Kelly criterion calculator
“For this edge, which fraction of capital per trade maximises the long-run growth rate — and what does betting more or less than that do?”
Kelly is the fraction that maximises the logarithm of capital over a long run of identical, independent bets. The curve either side of it is the useful part: growth falls away on both sides, and past the peak it turns negative, which is what over-betting a real edge does to capital.
Free to use, nothing to sign up for, and nothing you type here is sent anywhere — the arithmetic runs in your browser.
What it computes
b = avg win / avg loss Kelly% = ((b x p) - q) / b x 100 growth per trade = p x ln(1 + f x b) + q x ln(1 - f)
What you type in
| Field | What it means | Example |
|---|---|---|
| Win rate % | Share of trades that win. | 55 |
| Average win | Mean winner. | $150 |
| Average loss | Mean loser. | $100 |
| Starting capital | For the simulation. | $10,000 |
| Number of trades | For the simulation. | 100 |
| Kelly fraction multiplier | A slider from 0.1x to 2x full Kelly. | 1x |
Reading the result
- The raw Kelly fraction, plus the same number halved and quartered — fractional Kelly is the common practice, because full Kelly's variance is severe by construction.
- The growth-rate curve against bet size, with the chosen fraction marked.
- A simulated equity path at the chosen fraction. Note the simulation caps risk at 25% of capital per trade regardless of what raw Kelly returns.
Worked example
55% win rate, $150 average win, $100 average loss.
- b = 1.5, so Kelly = 25.0% of capital per trade
- Growth at full Kelly: +4.57% per trade (log growth)
- Growth at half Kelly (12.5%): +3.44% per trade
- The 100-trade simulation at full Kelly ends around $964,700 from $10,000
That last figure is worth showing precisely because it is absurd. It is what compounding a 25% bet looks like when the inputs hold perfectly for 100 consecutive trades, and it is nothing like a real account. Half Kelly returns three-quarters of the growth for half the bet size, which is the standard argument for fractional Kelly.
What trips people up
- Kelly maximises growth, not comfort. Full Kelly's drawdowns are severe by construction.
- The formula is exquisitely sensitive to the win rate: a 55% estimate that is really 50% turns a 25% optimal bet into an over-bet.
- It assumes each trade is independent and the edge is stable. Neither is guaranteed.
- This is arithmetic on the numbers typed in, not a recommendation to risk any particular share of an account.
Questions
- Why do people use half Kelly?
- Because the growth curve is flat near its peak and the variance is not. Halving the fraction gives up a small share of the growth rate and cuts the swings substantially — the tool shows both numbers so the trade-off is visible rather than asserted.
- Can Kelly return a negative number?
- Yes, and it means the inputs describe a losing edge. There is no fraction of capital that grows a negative expectancy.
Related calculators
These are the same calculators built into Ledger of Alpha, where they read your own trade history instead of numbers you re-type. See the full product
Keep the record these numbers come from
A free account logs the trades you size here, so the win rate and averages you type into these calculators come from your own history rather than a guess.