`SEM = sigma/sqrt(n)`

Enter a value for all fields

The Standard Error of the Mean (SEM) calculator estimates how much the mean would vary across repeated samples of a population based on a standard deviation value and the sample size..

INSTRUCTIONS: Enter the following:

• (s) Standard Deviation of Sample
• (n) Sample Size

Standard Error of the Mean (SEM): The error is returned as a real number.

The Math / Science

The Standard Error of the Mean (SEM) is the standard deviation divided by the square root of the number of data items. This quantity is useful in that it helps quantify the uncertainty in the estimate of the mean.  

This equation is shown as:    `sigma_m = sigma/(sqrt(N))`  

    where:  sigma = standard deviation of the data set and N = number of data items

One of the most common mix-ups in statistics is between standard deviation (SD) and standard error (SEM). They sound similar, but they describe two completely different things—and using the wrong one can lead to misleading conclusions. 

•  Standard Deviation (SD): SD measures how spread out individual values are in your sample. It tells you about the variability within the data set. Example: How much do individual incomes vary in a sample of 1,000 people?
•  Standard Error (SE): SE measures how much an estimate (like a mean or proportion) would vary across repeated samples. It tells you how precise your estimate is. Example: How much would the sample mean income change if you ran the survey again?

As your sample gets larger, SE gets smaller because you're more confident in your estimate. But SD often stays about the same since it reflects the natural spread in the data, not how many observations you have. Use SD to describe the data, and SE to describe the reliability of the estimate.