# Risk Calculator

URL: https://speedycalculator.com/calculators/statistics/risk/
Last updated: 2026-10-30

> The risk calculator compares two options by their expected loss: probability of failure multiplied by the loss if failure happens. Enter both options’ failure chances and losses to see each risk, which option is less risky and by how much.

## Inputs

- Option A – probability of failure (%)
- Option A – loss if it fails
- Option B – probability of failure (%)
- Option B – loss if it fails

## Results

- Option A – risk (expected loss)
- Option B – risk (expected loss)
- Lower risk
- Difference in risk (A − B)
- Risk ratio (A ÷ B)
- Option A – chance of no failure
- Option B – chance of no failure

## Formula

```
Risk = Probability of failure × Loss if failure occurs
Loss = Risk ÷ Probability · Probability = Risk ÷ Loss
```

## Explanation

In everyday decision-making and finance, "risk" is often quantified as an expected loss. A project with a 10% chance of failing and a 1,500 loss if it fails carries a risk of 0.10 × 1,500 = 150. This single number lets you compare options with very different profiles – a likely small loss against an unlikely large one.

Enter the probability of failure and the loss for option A and option B. The calculator shows both risks, the difference between them, their ratio and which option is less risky by this measure. Losses can be in any currency or unit (money, hours, units of product); just use the same one for both options.

This simple model looks only at the downside – it ignores the profit you might make if things go well, and it treats a certain small loss the same as an unlikely large one with the same product. For decisions with big potential gains, use the expected value calculator, and for losses you could not survive, consider the worst case as well as the average.

### How to use the Risk Calculator

- **Option A – probability of failure**
- **Option A – loss if it fails**
- **Option B – probability of failure**
- **Option B – loss if it fails**

Results update as you type, and everything is calculated in your browser.

### How it works

Each option’s probability of failure (as a decimal) is multiplied by its loss. The option with the smaller product has the lower expected loss. The ratio shows how many times riskier one option is than the other.

### Worked example

Option A fails with probability 10% and would lose 1,500: risk = 0.10 × 1,500 = 150. Option B fails with probability 4% and would lose 3,000: risk = 0.04 × 3,000 = 120. B has the lower expected loss by 30, and A is 1.25 times as risky – even though B’s worst case is twice as large.

### When expected loss is not the whole story

- Compare the worst cases if a loss would be ruinous.
- Probabilities from small samples are uncertain – try a range.
- Failures may not be independent across options (one economic shock can hit both).

### Inputs explained

FieldWhat to enterOption A – probability of failureIn %Option A – loss if it failsA numberOption B – probability of failureIn %Option B – loss if it failsA number

### What each result means

- **Option A – risk (expected loss)** = [Option A – probability of failure]÷100×[Option A – loss if it fails]
- **Option B – risk (expected loss)** = [Option B – probability of failure]÷100×[Option B – loss if it fails]
- **Difference in risk (A − B)** = [Option A – risk (expected loss)] - [Option B – risk (expected loss)]
- **Risk ratio (A ÷ B)** = [Option A – risk (expected loss)]÷[Option B – risk (expected loss)]
- **Option A – chance of no failure** = 100 - [Option A – probability of failure]
- **Option B – chance of no failure** = 100 - [Option B – probability of failure]

### Example values

How the main result changes when **Option A – probability of failure** changes and everything else stays at the example values above:

Option A – probability of failure (%)Option A – risk (expected loss)5757.5112.51015012.5187.51522520300

## Worked example

Inputs — Option A – probability of failure: 10 %; Option A – loss if it fails: 1,500; Option B – probability of failure: 4 %; Option B – loss if it fails: 3,000.

Results — **Option A – risk (expected loss) = 150**; Option B – risk (expected loss) = 120; Lower risk = Option B; Difference in risk (A − B) = 30; Risk ratio (A ÷ B) = 1.25; Option A – chance of no failure = 90 %; Option B – chance of no failure = 96 %.

## Key terms

- **Risk**: Expected loss, probability of failure × loss.
- **Probability of failure**: The chance that the option fails, between 0% and 100%.
- **Expected loss**: The average loss per decision if the same choice were repeated many times.

## FAQ

**How do you calculate risk?**
Multiply the probability of failure by the loss. A 12% chance of losing 1,000 is a risk of 120.

**How do I find the loss from the risk?**
Divide the risk by the probability: a risk of 150 at 10% corresponds to a loss of 1,500.

**How do I find the probability from the risk?**
Divide the risk by the loss: a risk of 120 on a 3,000 loss means a 4% failure probability.

**Which option should I choose?**
By this measure, the one with the lower expected loss – here option B (120) rather than A (150). Also check whether you could afford B’s larger worst-case loss.

**Does this include potential profits?**
No. It measures the downside only. Use expected value to weigh gains and losses together.

**Is this the same as risk in a risk matrix?**
Very similar: a risk matrix multiplies likelihood by impact, usually on 1–5 scales instead of actual probabilities and amounts.


## Sources

- [OpenStax – Introductory Statistics 2e](https://openstax.org/details/books/introductory-statistics-2e)
- [Khan Academy – Statistics and probability](https://www.khanacademy.org/math/statistics-probability)