Kelly Criterion Calculator — Optimal Position Size
The Kelly formula tells you what percentage of capital to risk per trade for maximum long-term growth. Includes Half-Kelly and Quarter-Kelly variants.
In $ or in R, same unit for both. Win/loss ratio b = 1.50.
Theoretically optimal % of capital to lose if the stop is hit — not the position size. Expectancy: +0.125R per trade. In practice, most traders use a fraction of this.
Keeps about three-quarters of full-Kelly growth at half the risk per trade.
For early-career traders still calibrating their edge.
| Fraction | Risk / trade | Log growth / trade | Per 100 trades | Share of max |
|---|---|---|---|---|
| 0.25× Kelly | 2.08% | 0.227% | +25.5% | 44% |
| 0.5× Kelly | 4.17% | 0.387% | +47.3% | 75% |
| 1× Kelly | 8.33% | 0.515% | +67.3% | 100% |
| 1.5× Kelly | 12.50% | 0.389% | +47.6% | 76% |
| 2× Kelly | 16.67% | 0.014% | +1.4% | 3% |
Growth assumes wins and losses arrive in exactly the proportions entered — the typical path, not a guarantee. At 2× Kelly the edge is roughly cancelled out (+1.4% per 100 trades here); beyond it, growth is negative even though every trade has a positive expectancy.
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What Kelly tells you
The Kelly Criterion answers a deceptively hard question: given a known edge, what % of bankroll should I bet to maximise long-term growth? The answer is f = p − q/b, where p is win rate, q is loss rate, and b is the win/loss ratio.
Why most traders use Half-Kelly
Full Kelly is theoretically optimal but assumes your edge is known with certainty. In real trading, you're estimating edge from a small sample — over-estimation by 2× means you blow up. Half-Kelly captures most of the long-term growth while cutting drawdown volatility roughly in half.
Negative Kelly
If Kelly returns a negative number, it's telling you the trade has negative expected value. Stop taking it. No amount of position sizing turns a losing edge into a winning one.
Kelly answers what fraction maximises long-run growth given an edge you are confident about. Converting a chosen fraction into an actual number of units, with a stop, is the job of the position size calculator.
How to use the Kelly Criterion Calculator
Takes about a minute. No signup, no download, your data stays in your browser.
- 1Open the tool. Scroll up to the Kelly Criterion Calculator above — it loads instantly in your browser, no install needed.
- 2Enter your values. The fields come pre-filled with realistic defaults so you can see how it works — replace them with your own numbers.
- 3Read the result. The output updates instantly. Copy or share it — nothing is uploaded to a server, everything stays on your device.
Frequently asked questions
Common questions about the Kelly Criterion Calculator.
What does the Kelly criterion actually compute?
The fraction of capital that maximises the long-run growth rate, given a probability of winning and the payoff ratio. It is a growth-optimal answer to a mathematical question, not a recommendation — and it assumes you know the probability and the payoff, which in real markets you do not.
Why do people use a fraction of the Kelly figure?
Because the full figure is very aggressive and extremely sensitive to the inputs. Overestimating your edge slightly produces a size that is too large by much more than slightly, and the resulting drawdowns are far deeper than most people will tolerate. Using a fraction trades some theoretical growth for a great deal less volatility.
What happens if the edge is negative?
The formula returns a negative fraction, which means the mathematically correct size is zero — there is no stake that improves long-run growth on a losing proposition. A negative result is the calculation telling you not to take the bet rather than to reverse it.
Is this trading advice?
No. It is arithmetic on the numbers you supply, and its output depends entirely on estimates of probability and payoff that are usually uncertain. Trading and betting carry substantial risk including total loss, and nothing here indicates whether any position is sound.
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