Standard Error of Mean Calculator
Enter a sample standard deviation and sample size and the tool returns the standard error of the mean, computed as the standard deviation divided by the square root of the sample size.
What this calculator does
The Standard Error of Mean Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Enter a sample standard deviation and sample size and the tool returns the standard error of the mean, computed as the standard deviation divided by the square root of the sample size. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Standard Error of Mean Calculator
This calculator returns the standard error of the mean (SEM) from just two numbers: your sample standard deviation and your sample size. It applies the formula SEM = s / √n, which describes how much a sample mean is expected to vary from sample to sample.
Use it when you already know a sample's spread and size and want the precision of its average, for example when building a confidence interval.
Formula & Mathematical Calculation
Standard Error of Mean = f(Sample standard deviation, Sample size (n))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
Enter a Sample standard deviation of 12 and a Sample size (n) of 36, then click Calculate.
The tool returns Standard Error of Mean = 2, with the note: “SEM = s/√n = 2.”
Key Benefits
- Calculates the standard error of the mean directly from a standard deviation and sample size
- Uses the standard s divided by square-root-of-n formula and shows it in the result note
- Rounds the result to five decimal places for small standard errors
- Rejects a negative standard deviation or a sample size below 1 with a specific error message
How to Use this Calculator
-
Enter the standard deviation
Type your sample standard deviation into the first field; it must be zero or positive. -
Enter the sample size
Type the number of observations (n) into the sample size field, using a whole number of at least 1. -
Calculate
Click Calculate to fill the Standard Error of Mean box. -
Read the SEM
Read the single result value, which is the standard deviation divided by the square root of n.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Standard Error of Mean Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.