Full Kelly The formula’s raw result
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- Dollar risk
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- Position Notional Total market exposure
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- vs. account balance
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A cash account with no leverage can’t hold this theoretical position.
EDUCATIONAL CALCULATOR
Kelly Criterion Calculator
The Kelly Criterion is a formula that uses your win rate and payoff ratio to calculate how much of your account one trade puts at risk.
Kelly fraction is a theoretical account-risk fraction, not a recommendation. It’s the share of your account you’d lose if the stop is hit — not how much money to put in.
STEP 1 · Your assumptions
Trade setup
Enter the assumptions for a single trade. Example values are filled in to start.
Example values show how the calculator works. They are not a recommendation.
STEP 3 · Understand the results
Kelly results
Inputs changed. Recalculate to update the results.
Nothing calculated yet
Review your inputs,
then press Calculate.
You’ll see Full, Half, and Quarter Kelly,
plus how many dollars each one puts at risk.
A Kelly fraction is a formula result, not a recommended allocation.
With this win rate and payoff ratio, the Kelly formula doesn’t produce a positive risk fraction.
Half Kelly ½ of Full
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- Dollar risk
- —
- Position Notional Total market exposure
- —
- vs. account balance
- —
A cash account with no leverage can’t hold this theoretical position.
Quarter Kelly ¼ of Full
——
- Dollar risk
- —
- Position Notional Total market exposure
- —
- vs. account balance
- —
A cash account with no leverage can’t hold this theoretical position.
Here, a Kelly fraction means “what share of the whole account is lost if one trade hits its stop.” Position notional is that dollar risk divided by the cost-adjusted stop distance. Leverage, maintenance margin, liquidation, price gaps, and changing slippage aren’t modeled. It’s a theoretical estimate, not a trade size to use.
Reading the numbers
What these results mean
These are educational results based on your assumptions. They don’t rate a strategy or an investment.
Advanced results · How it’s calculated Cost-adjusted values · Raw Kelly
One trade after costs
- Round-trip cost
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- Net profit per win
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- Net loss per loss
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- Payoff ratio (net win ÷ net loss)
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- Break-even win rate
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- Your win rate − break-even
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Kelly formula steps
- p (win rate)
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- q = 1 − p
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- b = net win ÷ net loss
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- Raw Kelly = p − q ÷ b
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- Shown Full Kelly = max(0, raw)
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The break-even win rate is where expected profit is zero after costs. When raw Kelly is zero or negative, all three levels show 0%. A negative raw value is just the formula’s output — it doesn’t mean you should short or take the other side.
Next step
See what happens to the account when the same win rate and payoff repeat 500 times.
Kelly describes one trade. The simulator runs 5,000 virtual accounts to show how much the balance can swing over hundreds of trades.
Already have a risk budget? Size the trade from your stop-lossKelly guide
What to know before you read a Kelly number
Eight short explainers to help you interpret the results.
What is the Kelly Criterion?
The Kelly Criterion comes from a 1956 paper by John L. Kelly Jr. at Bell Labs. If you know your odds of winning and the size of each win and loss, and the same bet repeats independently, it finds the fraction that maximizes long-run growth of your bankroll (on a log scale).
This calculator uses p − q ÷ b, where p is your win rate, q = 1 − p, and b is the payoff ratio after costs. The result is shown as a risk fraction: the share of the account lost if one trade hits its stop.
What is Full Kelly?
Full Kelly is the formula’s answer, used as-is. Under ideal conditions — your inputs are exactly right and trading goes on indefinitely — it’s the level with the highest long-run growth rate.
It also comes with big swings. Deep drawdowns are common even in theory, and if your true win rate is even a little lower than you entered, growth falls off quickly.
Half Kelly and Quarter Kelly
Half Kelly uses ½ of the Full Kelly value, and Quarter Kelly uses ¼. In the standard continuous approximation, Half Kelly keeps about 75% of Full Kelly’s growth rate while cutting volatility roughly in half.
Traders often compare fractional Kelly because win rates and payoffs are easy to overestimate. This calculator shows all three side by side; it doesn’t tell you which one to use.
