Calculating your required sample size is straightforward once you know the Sample Size formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Sample Size Calculator.
What is Sample Size?
The Sample Size calculation tells you your required sample size from a few simple inputs. The figure you are solving for here is the required sample size.
The Sample Size formula
This calculation combines several inputs through a multi-step method rather than a single one-line formula. Enter the values below and the calculator resolves each step in order. The inputs it needs are:
- Margin of error — a percentage, such as an annual rate. Example: 5%.
- Proportion — a number. Example: 0.5.
- Confidence level — one of: 90% (z = 1.645), 95% (z = 1.96), 99% (z = 2.576). Example: 95% (z = 1.96).
How to calculate it step by step
- Write down the margin of error (for example, 5%).
- Write down the proportion (for example, 0.5).
- Choose the confidence level (for example, 95% (z = 1.96)).
- Apply the formula above to get your required sample size.
- Double-check the result with the Sample Size Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Margin of error | 5% |
| Proportion | 0.5 |
| Confidence level | 95% (z = 1.96) |
| Required sample size | 385 |
With margin of error of 5%, proportion of 0.5 and confidence level of 95% (z = 1.96), the required sample size works out to 385.
Example 2
With margin of error of 1%, proportion of 0.5 and confidence level of 95% (z = 1.96), the required sample size works out to 97.
| Result | Value |
|---|---|
| Required sample size | 97 |
Example 3
With margin of error of 2.5%, proportion of 0.5 and confidence level of 95% (z = 1.96), the required sample size works out to 1,537.
| Result | Value |
|---|---|
| Required sample size | 1,537 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Sample Size Calculator does it instantly, for free, with the formula and a worked example built in.
Related calculators
Continue exploring math calculators with these tools: Margin of Error Calculator, Confidence Interval Calculator, Coefficient of Variation Calculator, Regular Heptagon Area Calculator, Odds to Probability Calculator.