Standard Error Calculator

Find the standard error of a mean, a proportion, or the difference between two means, with the working shown step by step.

Your data

10 values read.

Population size (optional)

Only if the sample is a big share of a small population.

Standard error

2.16128

mean = 82.6

s = 6.8346, n = 10: SE = s ÷ √n = 6.8346 ÷ √10 = 2.16128

The standard error measures how much this statistic would typically vary from one sample to another. Quadrupling the sample size would halve it.

How to use this tool

Choose what you are estimating: a mean (from pasted data or from a standard deviation and sample size), a proportion, or the difference between two means.
Enter your values. For raw data, separate numbers with commas, spaces, or new lines.
Optionally enter the population size if your sample is a large share of a small population.
Read the standard error and the formula with your numbers filled in.

Formula Reference

SE of a mean

SE = s ÷ √n

SE of a proportion

SE = √[ p̂(1 − p̂) ÷ n ]

SE of a difference of means

SE = √( s₁²/n₁ + s₂²/n₂ )

Finite population correction

× √[ (N − n) ÷ (N − 1) ]

ArticleStandard Error Explained ArticleThe Central Limit Theorem ArticleThe Finite Population Correction CalcMargin of Error Calculator CalcConfidence Interval Calculator GlossaryGlossary: Standard Error

Frequently Asked Questions

What is the difference between standard deviation and standard error?+

The standard deviation describes how spread out individual values are. The standard error describes how much a statistic, such as the sample mean, would vary from sample to sample. It equals the standard deviation divided by the square root of the sample size, so it is always smaller.

Why does a bigger sample give a smaller standard error?+

Averages of more values fluctuate less. Because the standard error shrinks with the square root of n, quadrupling the sample size cuts it in half.

Which standard deviation goes into the formula?+

Use the sample standard deviation s, which divides by n − 1, when you estimate from data. Use the population standard deviation only if it is truly known.

Does a small standard error mean my result is accurate?+

It means the estimate is precise, meaning repeatable across samples. It says nothing about bias from a poor sampling method or a faulty measurement.

How to use this tool

Choose what you are estimating: a mean (from pasted data or from a standard deviation and sample size), a proportion, or the difference between two means.

Enter your values. For raw data, separate numbers with commas, spaces, or new lines.

Optionally enter the population size if your sample is a large share of a small population.

Read the standard error and the formula with your numbers filled in.