Standard Error of the Mean Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Enter the standard deviation σ of a single observation (in your measurement's units).
- Enter the number of observations n you averaged.
- Read the standard error of the mean and the 95% confidence half-width.
How it works
Averaging readings reduces random error: the standard error of the mean is SE = σ ÷ √n. So nine readings are three times more precise than one (√9 = 3).
The 95% confidence half-width is about ±1.96 × SE — the mean is expected to lie within that band of the true value 95% of the time, assuming only random error.
Worked example
σ = 0.012 m over 9 readings. SE = 0.012 ÷ √9 = 0.004 m, and the 95% half-width is ±1.96 × 0.004 ≈ ±0.00784 m.
Frequently asked questions
What's the difference between standard deviation and standard error?
Standard deviation describes the spread of single readings; standard error describes the spread of their average. SE is always smaller — it shrinks as you take more readings (÷√n).
How many readings do I need to halve the error?
Four times as many. Because SE ∝ 1/√n, cutting the error in half needs n to go up by 4 (√4 = 2).
Is this official course material?
No. It is free study support mapped to surveying course levels — not official North Metropolitan TAFE content or advice. Always follow your lecturer and the official assessment brief, and check your own working.
Related tools
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.