Kelly Criterion Calculator
Most traders size positions by gut feeling or fixed percentages. The Kelly Criterion calculates the mathematically optimal position size to maximize long-term growth — but full Kelly is risky. This calculator shows optimal Kelly position size, fractional Kelly recommendations (safer), expected growth rate, and risk of ruin so you can balance growth with safety.
Works for all trading strategies. Calculates full Kelly, fractional Kelly (half/quarter), expected growth rate, and risk of ruin. Essential for position sizing optimization.
Your historical win rate percentage
Average win amount / Average loss amount (e.g., 2:1)
Total account capital
Fractional Kelly reduces risk while maintaining most growth benefits
Kelly Criterion Results
Full Kelly Position Size
$2500.00
Position Size Comparison
Compare position sizes across different Kelly fractions and fixed sizing strategies.
Expected Growth Rate Comparison
Compare expected growth rates across different position sizing strategies.
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Calculation Methodology
The Kelly Criterion calculates the optimal position size to maximize long-term growth while balancing risk. It's based on the mathematical formula developed by John L. Kelly Jr. in 1956:
Key Insight: Full Kelly maximizes growth but has high risk of ruin (can wipe out your account). Fractional Kelly (half or quarter) reduces risk significantly while maintaining 70-90% of full Kelly's growth. Most professional traders use half or quarter Kelly for this reason. Never use full Kelly unless you can handle complete account loss.
Learn more about position sizing and Kelly Criterion:
Risk management guideExample Scenario
Setup: 50% win rate, 2:1 win/loss ratio, $10,000 account, half Kelly
What this means: With 50% win rate and 2:1 R:R, full Kelly suggests 25% position size ($2,500), but this has 6.25% risk of ruin. Half Kelly uses 12.5% position size ($1,250) with only 0.01% risk of ruin, while maintaining most of the growth benefits. Half Kelly is the sweet spot for most traders.
Note: This assumes fixed win rate and R:R. In reality, these vary, so use fractional Kelly and adjust based on actual performance. Track your real win rate and R:R over 50-100 trades.
Common Mistakes & Warnings
- ⚠Using full Kelly: Full Kelly maximizes growth but has high risk of ruin (10-30%). Even with positive expected value, you can wipe out your account during losing streaks. Always use fractional Kelly (half or quarter) unless you can handle complete account loss.
- ⚠Overestimating win rate or R:R: Most traders overestimate their win rate and R:R. If you think you have 60% win rate but actually have 45%, Kelly will suggest positions that are too large. Track your actual win rate and R:R over 50-100 trades before using Kelly.
- ⚠Using Kelly for single trades: Kelly Criterion is for long-term position sizing across many trades, not individual trades. Use Kelly to determine base position size, then adjust for trade-specific factors (volatility, correlation, market conditions).
- ⚠Ignoring risk of ruin: Even with positive expected value, you can still go broke. Check risk of ruin — if it's >10%, use fractional Kelly or reduce position size. Risk of ruin >20% means you'll likely wipe out your account eventually.
- ⚠Not adjusting for varying edge: Kelly assumes fixed win rate and R:R, but reality varies. Your edge changes with market conditions. During high volatility or drawdowns, reduce position size. During strong trends, you might increase slightly. Use Kelly as a guide, not a rigid rule.
- ⚠Using Kelly with negative expected value: If Kelly suggests 0% or negative, your strategy has negative expected value (losing strategy). Don't trade it. Improve your win rate or R:R first, or find a different strategy.
Example Scenarios
Try these realistic scenarios to understand Kelly Criterion in different trading setups.
Scenario 1: Standard 50% Win Rate, 2:1 Risk/Reward
Common professional setup. Full Kelly suggests 25% position size. Half Kelly (12.5%) is recommended for safety.
Step-by-Step Calculation:
- Full Kelly: (0.5 × 2 - 0.5) / 2 = 0.25 (25%)
- Half Kelly: 0.25 × 0.5 = 0.125 (12.5%)
- Position Size: $10,000 × 0.125 = $1,250
- Expected Growth: 0.5 × ln(1 + 0.125×2) + 0.5 × ln(1 - 0.125) ≈ 0.58%
- Risk of Ruin (Half): ≈ 0.01%
What this means: With 50% win rate and 2:1 R:R, full Kelly suggests 25% position size, but this has 6.25% risk of ruin. Half Kelly uses 12.5% position size with only 0.01% risk of ruin, while maintaining most growth benefits. This is the sweet spot for most traders.
Scenario 2: High Win Rate (60%), Lower R:R (1.5:1)
High win rate strategy. Full Kelly suggests 20% position size. Quarter Kelly (5%) is safer.
Step-by-Step Calculation:
- Full Kelly: (0.6 × 1.5 - 0.4) / 1.5 = 0.333 (33.3%)
- Quarter Kelly: 0.333 × 0.25 = 0.083 (8.3%)
- Position Size: $10,000 × 0.083 = $833
- Expected Growth: 0.6 × ln(1 + 0.083×1.5) + 0.4 × ln(1 - 0.083) ≈ 0.42%
- Risk of Ruin (Quarter): ≈ 0.001%
What this means: With 60% win rate and 1.5:1 R:R, full Kelly suggests 33.3% position size, which is very risky. Quarter Kelly uses 8.3% position size with minimal risk of ruin. High win rate strategies can use larger positions, but still use fractional Kelly for safety.
Scenario 3: Lower Win Rate (40%), Higher R:R (3:1)
Trend-following setup. Full Kelly suggests 20% position size. Half Kelly (10%) balances growth and risk.
