Risk Calculator

What the risk calculator does

This calculator weighs two risky options by their expected cost. For each option you give the chance that something goes wrong and how much you would lose if it did, and it works out the risk of each and tells you which one is the safer bet. It is a tool for decisions where both the odds and the stakes matter.

Risk here is not just how likely a bad outcome is, but how likely it is combined with how bad it would be. Below is how that combination works.

How to use it

1. For option A, enter the probability of failure as a percentage and the loss if failure occurs.
2. For option B, enter the same two figures.
3. Press Calculate for the risk of each option and which is safer, or Reset to clear it.

How risk is worked out

The risk of an option is its chance of failure multiplied by the loss that failure would bring:

Risk = probability of failure × loss if it occurs

This is the expected loss, the average cost you would bear if you faced the same situation many times over. Most of the time nothing goes wrong and the cost is zero, but occasionally it does and the full loss lands. Averaging those outcomes, weighted by how often each happens, gives the risk. It is the same expected value idea that underlies decisions under uncertainty, applied to the downside.

Why both parts matter

The key insight is that neither the probability nor the loss tells the whole story on its own. A very likely failure that costs almost nothing may be a smaller risk than a rare failure that would be ruinous. Multiplying the two is what balances them.

This is why a low-probability, high-consequence event, and a high-probability, low-consequence one, can carry exactly the same risk. It is also why people misjudge risk so often: a dramatic but unlikely danger can feel larger than a dull but frequent one, even when the expected loss is the same or smaller. Putting a number on both parts and combining them cuts through that gut reaction.

Comparing two options

With the risk of each option in hand, the comparison is straightforward: the option with the lower expected loss is the less risky choice. The calculator does this comparison and points to the safer option, or tells you when the two carry equal risk.

It is worth remembering that this compares options on expected loss alone. It does not account for how much a given loss would hurt you specifically, which can matter when one option carries a small chance of a loss you simply could not absorb. For weighing everyday choices where the losses are survivable, though, expected loss is a sound and clarifying way to decide.

A worked example

Suppose option A has a 10 percent chance of failure with a loss of 5,000, and option B has a 40 percent chance of failure with a loss of 1,000.

The risk of A is 0.10 times 5,000 = 500, and the risk of B is 0.40 times 1,000 = 400. So option B is the safer choice, even though it fails four times as often, because each failure costs so much less. This is the sort of result that is easy to get wrong by instinct, since A fails rarely, yet its larger loss makes it the riskier option on average.

Entering your values

Enter each option's probability of failure as a percentage between 0 and 100, and its loss as a non-negative amount. The calculator returns the expected loss for each and names the safer option. Both options are compared on the same footing, so the figures only need to be consistent with each other.

Questions people ask

What does risk mean here?

The expected loss of an option, its chance of failure multiplied by the loss failure would cause. It combines how likely a bad outcome is with how bad it would be.

Why multiply probability by loss?

Because both matter. A rare but severe failure and a frequent but minor one can carry the same risk. Multiplying balances the odds against the stakes.

How does it decide which option is safer?

By comparing the expected loss of each. The option with the lower expected loss is the less risky choice.

Does it account for a loss I could not afford?

No. It compares options on expected loss alone, not on how much a loss would hurt you. A small chance of a loss you could not absorb may deserve extra caution beyond the numbers.

References

A quick note on where the methods here come from. Expected value, the basis of this expected-loss measure of risk, is set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook covering expected value and decision making under uncertainty.

1. NIST/SEMATECH e-Handbook of Statistical Methods (expected value and risk). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (expected value). https://openstax.org/details/books/introductory-statistics-2e