Standard Error Calculator

Calculate the standard error of the mean using the standard deviation and sample size. Get accurate statistical results instantly with our easy-to-use tool.

Calculate Standard Error

Enter the standard deviation and sample size to calculate the standard error of the mean.

Standard Deviation

Enter the standard deviation of your sample.

Sample Size

Enter the number of observations in the sample.

Sample Mean (Optional)

Optional: enter the sample mean for additional context.

Example: If the standard deviation is 12 and the sample size is 36, the standard error is 12 ÷ √36 = 2.

Standard Error Result

0.0000

Standard Deviation 0

Sample Size 0

Square Root of n 0

Measure	Value	Formula / Detail
Standard Deviation	—	Given value
Sample Size	—	Given value
√ Sample Size	—	√n
Standard Error	—	SD ÷ √n
Standard Error		SD / √n

What Is Standard Error?

Standard error is a statistical measure that describes how much the sample mean is expected to vary from one sample to another. It is commonly used to evaluate the precision of a sample mean as an estimate of a population mean.

A smaller standard error generally indicates that the sample mean is estimated with greater precision. The standard error becomes smaller as the sample size increases, assuming the standard deviation remains unchanged.

Standard Error = Standard Deviation ÷ √Sample Size

How to Calculate Standard Error

The standard error of the mean can be calculated using the sample standard deviation and the number of observations in the sample.

Enter the standard deviation of your sample.
Enter the sample size, which represents the number of observations.
Calculate the square root of the sample size.
Divide the standard deviation by the square root of the sample size.
The result is the standard error of the mean.

Standard Error Formula

The standard error of the mean is calculated using the following formula:

SE = s / √n

SE = Standard Error
s = Sample Standard Deviation
n = Sample Size

Example Calculation

Suppose a sample has a standard deviation of 12 and contains 36 observations.

SE = 12 / √36
SE = 12 / 6
SE = 2

Therefore, the standard error of the mean is 2.

Standard Error vs Standard Deviation

Standard Deviation

Standard deviation measures the spread or variability of individual observations within a data set. It tells you how far data values typically vary from the mean.

Standard Error

Standard error measures the variability of a sample statistic, most commonly the sample mean. It is used to describe the precision of an estimated population mean.

Larger Sample Size → Smaller Standard Error

Why Is Standard Error Important?

Measures Precision

Standard error provides information about how precisely a sample mean estimates the population mean.

Used in Confidence Intervals

Standard error is an important component of many confidence interval calculations.

Used in Hypothesis Testing

Standard error is also used in statistical tests and test statistics that compare sample results with hypothesized population values.

Sample Size Effect

Increasing the sample size generally reduces the standard error, making estimates of the population mean more precise.

Frequently Asked Questions

The standard error of the mean is calculated as the sample standard deviation divided by the square root of the sample size: SE = s / √n.

Standard deviation describes the variability of individual observations, while standard error describes the variability or precision of a sample statistic such as the sample mean.

Yes. When the standard deviation remains constant, increasing the sample size decreases the standard error because the standard deviation is divided by the square root of the sample size.

Yes. If the standard deviation is zero, the standard error is also zero because there is no variation in the observations.

Standard error decreases as sample size increases, following the inverse square-root relationship SE = s / √n.

Yes. The calculator accepts decimal values for standard deviation and produces a precise standard error result.

A smaller standard error generally indicates that the sample mean has greater precision as an estimate of the population mean.

No. The standard error of the mean can be calculated from the sample standard deviation and sample size. The sample mean is not required for the basic formula.