# Kelly Criterion Calculator

> The Kelly criterion gives the bet fraction that maximises the long-run growth rate of capital: f* = (b·p − q) ÷ b, where p is the win rate, q is 1 − p, and b is the payoff ratio. At a 45% win rate with 2:1 payoff, full Kelly is 17.5% of capital per trade. Almost no one trades that: full Kelly is optimal only when the edge is known exactly, and with an estimated edge it produces drawdowns above 50% as a routine event, which is why half- or quarter-Kelly is the practical setting.

Canonical HTML page: https://qanterion.com/tools/kelly-criterion-calculator
Updated: 2026-08-18

## The formula

```
f* = (b · p − q) ÷ b

  p = win rate            q = 1 − p
  b = payoff ratio (average win ÷ average loss)

Expectancy per unit risked = b · p − q
Break-even win rate        = 1 ÷ (b + 1)

Assumes a known, stationary edge and independent outcomes.
```

## Worked example (the page defaults)

- Win rate: 45 %
- Payoff ratio (avg win : avg loss): 2 :1

Result:

- Full Kelly: 17.5%
- Half Kelly: 8.75%
- Quarter Kelly: 4.38%
- Expectancy per unit risked: 0.35
- Break-even win rate: 33.33%

## How to use it

1. Enter the win rate from a sample large enough to be statistically meaningful.
2. Enter the payoff ratio: average winning trade divided by average losing trade.
3. Read full Kelly, then look at the half and quarter figures — those are the ones to work from.
4. Check your win rate against the break-even figure to confirm the edge exists at all.

## Why practitioners use a fraction of Kelly

Full Kelly maximises growth for a known edge, and trading edges are never known — they are estimated from a finite sample of a non-stationary process. Half-Kelly gives about 75% of the growth rate with roughly half the volatility and far shallower drawdowns; quarter-Kelly gives up more growth for a curve most people can hold through. Since the strategy that gets abandoned in a drawdown returns nothing at all, the fraction that survives is the one that compounds.

## A negative Kelly is the useful answer

When f* comes out negative, the win rate and payoff ratio together have no edge — expectancy is below zero and no position size fixes that. This is the calculator’s most valuable output, because it is testable before capital is committed. Compare your win rate against the break-even figure: at 2:1 payoff you need better than 33.3%, and at 1:1 you need better than 50%.

## Frequently asked

### What is a realistic Kelly fraction to actually trade?

Most systematic practitioners run between a quarter and a half of full Kelly. The reasoning is not conservatism for its own sake: the inputs are estimates, and Kelly’s optimality guarantee evaporates when they are wrong in the optimistic direction — which is the direction estimation error usually points.

### Can I apply Kelly across several strategies at once?

Not by computing it independently for each. Simultaneous positions interact through correlation, and summing individual Kelly fractions overstates total safe exposure — sometimes badly, since correlations rise precisely in the stressed conditions where sizing matters. Treat the single-strategy figure as a ceiling, then scale down for portfolio overlap.

### How does Kelly relate to fixed-percentage risk?

They answer different questions. Kelly says what fraction of capital to expose given an edge; fixed-fractional sizing says how to translate a chosen risk budget into an order size. In practice Kelly informs the risk percentage, and the position size calculator turns that percentage into a quantity given the stop distance.

## Related tools and reading

- Risk of Ruin Calculator: https://qanterion.com/tools/risk-of-ruin-calculator
- Position Size Calculator: https://qanterion.com/tools/position-size-calculator
- Strategy selection and risk budget: https://qanterion.com/blog/strategy-selection-risk-budget
- Expectancy: https://qanterion.com/glossary/expectancy
- Quant Trading Glossary: https://qanterion.com/glossary
- Crypto backtesting platform: https://qanterion.com/backtesting

## Sources

- [A New Interpretation of Information Rate](https://www.princeton.edu/~wbialek/rome/refs/kelly_56.pdf) — Bell System Technical Journal (AT&T Bell Laboratories)
- [Good and bad properties of the Kelly criterion](https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf) — L.C. MacLean, E.O. Thorp & W.T. Ziemba, 2010 author preprint (hosted by the UC Berkeley Department of Statistics)

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## Machine-readable resources

- Product facts: https://qanterion.com/llms.txt
- Full knowledge base: https://qanterion.com/llms-full.txt
- All calculators: https://qanterion.com/tools

## Risk notice

Educational calculator. Outputs describe arithmetic under the assumptions you enter — they are not a forecast, a recommendation, or investment advice. Quantitative trading can lose money.