How to use the Kelly criterion calculator
- Enter your win rate as the percentage of trades that finish in profit.
- Enter your payoff ratio, the average win divided by the average loss. A payoff of 2 means your average win is twice your average loss.
- Enter your own risk per trade if you want it plotted against the Kelly levels. It is optional.
You get the full Kelly risk, half and quarter Kelly, the edge per trade in R, the expected growth per trade at each level, and the risk above which growth turns negative. A curve shows growth against risk with full, half and quarter Kelly marked, and a bar list compares how much of the best growth each level keeps. If your numbers have no edge, the calculator says so: Kelly is then zero and the advice is not to bet.
The Kelly criterion formula
Kelly fraction f* = p − q / b
growth per trade g(f) = p × ln(1 + b × f) + q × ln(1 − f)
- p is the win rate as a fraction, and q is 1 − p, the loss rate.
- b is the payoff ratio: average win divided by average loss.
- f is the fraction of the account risked on each trade, meaning the amount lost when the stop is hit.
The first line gives the risk that grows the account fastest in the long run. The second gives the expected natural-log growth per trade at any risk f, which is close to the average compound gain per trade for the sizes shown here. It rises to a peak at f*, falls on either side, and eventually turns negative. The edge in R, p × b − q, is the numerator of the Kelly fraction before dividing by b.
John Kelly of Bell Labs published the idea in 1956 in a paper about information rate in the Bell System Technical Journal. It was later applied to betting and to investing.
Worked example
A trader wins 45% of trades and the average win is twice the average loss. They risk 2% of the account per trade today.
These are the numbers the calculator opens with. The edge is real, 0.35R per trade, but the risk that the formula recommends is large: 17.5% of the account on each trade.
Why full Kelly is too aggressive in practice
The formula is exact for the numbers you give it. The trouble is that you never know those numbers exactly.
Your estimates are noisy. A win rate and a payoff measured over a limited number of trades are estimates, and they carry a margin of error that shrinks only slowly with more trades. The sample size entry explains how many trades you need. Suppose the true win rate in the example is 40% rather than 45%, and nothing else changes. The true Kelly fraction is then 10%, not 17.5%. Risking 17.5% still grows the account, but at 0.46% per trade instead of 2.92%. At a true win rate of 38%, the 17.5% risk shrinks the account by 0.52% per trade, even though the edge is still positive. Half Kelly (8.75%) still grows at 0.45% per trade in that case.
The drawdowns are deep. Kelly maximises growth and pays no attention to the ride. With a 45% win rate, the chance of a run of at least four losses somewhere in 100 trades is above 99%, and a run of at least six is about 73%. At full Kelly four losses in a row cost 53.7% of the account, because 0.825 to the power of four is 0.463. Six cost 68.5%. At half Kelly four losses cost 30.7%, at quarter Kelly 16.4%, and at 2% risk 7.8%. Recovering a 53.7% drawdown needs a gain of 116%, as the drawdown recovery calculator shows.
Too much risk costs more than too little. In the example, betting half of Kelly gives up about a quarter of the growth. Betting twice Kelly (35%) keeps only about 6% of it, and beyond 35.6% the growth is negative: more risk makes the account shrink despite a positive edge. Underestimating your edge costs a little growth. Overestimating it and betting full Kelly can turn a good system into a losing one.
Real trades are not the model. Kelly assumes independent trades of the same size, with a known loss on each. Real trades can overlap and correlate, stops can slip, and the payoff and win rate drift as markets change. The risk of ruin calculator simulates what a given risk does to your chances of a deep drawdown.
Why traders use half or quarter Kelly
Fractional Kelly gives up some growth in exchange for a much smoother ride. In the example, half Kelly keeps 76% of the best growth at half the risk, and quarter Kelly keeps 45% at a quarter of it. The drawdowns shrink faster than the growth does.
