Kelly Criterion Calculator
Estimate full and fractional Kelly bet size from win rate and payoff ratio.
Kelly bet size
Live tool- ⚠ Full Kelly above 25% of capital can create severe drawdowns and is highly sensitive to bad assumptions.
Win rate and payoff ratio must come from a meaningful sample of trades, not a few results. This binary win/loss Kelly approximation uses averaged wins and losses, which can overstate the true optimal fraction when trade outcomes vary widely.
How it works
The Kelly Criterion turns two things you can measure from a trading record — how often you win, and how big your average win is compared to your average loss — into a suggested percent of capital to risk. Enter your win rate as a percent-number (55 means 55%), your payoff ratio (a ratio of 1.5 means the average win is 1.5 times the average loss), and your account capital.
Full Kelly is the raw formula output. Because it is famously aggressive and very sensitive to input errors, this calculator also shows fractional Kelly (the full result scaled down by your Kelly fraction — 0.5 is “half Kelly”) and a capped result that never exceeds your maximum risk cap. If the inputs imply no positive mathematical edge, every suggested risk figure is clamped to zero — the formula never suggests risking money on a losing system.
The formula
- winRateDecimal = winRate ÷ 100
- lossProbability = 1 − winRateDecimal
- rawFullKellyDecimal = winRateDecimal − (lossProbability ÷ payoffRatio)
- fullKellyDecimal = max(0, rawFullKellyDecimal)
- fullKellyPct = fullKellyDecimal × 100
- fractionalKellyPct = fullKellyPct × kellyFraction
- fullKellyDollarRisk = capital × fullKellyDecimal
- fractionalKellyDollarRisk = capital × (fractionalKellyPct ÷ 100)
- cappedRiskPct = min(fractionalKellyPct, maxRiskCapPct) — or fractionalKellyPct if no cap is set
- cappedDollarRisk = capital × (cappedRiskPct ÷ 100)
Symbols: winRate = percent of trades that win; payoffRatio = average win divided by average loss; kellyFraction = conservative multiplier applied to full Kelly; capital = total account capital. If the system has no positive mathematical edge, Kelly risk is clamped to zero before any cap is applied.
Worked example
Inputs: winRate = 55; payoffRatio = 1.5; kellyFraction = 0.5; capital = $25,000; maxRiskCapPct = 2.
- winRateDecimal = 55 ÷ 100 = 0.55
- lossProbability = 1 − 0.55 = 0.45
- fullKellyDecimal = 0.55 − (0.45 ÷ 1.5) = 0.55 − 0.30 = 0.25
- fullKellyPct = 0.25 × 100 = 25.00%
- fractionalKellyPct = 25.00% × 0.5 = 12.50%
- fullKellyDollarRisk = $25,000 × 0.25 = $6,250.00
- fractionalKellyDollarRisk = $25,000 × 0.125 = $3,125.00
- cappedRiskPct = min(12.50%, 2.00%) = 2.00%
- cappedDollarRisk = $25,000 × 0.02 = $500.00
Negative-edge clamp example: winRate = 40; payoffRatio = 1.0; kellyFraction = 0.5; capital = $25,000; maxRiskCapPct = 2.
- winRateDecimal = 40 ÷ 100 = 0.40
- lossProbability = 1 − 0.40 = 0.60
- rawFullKellyDecimal = 0.40 − (0.60 ÷ 1.0) = −0.20
- fullKellyDecimal = max(0, −0.20) = 0
- fullKellyPct = 0 × 100 = 0.00%
- fractionalKellyPct = 0.00% × 0.5 = 0.00%
- cappedRiskPct = min(0.00%, 2.00%) = 0.00%
- cappedDollarRisk = $25,000 × 0 = $0.00
- emitted riskPct = 0
FAQ
What is the Kelly Criterion?
The Kelly Criterion is a formula for estimating position size from win probability and payoff ratio.
What is half Kelly?
Half Kelly uses 50% of the full Kelly result to reduce volatility and protect against overconfident assumptions.
Can Kelly be negative?
Yes. A negative Kelly result means the entered win rate and payoff ratio do not show a positive mathematical edge.
Should traders use full Kelly?
Full Kelly can be aggressive and highly volatile. Many traders study fractional Kelly for educational risk management.
Does this calculator prove a trading system works?
No. It only calculates sizing from the inputs. The quality of the result depends on whether the win rate and payoff ratio are reliable.
Continue your analysis
Educational disclaimer
Kelly sizing is assumption-sensitive and can recommend dangerously large risk when the win rate or payoff ratio is overestimated. Win rate and payoff ratio must come from a meaningful sample of trades, not a few results, and this binary approximation can overstate the true optimal fraction when trade outcomes vary widely. This calculator is educational only — it is not financial advice and not a recommendation to risk the calculated amount.