Step-by-Step Calculation:
- Full Kelly: (0.4 × 3 - 0.6) / 3 = 0.2 (20%)
- Half Kelly: 0.2 × 0.5 = 0.1 (10%)
- Position Size: $10,000 × 0.1 = $1,000
- Expected Growth: 0.4 × ln(1 + 0.1×3) + 0.6 × ln(1 - 0.1) ≈ 0.52%
- Risk of Ruin (Half): ≈ 0.1%
What this means: With 40% win rate and 3:1 R:R, full Kelly suggests 20% position size. Half Kelly uses 10% position size with low risk of ruin. Lower win rate strategies need higher R:R to be profitable, and Kelly adapts position size accordingly.
Warning: Low win rate strategies (30-40%) work mathematically but are mentally challenging. You'll have many losing streaks (5-7 losses in a row is normal). Can you handle that psychologically? Only use if you have strong discipline.
What If Variations
Explore how changing parameters affects your Kelly position size:
What if I improve win rate from 50% to 60%?
Full Kelly increases from 25% to 33.3% (with 2:1 R:R). Higher win rate = larger optimal position size. However, verify your actual win rate — most traders overestimate. Track your real win rate over 50-100 trades.
What if I improve R:R from 2:1 to 3:1?
Full Kelly increases from 25% to 33.3% (with 50% win rate). Higher R:R = larger optimal position size. Improving R:R is often easier than improving win rate, and it has similar effect on Kelly position size.
What if I use half Kelly instead of full Kelly?
Position size halves, risk of ruin drops dramatically (e.g., 6.25% to 0.01%), but expected growth only drops slightly (e.g., 0.7% to 0.58%). Half Kelly gives you 80-90% of full Kelly's growth with 50% less risk. This is why most traders use fractional Kelly.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that calculates the optimal position size to maximize long-term growth. It balances growth potential with risk of ruin. The formula is: f* = (p × b - q) / b, where p is win rate, q is loss rate (1-p), and b is win/loss ratio. Full Kelly maximizes growth but has high risk of ruin. Most traders use fractional Kelly (half or quarter) for safety.
When should I use Kelly Criterion?
Use Kelly Criterion when you have a consistent trading edge (positive expected value) and want to maximize long-term growth. It works best for: (1) Strategies with stable win rates and R:R ratios, (2) Long-term position sizing (not single trades), (3) When you can handle the volatility. Don't use Kelly if your win rate or R:R varies significantly, or if you can't handle large drawdowns.
What is fractional Kelly?
Fractional Kelly uses a percentage of the full Kelly position size. Half Kelly uses 50% of full Kelly, quarter Kelly uses 25%. Fractional Kelly reduces risk of ruin and drawdowns while still capturing most of the growth benefits. Most professional traders use half or quarter Kelly because full Kelly has high risk of ruin (can wipe out your account during losing streaks).
What is risk of ruin?
Risk of ruin is the probability of losing enough capital to wipe out your account. Full Kelly has higher risk of ruin because it uses larger position sizes. Even with positive expected value, you can still go broke if you hit a bad streak. Fractional Kelly reduces risk of ruin significantly. For example, half Kelly might have 5% risk of ruin vs 25% for full Kelly.
What if Kelly suggests >50% position size?
If Kelly suggests >50% position size, your strategy has very high expected value (high win rate + high R:R). However, this is extremely risky — you're over-leveraged. Consider: (1) Using fractional Kelly (half or quarter), (2) Verifying your win rate and R:R are accurate (most traders overestimate), (3) Reducing position size to 10-20% max. Never risk >50% of account on a single position.
What if Kelly suggests 0% or negative?
If Kelly suggests 0% or negative, your strategy has negative expected value (losing strategy). This means your win rate and R:R don't produce profits. You need to either: (1) Improve your win rate, (2) Improve your R:R ratio, or (3) Accept that this strategy loses money long-term. Don't trade strategies with negative expected value.
How accurate is Kelly Criterion?
Kelly Criterion assumes: (1) Fixed win rate and R:R ratio (reality varies), (2) Infinite time horizon (you can trade forever), (3) No transaction costs (fees reduce growth). In practice, Kelly is a guide, not exact. Your actual win rate and R:R will vary, so use fractional Kelly and adjust based on real performance. Track your actual results and adjust position sizes accordingly.
Should I use Kelly for every trade?
No. Kelly Criterion is for long-term position sizing across many trades, not individual trades. Use Kelly to determine your base position size, then adjust for: (1) Trade-specific factors (volatility, correlation), (2) Market conditions (high volatility = reduce size), (3) Account drawdown (reduce size during drawdowns). Kelly gives you the optimal size for your edge, but you still need to adapt to market conditions.
How does Kelly compare to fixed position sizing?
Fixed position sizing (e.g., always risk 2% per trade) is simpler but suboptimal. Kelly adapts to your edge — if you have high win rate + high R:R, Kelly suggests larger positions. If your edge is weak, Kelly suggests smaller positions. Kelly maximizes growth, but fixed sizing is safer and easier. Most traders use a hybrid: Kelly to determine base size, then cap it at 5-10% max per trade.
What's a good expected growth rate?
Expected growth rate depends on your Kelly fraction and edge. Full Kelly might show 5-10% growth per trade cycle, but has high risk. Half Kelly might show 2-5% growth with lower risk. Quarter Kelly shows 1-3% growth with very low risk. Compare growth rates across different Kelly fractions — if half Kelly gives 80% of full Kelly's growth with 50% less risk, half Kelly is better. Focus on risk-adjusted growth, not just raw growth.
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