Expected Value Calculator
Enter each possible outcome and its probability, then calculate the expected value (EV). You can use decimal probabilities (0 to 1) or percentages (0 to 100).
Tip: If probabilities do not add to exactly 1 (or 100%), the calculator will normalize them automatically.
What is expected value?
Expected value is the probability-weighted average of all possible outcomes. It tells you the long-run average result if the same uncertain situation happened many times.
In plain language: multiply each outcome by how likely it is, then add everything together.
Why expected value matters
Expected value is one of the most practical tools in decision-making. It helps with:
- Comparing investment choices with different upside/downside profiles
- Evaluating bets, promotions, and lotteries
- Pricing insurance and understanding risk transfer
- Making business decisions under uncertainty
How to use this expected value calculator
1) List outcomes
Each row should represent one possible result. Outcomes can be positive, negative, or zero. For example: +$100, $0, or -$50.
2) Enter probabilities
Pick a format first:
- Decimal mode: probabilities like 0.10, 0.35, 0.55
- Percent mode: probabilities like 10, 35, 55
3) Calculate and interpret
Click Calculate EV to see:
- Expected Value (the average long-run result)
- Variance and Standard Deviation (how spread out outcomes are)
- Probability of gain and probability of loss
Quick examples
Example A: Simple game
You win $20 with 40% probability and lose $10 with 60% probability.
EV = (20 × 0.40) + (-10 × 0.60) = 8 - 6 = $2. Over many rounds, average profit is $2 per play.
Example B: Investment scenario
Possible one-year returns are +15% (30%), +5% (50%), and -8% (20%).
EV = (15 × 0.30) + (5 × 0.50) + (-8 × 0.20) = 4.5 + 2.5 - 1.6 = 5.4%.
Important limitations
Expected value is powerful, but it is not the whole story.
- Risk matters: two choices can have the same EV but very different volatility.
- Time horizon matters: EV describes long-run averages, not short-run certainty.
- Probability quality matters: bad assumptions produce bad outputs.
- Personal context matters: utility and risk tolerance differ by person.
Common mistakes to avoid
- Mixing probability formats (decimals and percentages together)
- Forgetting negative outcomes (costs, losses, penalties)
- Using probabilities that do not represent realistic scenarios
- Confusing a positive EV with guaranteed profit in any single trial
Bottom line
If you want clearer choices under uncertainty, start with expected value. Use this calculator to quantify outcomes, compare alternatives, and make decisions based on math instead of guesswork.