About this calculator
This calculator is for education only and does not constitute investment advice. It sizes one long trade from two caps: the risk cap (how much you accept losing) and the Kelly cap (how much edge your past win rate and win/loss ratio imply). The recommended size is the smaller of the two, so neither cap can inflate the trade alone. A win rate estimated from past trades does not guarantee future results. Past returns do not guarantee future results.
Full Kelly is shown for reference and is deliberately not the recommendation. Full Kelly maximizes long-run growth in theory but with swings — including drawdowns of half the account or more — that most traders cannot sit through, and it assumes your win rate and win/loss ratio are exactly right, which they never are. That is why the default here is half Kelly, and why the table shows quarter, half, three-quarter and full Kelly side by side. With leverage, losses can exceed your principal, and a stop-loss order does not guarantee a fill at the stop price: gaps and fast markets can fill you worse.
How to use it
- Enter your account size and the share of it you accept losing on this one trade.
- Enter the entry price and the stop price (below the entry for a long trade); the distance between them is the loss per share.
- Enter your estimated win rate and win/loss ratio, and the fraction of Kelly you want to use — 50% is the usual starting point.
- Read the recommended shares: the smaller of the risk-based size and the Kelly-based size. Round down to whole shares if your broker requires it.
The formula
The risk formula guarantees that a stop-out at exactly the stop price loses exactly the risk amount — no more, no less — before fees, slippage and gaps. The Kelly formula needs p (win rate) and b (average win divided by average loss): if b·p is less than q, the edge is negative, full Kelly is zero or negative, and the calculator recommends zero shares rather than a negative size. Fractional Kelly scales the Kelly stake down: half Kelly roughly halves the volatility for about three quarters of full Kelly’s growth, which is why it is the common compromise. For a short trade the same arithmetic applies with the stop above the entry and the distance measured the same way.
Worked example
Account $100,000, risk 1% ($1,000), entry $50, stop $48: the stop distance is $2 a share, so risk alone allows 500 shares ($25,000). With a 55% win rate and a win/loss ratio of 2, full Kelly is (2×0.55 − 0.45) / 2 = 32.50%; half Kelly is 16.25%, or $16,250 — 325 shares. The recommendation is the smaller figure, 325 shares ($16,250), whose loss if stopped out is $650, inside the $1,000 risk budget. In the table, quarter Kelly gives 162.50 shares and full Kelly 650 shares — more than the risk cap allows, which is exactly why the two caps are combined.
Sources: Risk sizing: shares = account × risk% / (entry − stop). Kelly criterion: f* = (bp − q) / b, where p is win rate, q = 1 − p, and b is the win/loss ratio. Prices and rates are entered by you; no market data is fetched. Last updated: October 2026.
Frequently asked questions
Why take the smaller of the two sizes?
Because each cap guards a different failure. Risk sizing alone lets a confident edge estimate justify a huge trade; Kelly alone lets a tight stop justify a huge trade. The smaller of the two is the size that satisfies both your loss budget and your edge — a trade that breaks either rule is not sized, it is gambled.
Why is full Kelly not the recommendation?
Full Kelly maximizes long-run growth only if your p and b are exactly right and you can tolerate the volatility. In practice estimates are noisy, and full Kelly stakes swing the account violently — drawdowns of 50% or more are normal, not exceptional. Fractional Kelly (half is the usual starting point) trades a little growth for much calmer equity curves.
What if Kelly comes out negative?
Then the strategy has no edge at those estimates: the expected value per trade is negative, and the correct Kelly stake is zero. The calculator recommends zero shares in that case. Fix the strategy or the estimates — do not override a negative Kelly with a risk-sized trade.
Can I lose more than the risk amount?
Yes. The risk amount assumes you are filled exactly at the stop price. Gaps, fast markets and illiquid names can fill you worse, and with leverage, losses can exceed your principal — you can owe more than you put in. The stop distance is a plan, not a guarantee.
What about short trades?
Mirror the inputs: the stop sits above the entry, and the stop distance is stop minus entry. This page validates the long case (stop below entry) so the distance is unambiguous; for a short, swap the two prices in your head and use the same distance — the share arithmetic is identical.
What formula does this position size calculator use?
Risk amount = account × risk%; stop distance = entry − stop; shares by risk = risk amount / stop distance; Kelly f* = (b·p − q) / b, with q = 1 − p; Kelly shares = account × f* × fraction / entry; recommended shares = min(shares by risk, Kelly shares) The risk formula guarantees that a stop-out at exactly the stop price loses exactly the risk amount — no more, no less — before fees, slippage and gaps. The Kelly formula needs p (win rate) and b (average win divided by average loss): if b·p is less than q, the edge is negative, full Kelly is zero or negative, and the calculator recommends zero shares rather than a negative size. Fractional Kelly scales the Kelly stake down: half Kelly roughly halves the volatility for about three quarters of full Kelly’s growth, which is why it is the common compromise. For a short trade the same arithmetic applies with the stop above the entry and the distance measured the same way. The worked example on this page applies the formula step by step with real numbers, so you can verify the result by hand.