Kelly Criterion Position Size Calculator
Estimate how much of your bankroll to risk when you believe you have an edge.
Educational tool only. Not financial advice.
What is the Kelly formula?
The Kelly formula (also called the Kelly criterion) is a position sizing method used in betting, trading, and investing. Instead of asking “Is this a good bet?”, Kelly asks a more practical question: “How much should I risk?” If your edge is real, Kelly helps you maximize long-term growth while limiting the chance of overbetting.
A Kelly formula calculator is especially useful when you already have a probability estimate and market odds. It converts those assumptions into a suggested bankroll percentage, helping you stay consistent and disciplined.
Kelly criterion formula (core equation)
Standard form
f* = (b × p - q) / b
- f*: optimal fraction of bankroll to risk
- b: net odds received (decimal odds - 1)
- p: probability of winning
- q: probability of losing = 1 - p
If f* is negative, the formula indicates no bet. If positive, it gives the full Kelly stake size.
Quick example
Suppose you estimate a 55% chance to win and are offered decimal odds of 2.00 (even money).
Then b = 1.00, p = 0.55, q = 0.45, and full Kelly is:
f* = (1.00 × 0.55 - 0.45) / 1.00 = 0.10 = 10%
On a $10,000 bankroll, full Kelly suggests $1,000. Half-Kelly would be $500.
How to use this Kelly formula calculator
- Enter your current bankroll.
- Estimate your win probability as a percentage.
- Enter decimal odds from your market.
- Choose a Kelly fraction (many people use 25% to 50% of full Kelly).
- Optionally set a max stake cap for extra risk control.
The calculator returns your recommended stake amount, stake percent, full Kelly value, and a plain-language interpretation.
Why many people use fractional Kelly
Estimation error is real
The biggest risk in Kelly sizing is not math error; it is input error. If your probability estimate is too optimistic, full Kelly can be too aggressive.
Fractional Kelly lowers volatility
Half-Kelly or quarter-Kelly generally reduces drawdowns and emotional stress. You may sacrifice some theoretical growth, but many investors and bettors find the tradeoff worth it.
- Full Kelly: highest theoretical long-run growth, highest volatility
- Half Kelly: common “balanced” choice
- Quarter Kelly: conservative and often easier to stick with
Kelly formula for investing and trading
Kelly is not limited to sports betting. It can also be used for position sizing in discretionary trading, quantitative systems, options strategies, and even concentrated investing—provided you can estimate edge and payoff ratio.
Where it can help
- Converting conviction into position size
- Avoiding oversized bets after a winning streak
- Keeping risk consistent during drawdowns
- Comparing opportunities with different odds/payoffs
Where caution is needed
- Correlated bets (Kelly assumes independence in simple form)
- Fat tails and gap risk
- Changing market regimes
- Overconfidence in probability estimates
Common mistakes to avoid
- Using payout odds incorrectly (remember Kelly uses net odds).
- Ignoring fees, spreads, and slippage.
- Betting full Kelly with noisy assumptions.
- Skipping a maximum position cap.
- Increasing risk after losses out of frustration.
Bottom line
A Kelly formula calculator is a practical bankroll management tool for anyone making repeated risk decisions. It combines expected value with position sizing discipline. Use it thoughtfully, apply conservative fractions, and pair it with strong risk management.
If you want consistency over the long run, the key is not just finding good opportunities— it is surviving long enough to benefit from them.