Kelly Allocation CalculatorFree online financial calculator — instant results, no sign-up
Calculate the nonnegative Kelly stake for a binary payoff with stated net win odds.
Estimates only, based on the inputs and assumptions shown. This is not financial, investment, tax, or legal advice. Prices, rates and local rules may change; crypto scenarios do not predict returns. Confirm important decisions with a qualified professional.
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About the Kelly Allocation Calculator
The Kelly Allocation Calculator estimates the nonnegative share of your bankroll to risk on a binary outcome using your win probability and stated net profit per dollar risked on a win. It reports both full Kelly and a chosen fraction of full Kelly, assuming a losing outcome forfeits the entire stake. With the default inputs, full Kelly is 10% and fractional Kelly is 5%.
- Win probability (%)
- Your estimated chance of the winning outcome, expressed as a percentage from 0% to 100%, with a default of 55%.
- Net profit per dollar risked on a win (ratio)
- The positive ratio of net profit to stake on a win, excluding the returned stake, with a default of 1 meaning $1 profit per $1 risked.
- Fraction of full Kelly (%)
- The percentage of the full Kelly stake you choose to use, with a default of 50% meaning half Kelly.
Formula and method
p = P / 100; c = C / 100; f = max(0, (b × p − (1 − p)) / b); A_full = 100 × f; A_fractional = 100 × c × f.
- PWin probability entered as a percentage.
- pWin probability converted to a decimal; 1 − p is the loss probability.
- bPositive net profit per dollar risked on a win.
- CSelected fraction of full Kelly entered as a percentage.
- cSelected fraction of full Kelly converted to a decimal.
- fFull Kelly bankroll fraction after replacing any negative result with zero.
- A_fullFull Kelly allocation expressed as a percentage of bankroll.
- A_fractionalFractional Kelly allocation expressed as a percentage of bankroll.
Convert the win probability and selected Kelly fraction from percentages to decimals. Multiply the win probability by the net win ratio, subtract the loss probability, and divide by the net win ratio. Set a negative result to zero, then multiply by the selected Kelly fraction to obtain fractional Kelly. With the defaults, p = 0.55, b = 1, and c = 0.50: f = max(0, (1 × 0.55 − 0.45) / 1) = 0.10. Full Kelly allocation is therefore 10%, and fractional Kelly allocation is 100 × 0.50 × 0.10 = 5%.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Win probability55 %
- Net profit per dollar risked on a win1 ratio
- Fraction of full Kelly50 %
Results
- Full Kelly allocation10%
- Fractional Kelly allocation5%
How to use the Kelly Allocation Calculator
- 1Enter your estimated win probability in Win probability (%); the default is 55%.
- 2Enter the net profit per dollar risked on a win, excluding the returned stake; the default ratio is 1.
- 3Choose Fraction of full Kelly (%); the default of 50% applies half of the full Kelly stake.
- 4Read the Full Kelly allocation output, which is 10% with the default inputs.
- 5Read the Fractional Kelly allocation output, which is 5% with the default inputs, and assess it against your bankroll and risk limits before acting.
Reading your result
Full Kelly allocation is the nonnegative percentage of bankroll that maximizes expected logarithmic wealth growth under the binary-payoff model; the default output of 10% means risking one-tenth of bankroll. Fractional Kelly allocation scales that stake by your selected percentage; the default output of 5% means risking 5% of bankroll, not expecting a 5% return. A zero allocation means the stated probability and payoff do not provide a positive edge for this bet direction.
Limitations
The model assumes exactly two outcomes: a win earns the stated net profit and returns the stake, while a loss forfeits the entire stake. Win probability must be between 0% and 100%, and the net win ratio must be positive. A conventional fractional Kelly setting is between 0% and 100%; values above 100% would amplify rather than reduce full Kelly. Results depend heavily on accurate probabilities and payoffs and do not separately account for fees, taxes, changing odds, liquidity, or correlations with other positions. Kelly targets long-run logarithmic growth, not guaranteed profit or protection against large drawdowns. Fractional Kelly reduces exposure but does not eliminate risk. This is an educational allocation estimate, not personalized investment advice.
Common questions
Does a net win ratio of 1 include the return of my stake?+
No. A ratio of 1 means the win produces net profit equal to the amount risked, in addition to returning the stake. Entering total proceeds instead of net profit would overstate the payoff and the Kelly allocation.
Why do the default inputs produce 10% full Kelly and 5% fractional Kelly?+
With a 55% win probability and a net win ratio of 1, the loss probability is 45%, so full Kelly is (0.55 − 0.45) / 1 = 0.10, or 10%. Selecting 50% of full Kelly halves that allocation to 5%.
When does this calculator return a zero stake?+
Full Kelly is zero when b × p is less than or equal to 1 − p, equivalently when p is less than or equal to 1 / (b + 1). Negative Kelly results are set to zero rather than treated as instructions to take the opposite side. Fractional Kelly is also zero if you select 0% of full Kelly.
Can I use this Kelly allocation for an investment with partial losses or variable gains?+
Not directly. This formula assumes a fixed net gain on a win and loss of the entire stake on a loss. Investments with partial losses, multiple outcomes, or variable returns require a model that represents those payoffs.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.