Standard Error
Calculator
Turn repeated measurements into mean, sample standard deviation, and standard error of the mean. Paste a list — get lab-ready statistics. No signup, no ads.
n = 0 measurements
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01How SEM Is Calculated
From n repeated measurements, compute the mean, the sample standard deviation (with Bessel's correction, n − 1), then SEM = s / √n. SEM is the uncertainty you typically attach to the mean in a lab report.
For when to use SD vs SEM, read standard error vs standard deviation.
02Worked Example
Measurements: 2, 4, 4, 4, 5, 5, 7, 9
n = 8
Mean x̄ = 40 / 8 = 5
Sample SD s = √[Σ(xᵢ − x̄)² / 7] = √(32/7) ≈ 2.138
SEM = s / √8 ≈ 0.756 → rounds to 0.8 at the tenths place for reporting
03Frequently Asked Questions
Q1What is the standard error of the mean?
SEM = s / √n, where s is the sample standard deviation and n is the number of measurements. It estimates the uncertainty in the mean, which is what you usually report in a lab report.
Q2Why use sample standard deviation (n − 1)?
Lab measurements are a sample of possible trials, not the entire population. Bessel's correction (dividing by n − 1) gives an unbiased estimate of the population variance from that sample.
Q3Should I report SD or SEM?
For a mean from repeated measurements, report the SEM as the uncertainty. Standard deviation describes the spread of individual readings; SEM describes how well you know the average.
Q4Is this calculator free?
Yes. ΔPropagator tools are free to use, with no signup, no ads, and no paywall.