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Standard Error Calculator

Calculate the standard error of a mean and how it shrinks with sample size.

About Standard Error Calculator

Because standard error scales with the square root of n, halving it requires quadrupling the sample. That square-root relationship is the fundamental economics of sampling. Doubling a survey sample improves precision by only about 30 per cent, which is why very large samples deliver diminishing returns.

Formula

Standard Error

SE = s ÷ √n; required n = (s ÷ target SE)²

√n
Standard error falls with the square root of sample size, not linearly

Worked example

With the default values below, Standard Error Calculator returns Standard Error of 1.500000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample standard deviationminimum 0
15
Sample sizeminimum 1
100
Target standard errorminimum 0
1

Results

Standard Error
1.500000
Sample Size Needed for the Target
225
Margin of Error at 95 Per Cent
2.93995
Relative Standard Error
10.0000%
Standard Error With Four Times the Sample
0.750000

Step by step

  1. 1Values used
  2. 2Standard Error
  3. 3Standard Error= 1.500000
  4. 4Sample Size Needed for the Target= 225
  5. 5Margin of Error at 95 Per Cent= 2.93995
  6. 6Relative Standard Error= 10.0000
  7. 7Standard Error With Four Times the Sample= 0.750000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Standard Error calculated?

SE = s ÷ √n; required n = (s ÷ target SE)² Because standard error scales with the square root of n, halving it requires quadrupling the sample. That square-root relationship is the fundamental economics of sampling.

Why does Standard Error matter?

Doubling a survey sample improves precision by only about 30 per cent, which is why very large samples deliver diminishing returns.

What values do I need to enter?

This calculator takes 3 inputs: Sample standard deviation, Sample size, Target standard error. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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