Standard Error of the Mean Calculator
Standard error from sample standard deviation and size.
Enter your values
Enter the sample standard deviation you are working with.
Enter the sample size you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Standard error
- 2
- Sample size
- 36
- 95% margin of error (approx)
- ±3.92
Quick answer
The standard error of the mean is the sample standard deviation divided by the square root of the sample size.
SE = s / sqrt(n)
At a glance
| What it does | Standard error from sample standard deviation and size. |
|---|---|
| Category | Statistics |
| Inputs needed | Sample standard deviation, Sample size |
| Main output | Standard error |
| Formula | SE = s / sqrt(n) |
| Cost | Free — no sign-up, no download |
How to use the Standard Error of the Mean Calculator
- 1Enter the sample standard deviation.
- 2Enter the sample size used to compute it.
- 3The standard error shrinks as the sample size grows, following a square-root relationship.
Inputs explained
- Sample standard deviation
- Enter the sample standard deviation you are working with.
- Sample size
- Enter the sample size you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Sample standard deviation12
- Sample size36
Results
- Standard error2
- Sample size36
- 95% margin of error (approx)±3.92
Frequently asked questions
Why divide by sqrt(n) instead of n?
Variance of the mean scales as variance/n, so standard deviation of the mean scales as s/sqrt(n).
How is SE different from standard deviation?
Standard deviation measures spread of individual data points; standard error measures the precision of the sample mean estimate.
What do I need to enter into the Standard Error of the Mean Calculator?
Just 2 values: sample standard deviation, sample size. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Standard Error of the Mean Calculator work out the answer?
The standard error of the mean is the sample standard deviation divided by the square root of the sample size. It applies the formula SE = s / sqrt(n) and shows the working so you can check each step by hand.
Is the Standard Error of the Mean Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.