Quantitative risk tool

Expected Monetary Value (EMV) Calculator

Compare expected costs, residual risk, and the break-even premium for two options with this free EMV and decision tree calculator.

Move the odds. Follow the cost.

Compare two options

Choose a scenario or adjust the costs and probabilities.

Amounts are in USD. Choose a scenario or enter your own values.

Paid on either route. $0 to $1,000,000.
Additional to base cost and premium. $0 to $1,000,000.
Chance of the extra loss, from 0% to 100%.
The risk left after paying the premium, from 0% to 100%.
Paid whether the risk happens or not. $0 to $1,000,000.

Compare the expected costs

Option A · No premium

Expected total cost

base + expected extra loss

Two possible outcomes

  1. · No extra loss
    Total cost:
  2. · Extra loss occurs
    Total cost:

Option B · Pay a premium

Expected total cost

base + premium + expected extra loss

Two possible outcomes

  1. · No extra loss
    Total cost:
  2. · Extra loss occurs
    Total cost:

Break-even premium for Option B

Show the formulas

Expected extra loss = probability / 100 × loss amount.

A = base cost + expected extra loss under A.

B = base cost + upfront premium + expected extra loss under B.

Break-even premium = (A probability − B probability) / 100 × loss amount.

Decision tree check: multiply each outcome's total cost by its probability, then add the two branches. Each route's probabilities add to 100%.

This is a cost comparison, so lower is better. Costs are shown as positive amounts. Each option has one modeled extra-loss event and two mutually exclusive outcomes. Benefits and other costs are assumed equal; costs share one time basis with no discounting. EMV describes an average, not a guaranteed bill or a safety decision.

For the worked example and reasoning, read the related study guide.

How it works

Enter a common base cost, the chance of an extra loss under each option, the loss amount, and Option B's upfront premium. Expected cost equals upfront cost plus probability times extra loss.

Example to try

At a $20,000 base cost, a $40,000 potential loss, and risks of 25% and 5%, Option B's $6,000 premium gives expected costs of $28,000 versus Option A's $30,000.

Read the result

Lower expected cost is preferable under this cost-only, risk-neutral model. The average is not a promised bill. Safety, affordability of the worst outcome, and risk tolerance still matter.