Kelly criterion calculator

Your numbers

The share of trades that win, from a large sample of your own records. Above 0 and below 100.

The average win divided by the average loss, for example 2 when winners average twice the size of losers.

The share of full Kelly to use: 25 for quarter Kelly, 50 for half Kelly, 100 for full Kelly.

Results

Risk per trade at your fraction
4.4%
Full Kelly (f*)
17.5%
Edge per 1R risked
+0.35R
Break-even win rate
33.3%
Share of full Kelly’s growth rate
44.9%

An educational tool: the result is only as good as the win rate and payoff you enter, which are estimates from a limited sample. Most traders risk well below full Kelly. Nothing you enter is sent or saved. Not investment advice.

How to use it

  1. Enter the win rate and the payoff ratio from a large sample of one strategy’s trades, after costs. A small sample gives unreliable estimates.
  2. Choose a fraction of full Kelly. Practitioners who use the formula at all usually take a quarter or a half, and many keep a fixed small risk per trade instead.
  3. Read the result as the share of the account lost if the stop is hit, not as the position value. Take it to the position size calculator to turn it into shares, and compare it with the risk per trade you could sustain through a long losing streak.

The formula

f* = p − (1 − p) ÷ b, where p is the win rate and b the payoff ratio (average win ÷ average loss). When every trade either wins b times the amount risked or loses that amount, f* is the share of the account to risk per trade that maximises the long-run growth rate.

Risk at your fraction = max(0, f*) × fraction. Edge per 1R = p × b − (1 − p), the expectancy in R. Break-even win rate = 1 ÷ (1 + b); below it, f* is negative.

Growth per trade g(f) = p × ln(1 + f × b) + (1 − p) × ln(1 − f). The last result is g at your fraction divided by g at full Kelly. As a property of the formula, half Kelly keeps about three quarters of full Kelly’s growth rate with each swing half the size, while risking about twice full Kelly brings the growth rate down to roughly zero.

The formula assumes the win rate and payoff are known exactly and stay constant, every win and loss is the same size, and trades are independent. None of this holds in trading: the inputs are estimates with sampling error, and overestimating the edge leads to over-betting, which lowers growth and deepens drawdowns.

Worked example

Illustrative numbers: a win rate of 45% and a payoff ratio of 2 give f* = 0.45 − 0.55 ÷ 2 = 17.5%. Quarter Kelly is about 4.4% risk per trade and keeps about 45% of full Kelly’s growth rate; half Kelly is 8.75% and keeps about 76%. The edge is +0.35R per trade and the break-even win rate 33.3%.

Even quarter Kelly here is far above the 0.5–2% many traders risk per trade, and the figure depends heavily on the inputs. If the true win rate were 35% rather than 45%, f* would be only 2.5%, and risking 17.5% per trade would give a negative long-run growth rate. A win rate measured over 100 trades has a standard error of about 5 percentage points.

Questions

How do I calculate the Kelly criterion from win rate and payoff?

Use f* = p − (1 − p) ÷ b, with p the win rate as a decimal and b the average win divided by the average loss. A 45% win rate with a payoff of 2 gives 0.45 − 0.55 ÷ 2 = 0.175: 17.5% of the account risked per trade at full Kelly.

Full Kelly or half Kelly: which is used in trading?

Few traders use full Kelly. It maximises growth only if the inputs are exact, and it produces deep drawdowns even then. Half Kelly keeps about three quarters of the growth rate with swings half the size, and quarter Kelly or a fixed small risk per trade leaves more room for estimation error. This is general information, not a recommendation for your account.

What does a negative Kelly result mean?

That on the numbers entered the system has no edge: the win rate is below the break-even win rate for that payoff ratio. The formula’s answer is to risk nothing on it, and the calculator shows 0% as the fractional result.

How many trades do I need before trusting the inputs?

There is no exact number, but more is better. With 100 trades and a 45% win rate the standard error of the win rate is about 5 percentage points, and at a payoff of 2 a win rate of 40% instead of 45% cuts full Kelly from 17.5% to 10%. Conservative estimates and a fraction of Kelly allow for that error.

Is the Kelly percentage the position size?

No. Here f* is the share of the account lost if the stop is hit. With about 4.4% risk and a stop 5% below the entry, the position would be about 88% of the account. The position size calculator turns a risk percentage into shares.

Related guides

Other calculators

From the calculation to the record

Save the entry, stop and target as a plan before the trade, then log the fills. The journal works out R, expectancy and drawdown from your own trades, and its AI score grades how closely each trade followed the plan. A free account is all it takes.