About the Standard Error Calculator
When you measure a sample, the average you get will differ a little from the true average of the whole group. The standard error tells you how much it typically varies from sample to sample. It is the standard deviation divided by the square root of the sample size, so it shrinks as you collect more data. This calculator works in three ways: paste a list of numbers and it works out the mean, standard deviation and standard error, enter a standard deviation and sample size directly, or enter a proportion and sample size to get the standard error of a percentage. It also shows an approximate 95 percent range.
Updated October 2026
How to use the Standard Error Calculator
- 1Choose whether you have a list of numbers, a standard deviation, or a proportion.
- 2Enter the numbers, or the standard deviation and sample size, or the proportion and sample size.
- 3Read the standard error in the large result.
- 4Check the mean, standard deviation and approximate range.
- 5Copy the result.
Worked example
Seven plants grow 12, 15, 11, 14, 18, 13 and 16 centimetres. The mean is 14.14, the sample standard deviation is 2.41 and the standard error is 2.41 divided by the square root of 7, about 0.91. A rough 95 percent range for the true average growth is 14.14 plus or minus 1.79, or from 12.4 to 15.9 centimetres. With a small sample like this, a t-based interval would be a little wider.
When to use which mode
- Raw numbers: you have the data and want everything calculated.
- SD and n: a paper or a report gave you only those two figures.
- Proportion: survey results such as 40% of 50 people said yes.
- Always check that the sample is random and independent.
- Do not use it for tiny samples without thinking about the t distribution.
Common mistakes
Do not mix up the population standard deviation and the sample standard deviation, which divides by n minus 1. Do not report the standard error as if it described the spread of individual observations. And remember that the formula assumes independent observations; repeated measures from the same person or clustered samples need a different approach.
Related tools
The Margin of Error Calculator turns a standard error into a confidence interval, the Confidence Interval Calculator gives full ranges, the Standard Deviation Calculator describes your data and the Sample Size Calculator tells you how many responses you need.
Features
- Standard error of the mean from raw data
- From standard deviation and sample size
- Standard error of a proportion
- Approximate 95% range
- Mean and standard deviation shown
- Clear input checks
Frequently asked questions
What is the standard error?
It is the standard deviation of a statistic, such as the sample mean, over repeated samples. It measures how precisely the sample estimates the true value. Smaller means more precise.
How do I calculate the standard error of the mean?
Divide the sample standard deviation by the square root of the sample size. For a standard deviation of 4.2 from 50 observations, the standard error is 4.2 ÷ 7.07 = 0.594.
What is the difference between standard deviation and standard error?
Standard deviation describes how spread out the individual values are. Standard error describes how uncertain the sample mean is. The first stays about the same as you collect more data, the second falls.
How does sample size affect the standard error?
Quadrupling the sample size halves the standard error, because of the square root. To make your estimate ten times more precise, you need a hundred times more data.
How do I find the standard error of a proportion?
Take the square root of p times (1 − p) divided by n. For 40 percent in a sample of 50, that is the square root of 0.24 ÷ 50, which is 0.0693, or about 6.9 percentage points.
How is the standard error used?
To build confidence intervals and margins of error, as in the mean plus or minus 1.96 times the standard error for about 95 percent confidence, and in significance tests. It also appears as error bars in charts.