Standard error calculator

Choose raw data, a standard deviation with a sample size, or a count of successes out of n trials. You get the standard error with the values used to find it.

Calculate for

Sample valuesUsed with raw data. Separate numbers with commas, spaces or semicolons.

Standard deviationUsed with SD and sample size. The sample standard deviation.

Successes (x)Used with a proportion. A whole number from 0 up to n.

Sample size (n)Used with SD and with a proportion. A whole number of at least 1.

Standard error0.755928946

Sample mean: 5
Standard deviation used: 2.138089935
Sample size: 8

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How to use it

Pick what you are measuring: a mean or a proportion.
Fill in the boxes that apply: raw values, or SD with n, or successes with n.
Read the standard error. Use the confidence interval calculator to turn it into a range.

How it works

For raw data the calculator uses the sample standard deviation (divide by n − 1) and then s / √n. For summary data it uses the SD you enter. For a proportion it uses √(p̂(1 − p̂)/n). Results show up to 10 significant digits.

Worked example

Values 2, 4, 4, 4, 5, 5, 7, 9:

Mean 5, sum of squared deviations 32
Sample SD: √(32 / 7) ≈ 2.138
Standard error: 2.138 / √8 ≈ 0.756

Tips

Quadrupling the sample size halves the standard error.
The proportion formula is the usual large-sample one; it is rough when p̂ is near 0 or 1 or n is small.

Frequently asked questions

What is the standard error?

It measures how much a sample statistic, such as the mean, would vary from sample to sample. A smaller standard error means the sample mean is a more precise estimate.

What is the formula for the standard error of the mean?

SE = s / √n, where s is the sample standard deviation and n the sample size. With s = 10 and n = 25 the standard error is 10 / 5 = 2.

What is the standard error of a proportion?

SE = √(p̂ × (1 − p̂) / n), where p̂ = x / n. For 40 successes in 100 trials, p̂ = 0.4 and SE = √(0.24 / 100) ≈ 0.049.

How is it different from the standard deviation?

The standard deviation describes the spread of the values themselves. The standard error describes the spread of the sample mean and shrinks as n grows.

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All tools in this category: Math ·Updated November 3, 2026