Statistics & Probability

Standard Error Calculator

Find the standard error from a standard deviation and sample size.

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Standard error of the mean
Standard error of the mean
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Standard error of the proportion
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Standard Error Calculator by TheCalcTools

How the Standard Error Calculator works

Enter the sample standard deviation and the sample size.

The standard error of the mean is s ÷ √n.

The proportion row uses √(p(1 − p) ÷ n).

The formula

SE(mean) = s ÷ √nSE(proportion) = √(p(1 − p) ÷ n)

Worked example

Using the default values shown in the calculator:

Standard deviation (s)12
Sample size (n)36
Proportion for comparison (%)40
  1. SE = 12 ÷ √36 = 2.00.
  2. For p = 40%: √(0.4 × 0.6 ÷ 36) = 8.16%.

Result:

Standard error of the mean2.0000
Standard error of the proportion8.16%

Frequently asked questions

What is the difference between standard deviation and standard error?

Standard deviation describes the spread of the data. Standard error describes how much the sample mean would vary between samples.

How can I reduce the standard error?

Increase the sample size. To halve the standard error you need four times the data.

Sources and further reading

Confidence Interval Calculator (Mean)Estimate a range likely to contain the true mean, using the normal (z) approximation Coefficient of Variation CalculatorCompare variability between data sets with different units or scales Margin of Error Calculator (Proportion)Find the margin of error for a poll or survey result Sample Size CalculatorHow many people do you need to survey?

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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.