Calculate the standard error and margin of error for a mean using a z critical value.
| Margin of error | – |
| Standard error | – |
Use this calculator when you already have a standard deviation and a sample size and want the half-width of a z-interval for a mean. It is the same margin that appears in a large-sample confidence interval, without needing the mean itself.
The formulas are: SE = s / √n and MoE = z × SE. Common z values are 1.645 (90%), 1.96 (95%), and 2.576 (99%). With s = 10, n = 100, and z = 1.96, SE = 1 and MoE ≈ 1.96.
This is for a mean, not for a proportion (that uses √(p(1 − p)/n) instead of s/√n). It uses z, not t. Independent observations and a positive n and s are assumed.
z: Normal critical value. 1.96 is the usual 95% choice.
Standard deviation (s): Sample (or known) standard deviation.
Sample size (n): Number of observations.
Margin of error: Half-width of the z-interval, z × s / √n.
Standard error: s / √n, the estimated SD of the sample mean.
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