Kelly Criterion Calculator for Trading: Half Kelly & Growth

A Kelly criterion calculator for trading takes your win rate and your average win and loss, and returns the share of the account to risk on each trade. The formula is f* = W − (1 − W) ÷ R, where W is the win rate and R is the average win divided by the average loss. With a 45% win rate, a $300 average win and a $200 average loss, R = 1.5 and f* = 0.45 − 0.55 ÷ 1.5 = 8.33%. Half Kelly is 4.17%.

You will also see it written as f* = p − q ÷ b, with p the probability of winning, q = 1 − p and b the payoff ratio. Same formula. It maximises the long-run growth rate of the account, and the growth table further down shows what you give up by betting less and what you lose by betting more.

Why Kelly for trading differs from Kelly for betting

In a bet, the stake is what you lose. In a trade with a stop-loss, you lose only the distance to the stop. So Kelly's f is the fraction of the account at risk. The amount invested is a different and usually much larger number, and getting from one to the other is a second step:

1. Account $25,000, half Kelly 4.17%: risk $1,041.67 on the trade.
2. Entry $50, stop $47.50: $2.50 of risk per share.
3. $1,041.67 ÷ $2.50 = 416 shares (rounded down), a $20,800 position. The amount at risk is $1,040.

The position is 83.2% of the account while only 4.17% is at risk. The position size calculator does this conversion for shares, and the same logic gives forex lots from a pip stop.

Kelly formula lookup table by win rate and win/loss ratio

Full Kelly, as the percentage of the account to risk. A dash means there is no edge and the Kelly fraction is negative.

Most of these figures sit far above the 1% to 2% per trade that many traders use as a rule of thumb. That gap tells you how aggressive full Kelly is, and how often a real edge gets overstated.

Full vs half Kelly in the growth table

The table under the inputs is what makes the calculator an analytic Kelly criterion simulator. For each fraction f it computes the expected log growth per trade, g(f) = p·ln(1 + b·f) + q·ln(1 − f), and shows it as growth over 100 trades, e^(100·g) − 1. That is the typical result if wins and losses arrive in the proportions you entered. For the 45% / 1.5 example:

Half Kelly and 1.5× Kelly grow at almost the same rate, and 1.5× takes three times the risk per trade to do it. At 2× Kelly the edge is almost exactly cancelled. Beyond that, growth turns negative even though every single trade still has positive expectancy. With a bigger edge, 2× is already negative: at a 55% win rate and R = 2, risking 65% per trade gives −76.1% per 100 trades. Any fraction of 100% or more is ruin, because one loss takes the whole account.

Why half Kelly is the standard

Two reasons, and both can be measured. First, drawdowns. In the standard continuous-time approximation, the chance that the account ever falls to half its starting value is 50% at full Kelly, 12.5% at half Kelly and 0.78% at quarter Kelly.

Second, your inputs are estimates. Say you measured 45% but your true win rate is 42%. Full Kelly (8.33%) now shrinks the account by 9.5% per 100 trades, while half Kelly (4.17%) still grows it by 8.1%. If the true rate is 40% there is no edge at all: full Kelly loses 39.9% per 100 trades and half Kelly 12.1%. Underbetting costs you a little. Overbetting costs you a lot.

How many trades before you trust the number

The uncertainty in a measured win rate is about √(W(1 − W) ÷ n). At a 45% win rate, the 95% range is ±13.8 percentage points after 50 trades, ±9.8 after 100, ±4.4 after 500 and ±3.1 after 1,000. With R = 1.5, a five-point error is the difference between an 8.33% Kelly and no Kelly at all. The average win and loss carry their own error, and one outsized win can inflate R for months.

Negative Kelly

A 35% win rate with R = 1.5 gives f* = −8.33%. Expectancy is −0.125R, so on average you lose an eighth of your risk unit per trade. The break-even win rate for any payoff ratio is 1 ÷ (1 + R), which here is 40%. A negative result says the correct size is zero. It does not say take the other side. The risk/reward calculator shows the break-even win rate for a planned setup.

Kelly and leverage

For a strategy with continuous returns, the Kelly leverage is (μ − r) ÷ σ², the excess return divided by the variance. An asset expected to beat cash by 6% a year with 18% volatility has a Kelly leverage of 1.85×. Half Kelly is about 0.93×, which is barely leveraged at all. The margin and leverage calculator shows the liquidation price for whatever leverage you pick.

How to use this calculator

1. Choose Average win & loss or Win / loss ratio.
2. Enter your win rate as a percentage, or drag the slider.
3. Enter your average win and average loss, in dollars or in R but in the same unit for both. The calculator shows the ratio b it derives. In ratio mode, type b directly.
4. Read off full, half and quarter Kelly as risk per trade, plus the expectancy in R.
5. Use the growth table to compare 0.25×, 0.5×, 1×, 1.5× and 2× Kelly. Rows at 100% risk or more show as ruin.

The output is arithmetic on your inputs. It is not a recommendation to take any trade or to use any size.

Common mistakes and limits

• Using the Kelly percentage as the position size. It is the amount you lose if the stop is hit.
• Treating open trades as independent. Kelly assumes one bet at a time, and three perfectly correlated positions at 4% risk each behave like one 12% bet.
• Assuming stops fill exactly. Gaps and slippage make some losses bigger than planned, which raises the average loss and lowers R.
• Feeding in backtest results. Live win rates and payoffs are almost always worse. Size from live or forward-tested results.
• Averages hide the distribution. The formula treats every win as the same size and every loss as the same size. Real outcomes vary, so the result is an approximation.