 75% of the growth rate with roughly half the volatility, and it is far more forgiving if your estimated edge turns out to be optimistic.
What if Kelly returns a negative number?
It means you have no edge — the expected value is negative. The correct size is zero.
Method and sources
Method. The Kelly fraction, f = (bp − q) / b, from the win probability and payoff ratio supplied, with fractional-Kelly scaling.
Assumptions
- The win rate and payoff ratio are known and stable. Kelly assumes you are estimating them correctly, which in trading is almost never true.
- Outcomes are independent, and the full fraction can be committed on each opportunity.
Limitations
- Kelly maximises long-run growth, not comfort. Full Kelly produces drawdowns most people abandon the strategy during, which is why fractional Kelly is the common practice.
- The formula is acutely sensitive to the inputs: overestimating the win rate leads to systematic overbetting, and overbetting past the optimum reduces growth and can be ruinous.
- Derived for a repeated bet with known odds. A market is neither.