Standard Error Calculator
Choose the mean or a proportion, enter the sample size and, if you sampled a sizeable part of a small population, the population size.
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Formula
- Mean:
SEM = s ÷ √n - Proportion:
SE = √(p × (1 − p) ÷ n) - Finite population correction (when N is given): multiply by
√((N − n) ÷ (N − 1)) - 95% margin of error:
1.96 × SE(normal approximation)
Worked example
- s = 15, n = 36: SEM = 15 ÷ √36 = 2.5, margin of error 1.96 × 2.5 = 4.90.
- p = 0.4, n = 100: SE = √(0.4 × 0.6 ÷ 100) = 0.0490.
- s = 15, n = 50 from N = 200: factor √(150 ÷ 199) = 0.8682, SEM = 2.1213 × 0.8682 = 1.8417.
Frequently asked questions
How do I calculate the standard error of the mean?
Divide the sample standard deviation by the square root of the sample size: SEM = s ÷ √n. For s = 15 and n = 36, SEM = 15 ÷ 6 = 2.5.
How do I calculate the standard error of a proportion?
SE = √(p × (1 − p) ÷ n). For p = 0.4 and n = 100, SE = √(0.24 ÷ 100) = 0.0490, about 4.9 percentage points.
When should I use the finite population correction?
When you sample without replacement and the sample is more than about 5% of the population. Multiply by √((N − n) ÷ (N − 1)). For N = 200 and n = 50 the factor is 0.868, so an SEM of 2.12 becomes 1.84.
What is the difference between standard deviation and standard error?
Standard deviation describes how spread out individual values are. Standard error describes how much a sample statistic, such as the mean, would vary between samples, and it shrinks as n grows.