Fractional Kelly also builds in a margin for error. If your edge turns out smaller than you measured, a half-Kelly bet is still well inside the zone where growth is positive. In the 40% win rate case above, half Kelly would be 8.75% against a true Kelly of 10%, comfortably below it.
Many traders go further and risk a small fixed percentage of the account, often well below what even quarter Kelly allows. Use Kelly as a ceiling and a way to understand the trade-off, not as a number to bet. If your chosen risk is far below the Kelly line, that is by design: you are buying safety with growth.
Common Kelly criterion mistakes
- Betting full Kelly. It assumes you know your edge exactly. You do not.
- Using the planned payoff. Use the average win and loss your trades actually delivered, after costs, not the target you hoped for.
- Using a win rate from a few trades. Ten or twenty trades say very little about a true win rate.
- Reading f as a position size. It is the share of the account lost if the stop is hit, so the position size comes from the stop distance. The position size calculator does that step.
- Applying it to every trade at once. If you hold several trades at the same time, the total risk matters, and correlated positions behave like one large trade.
- Ignoring a negative Kelly. When the Kelly fraction is zero or less, there is no edge to bet on at any size.
What the calculator does not know
The calculator assumes every trade has the same win probability, risks the same fraction of the account and either loses that fraction or wins the payoff multiple of it. It does not know your costs, slippage, gaps, correlated positions, changing market conditions or how your win rate and payoff vary by setup. It takes your numbers as exact, which they are not. The growth shown is an expected value per trade, not a result you will see over any particular stretch, and the account can fall deeply even at a good Kelly fraction. Use the result as a ceiling to stay well under, and check your inputs with the expectancy calculator. Nothing here is investment advice.
Frequently asked questions
What is the Kelly criterion in trading?
It is a formula for the fraction of your account to risk on each trade so that the account grows as fast as possible in the long run. With a win rate p, a loss rate q and a payoff ratio b, the fraction is p − q ÷ b. It only applies when you have an edge.
How do you calculate the Kelly criterion?
Subtract the loss rate divided by the payoff ratio from the win rate. With a 45% win rate and a payoff of 2, that is 0.45 − 0.55 ÷ 2 = 0.175, or 17.5% of the account risked per trade. The calculator also gives half and quarter Kelly.
What is half Kelly?
Half Kelly is half the Kelly fraction. In the example it is 8.75% instead of 17.5%. It keeps about 76% of the best growth with half the risk and much shallower drawdowns, which is why many traders prefer it.
Is the Kelly criterion safe to use?
Not at full size. It assumes your win rate and payoff are known exactly and that trades are independent. Errors in either, losing streaks and slippage can turn a full-Kelly bet into a deep drawdown. Fractions of Kelly, and often much smaller fixed risks, are safer.
What if my Kelly fraction is negative?
A negative or zero fraction means your numbers have no edge: the average trade loses or breaks even. Kelly then says to risk nothing. No risk size grows the account, so improve the edge before sizing anything.
What win rate and payoff should I use?
Use the averages from your real trades for one setup or strategy, after costs, over as many trades as you can. Do not use your plan or your best months. A journal gives you these figures by setup and symbol.
How is Kelly different from risking 1% per trade?
A fixed 1% is a rule you choose for safety, with no regard for your edge. Kelly links the risk to the edge: a bigger edge allows more, no edge allows none. With a 45% win rate and a payoff of 2, 1% is about 6% of full Kelly, a very conservative level.
Why does growth turn negative above about twice Kelly?
Because growth compounds, a loss of x% needs a gain bigger than x% to repair. Past roughly twice the Kelly fraction, the repair needed after the losses outweighs the gains from the wins, so the account shrinks on average even with a positive edge. In the example this happens at 35.6%.
How many trades do I need before trusting my Kelly number?
More than most people have. A hundred trades give only a rough estimate of the win rate, and the Kelly fraction can move a lot with a few points of difference. Treat the number as a ceiling and update it as your sample grows.