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Expected value calculator

Compute the expected value from a list of outcomes and their probabilities.

Related tools

All Statistics & probability tools →
p-Value CalculatorTurns a z, t, χ² or F statistic into a p-value, one- or two-tailed, with the density curve and the rejected area drawn. The reading in words is included, because a p-value is the most misread number in statistics.Coefficient of variation calculatorCompute the coefficient of variation (CV) of a dataset — its relative variability.Correlation coefficient calculatorCompute Pearson's correlation coefficient between two lists of numbers.Geometric mean calculatorCompute the geometric mean of a list of positive numbers.Harmonic mean calculatorCompute the harmonic mean of a list of positive numbers.Interquartile range (IQR) calculatorCompute the first quartile, third quartile and interquartile range of a dataset.Mean absolute deviation (MAD) calculatorCompute the mean absolute deviation of a data set around its mean.Midrange calculatorCompute the midrange (the average of the smallest and largest value) of a list.

Enter Outcomes (comma-separated), Probabilities, adding up to 1 and the Expected value calculator works out Expected value straight away. For instance, with Outcomes (comma-separated) = 10, 20, -5 and Probabilities, adding up to 1 = 0.5, 0.3, 0.2 it returns Expected value = 10.

How to use it

  1. Enter your values: Outcomes (comma-separated), Probabilities, adding up to 1.
  2. Read the result instantly: Expected value.

Frequently asked questions

What does the Expected value calculator actually compute?

It takes Outcomes (comma-separated) and Probabilities, adding up to 1 and derives Expected value from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

2 values: Outcomes (comma-separated) and Probabilities, adding up to 1. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Outcomes (comma-separated) = 10, 20, -5 and Probabilities, adding up to 1 = 0.5, 0.3, 0.2, the calculator returns Expected value = 10. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

What is the difference between the Expected value calculator and the p-Value Calculator?

This one returns Expected value; the p-Value Calculator returns Result. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Coefficient of variation calculator is the closest one after this: Compute the coefficient of variation (CV) of a dataset — its relative variability.

What else is worth having open alongside it?

Correlation coefficient calculator and Geometric mean calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from, and how current are they?

Distributions and test statistics are computed from their standard definitions, not from a lookup table, so results carry more digits than a printed table would. The assumptions each test makes are stated with it.

Further reading

All guides →
ExplainerThe Expected Value Is a Number That Never HappensOutcomes of 10, 20 and −5 with probabilities 0.5, 0.3 and 0.2 give an expected value of 10. Shift the probabilities slightly and it becomes 10.5 — a result none of the three outcomes can produce.ExplainerForty Out and Sixty Back Averages Forty-EightThe harmonic mean of 40 and 60 is 48, not 50, because the slower leg takes longer and therefore counts for more. For 1, 2 and 4 it is 1.714 against an arithmetic mean of 2.33.ExplainerTurn 30 Into 300 and the Interquartile Range Does Not MoveFor 2, 5, 7, 8, 10, 13, 18, 21, 25, 30 the range is 28, the standard deviation 9.24 and the IQR 13. Replace the last value with 300 and only the IQR survives unchanged.ExplainerAn r of 0.85 That Proves NothingFive points give r = 0.853, which sounds strong. The threshold for significance at five points is 0.878, so this one falls short — and a perfect parabola scores exactly zero.ExplainerThe Same Three Temperatures Give Three Different Coefficients of VariationFor 2, 4, 4, 4, 5, 5, 7, 9 the coefficient of variation is 42.76 %. It is the right tool for comparing spread across different scales — and completely wrong for any scale whose zero was chosen by convention.ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.