Expected Risk Calculator

Quantify uncertainty with probabilities, impacts, and weighted outcomes. Review variance, deviation, and exposure quickly today. Turn scenario data into clearer statistical risk insights fast.

Calculator Inputs

Positive impact values represent losses. Negative values can represent gains, offsets, or recoveries.

Reset
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5

Example Data Table

This example uses percentage inputs. It demonstrates how different scenarios contribute to the overall expected risk.

Scenario Probability (%) Impact / Loss Expected Contribution
Routine operations 45 2,000 900
Minor disruption 25 8,000 2,000
Supplier delay 15 18,000 2,700
Major outage 10 45,000 4,500
Unexpected recovery 5 -6,000 -300
Total 100 — 9,800

Formula Used

Expected Risk
ER = Σ (pi × xi)
Variance
Var(X) = Σ [pi × (xi − ER)2]
Standard Deviation
SD = √Var(X)
Expected Adverse Loss
EAL = Σ [pi × max(xi, 0)]
Exceedance Probability
P(X ≥ Threshold) = Σ pi for all scenarios meeting the threshold

Here, pi is the probability of scenario i, and xi is the loss or impact tied to that scenario.

How to Use This Calculator

  1. Select whether probabilities are entered as percentages or decimals.
  2. Set a loss threshold if you want exceedance probability.
  3. Enter each scenario label, its probability, and its impact.
  4. Enable normalization when probabilities may not total exactly 1.0.
  5. Click Calculate Expected Risk to generate metrics and the chart.
  6. Review the result cards, scenario table, and contribution graph.
  7. Download the results as CSV or PDF if needed.

Frequently Asked Questions

1) What does expected risk mean?

Expected risk is the probability-weighted average of all listed outcomes. It estimates the long-run average loss or impact when the same uncertain situation repeats many times.

2) Why does the calculator include variance and standard deviation?

Expected risk gives the average outcome, but it does not show spread. Variance and standard deviation reveal how widely scenario impacts differ around that average.

3) Can I use percentages instead of decimals?

Yes. Select percent mode for values like 25, or decimal mode for values like 0.25. The calculator converts the inputs consistently before computing results.

4) What happens when probabilities do not total 1?

If normalization is enabled, the tool rescales them into a valid probability distribution. If normalization is off, probabilities must already total 1.0.

5) Can impacts be negative?

Yes. Negative impacts can represent gains, recoveries, or offsets. They reduce the expected risk because they contribute favorable outcomes to the weighted average.

6) What is exceedance probability?

Exceedance probability is the total probability of scenarios whose impacts meet or exceed your chosen threshold. It helps evaluate tail risk above a critical loss level.

7) When should I use expected adverse loss?

Use expected adverse loss when you want to focus only on harmful outcomes. It ignores favorable scenarios and highlights the weighted average of positive losses only.

8) Is this suitable for finance, quality, and operations work?

Yes. The method works anywhere discrete scenarios can be assigned probabilities and impacts, including project risk, process quality, compliance exposure, and financial loss estimation.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.