Does a higher win rate mean a higher Kelly?
Not on its own. A 90% win rate with +1% wins and −10% losses has a payoff ratio of 0.1, so Kelly is 0.9 − 0.1 ÷ 0.1 = −0.1. The calculator shows that as 0%.
Kelly depends on win rate and payoff together. Looking only at how often you win hides how much one loss can cost.
Why the payoff ratio matters
At a 50% win rate, a payoff ratio of 1 gives Kelly = 0.5 − 0.5 ÷ 1 = 0%, while a ratio of 2 gives 0.5 − 0.5 ÷ 2 = 25%. The bigger your wins relative to your losses, the higher Kelly goes at the same win rate.
A lower payoff ratio also raises the break-even win rate. Comparing your win rate to break-even shows why Kelly comes out where it does.
How fees and slippage change Kelly
Round-trip costs shrink wins and deepen losses. With the example inputs (3% profit, 2% loss, 55% win rate) and no costs, the payoff ratio is 1.5, Full Kelly is 25%, and break-even is 40%. Add a 0.05% fee and 0.02% slippage per side, and those become about 1.34, 21.3%, and 42.8%.
Costs matter more when your profit target is small. If a win doesn’t cover the round-trip cost, Kelly can’t be calculated at all.
Kelly fraction vs. position size
The original Kelly bet assumes you lose the whole stake. A trade usually loses only part of the position at the stop, so this calculator treats Kelly as the share of the account at risk and then works out position size as dollar risk ÷ cost-adjusted stop distance.
Risk 21.3% of the account with a 2.14% cost-adjusted stop, and the theoretical position is about 9.97x the account. Tighter stops push that number higher. It’s not a size you can necessarily hold, and it’s not a recommendation.
Calculator limitations
It assumes every trade has the same win rate and payoff and is independent of the others. In practice you never know your true win rate, it changes with market conditions, and estimates from past trades carry error.
Price gaps through your stop, changing slippage, leverage, maintenance margin, liquidation, correlated positions held at the same time, and taxes aren’t included. Results are educational and don’t guarantee any investment outcome.
FAQ
Kelly Criterion FAQ
What is the Kelly Criterion?
It’s a formula for the fraction of capital that maximizes long-run growth when you know your odds and payoffs and the same bet repeats. Here it’s p − q ÷ b: win rate, loss rate (1 − p), and the cost-adjusted payoff ratio.
Is the Kelly % how much money I should invest?
No. In this calculator, Kelly % is the share of your account you’d lose if the trade hits its stop. The position size is dollar risk ÷ stop distance, which can be much larger — it’s shown separately as position notional.
What does a negative Kelly mean?
Your win rate is at or below the break-even win rate after costs, so the formula gives zero or less. There’s no positive risk fraction, and all three levels show 0%. You can see the raw value under “Advanced results.”
What is Half Kelly?
It’s half of the Full Kelly value. Theoretical growth is a bit lower, but volatility drops sharply, which is why it’s often compared when your inputs might be off. Quarter Kelly is one quarter of Full.
Should I include fees?
The calculator is built to include them. Fees and slippage lower your net win, raise your net loss, and reduce the payoff ratio and Kelly together. Setting them to zero makes Kelly look larger than it would be in practice.
Can I use it for stocks and crypto?
Yes. It works with percentage moves and doesn’t assume an asset type. Taxes, tick sizes, trading hours, and exchange liquidation rules aren’t included.
Does it account for leverage?
No. If the theoretical position is larger than your account, the calculator notes that a cash account can’t hold it — it doesn’t assume or suggest leverage. Leverage adds maintenance margin and liquidation risk that aren’t modeled here.
Does it predict real trading results?
No. It shows the Kelly formula’s output assuming your win rate and payoffs are exact and constant. It doesn’t check those assumptions against real markets or recommend any investment.
Before you rely on it
What this calculator doesn’t capture
An educational calculator that explains the Kelly formula.
It doesn’t guarantee any investment result.
Win rate, profit, and loss are the same on every trade and independent. Costs are applied round trip on the position value. A Kelly fraction is an assumption-based calculation, not investment advice.