Free certainty equivalent calculator: what a gamble is really worth to you.
List the outcomes and their chances, answer one plain question about your risk attitude, and get the certainty equivalent, the risk premium and your utility curve, with every step of the calculation shown. Nothing leaves your browser.
List what could happen, and how likely each outcome is. Use negative values for losses. If the chances do not add up to 100 percent, they are rebalanced automatically.
How do you feel about risk? Pick the line that sounds like you.
One question sets your risk tolerance. Imagine a coin flip: heads you win an amount X, tails you lose half of X. What is the largest X where you would still take the bet?
R is negative, so the utility curve is convex and the gamble is worth more than its expected value. A larger magnitude means milder risk-seeking, approaching the risk-neutral case.
Risk-neutral utility is a straight line: the certainty equivalent simply equals the expected value, and the risk premium is zero.
This is the certainty equivalent of one gamble under one utility function. To model a whole decision tree, fit a utility function to your own risk profile and run sensitivity analysis, use the full Rational Will.
See the full calculation, step by step
All computation happens in this browser. Your gamble and your risk profile are never uploaded.
From a risky gamble to one sure number.
Expected value ignores how much the downside hurts you. The certainty equivalent puts your risk attitude into the arithmetic, so two people can honestly disagree about what the same gamble is worth.
- Describe the gamble. Each outcome is an amount you could end up with, and a chance in percent. Losses are negative amounts.
- Set your risk attitude. One question calibrates your risk tolerance R, following Howard's classic elicitation: the largest coin-flip bet, win X or lose X/2, that you would still accept. Risk-neutral and risk-seeking attitudes are one click.
- Read the certainty equivalent. The tool converts every outcome to utility, averages them into the expected utility, and inverts the utility function: CE = U-1(EU). The risk premium EV - CE is what the risk itself costs you.
For the theory behind these numbers, the formulas and a worked example by hand, see the certainty equivalent calculation guide in the documentation, and the companion pages on the exponential utility function and the risk premium.
When one gamble is not the whole decision.
This page prices a single gamble under one utility function. Real decisions are trees of gambles, and that is what the desktop software is for.
- Full decision trees with chance and decision nodes, rolled back by certainty equivalent
- Utility functions fitted to your own risk profile, not just a slider
- Exponential, logarithmic and custom utility over money, time or any measure
- Sensitivity analysis: watch the best choice flip as probabilities move
- Value of information: what a forecast is worth before you pay for it
- Reports you can hand to a committee
- Runs offline on Windows, no cloud dependency
For decisions with many objectives on top of risk, uncertainty and time, Rational Will carries the same utility machinery across every criterion at once.
Certainty equivalents, risk premium and risk tolerance.
What is a certainty equivalent?
The certainty equivalent of a gamble is the guaranteed amount that is worth exactly as much to you as the gamble itself. If a 50/50 chance of winning 1000 or losing 500 has a certainty equivalent of 120 for you, then a sure 120 and that gamble leave you equally well off. It depends on your risk attitude: a risk-averse person's certainty equivalent sits below the expected value, a risk seeker's sits above it.
What is the certainty equivalent formula?
First compute the expected utility EU as the probability-weighted average of U(x) over the outcomes, then invert the utility function: CE = U-1(EU). For exponential utility U(x) = 1 - e-x/R the formula is CE = -R ln(1 - EU), where R is the risk tolerance. For logarithmic (Bernoulli) utility U(x) = ln x it is CE = eEU, which equals the probability-weighted geometric mean of the outcomes. For risk-neutral (linear) utility the certainty equivalent is simply the expected value.
How do I calculate a certainty equivalent step by step?
Four steps: 1) list every outcome with its probability, 2) convert each outcome to utility with your utility function, 3) take the probability-weighted average to get the expected utility, 4) invert the utility function at that expected utility. The result is the certainty equivalent. This calculator shows all four steps with your own numbers, and the documentation walks through a worked example by hand.
What is the risk premium and how is it calculated?
The risk premium is RP = EV - CE, the expected value minus the certainty equivalent. It is the amount of expected value you are willing to give up to escape the risk. A positive risk premium means you are risk-averse for this gamble; zero means risk-neutral; negative means risk-seeking, that is, the gamble is worth more to you than its average. This calculator reports the risk premium alongside the certainty equivalent.
What is risk tolerance R and how do I find mine?
In exponential utility, the risk tolerance R controls how strongly losses bite: a larger R means less risk-averse, and a very large R approaches risk neutrality. A classic way to estimate it, due to Ronald Howard: find the largest X for which you would accept a coin flip that wins X or loses X/2. Your R is approximately that X (precisely X divided by 0.9624). This calculator asks exactly that question and sets R from your answer.
Is this certainty equivalent calculator free?
Yes. It runs entirely in your browser, with no account, no sign-up, no usage limit and nothing sent to a server. For a full decision tree with utility functions fitted to your own risk profile, sensitivity analysis and reports, that is what the SpiceLogic decision analysis software is for.