# Sample Size Calculator

Free sample size calculator. Determine the minimum sample size for surveys and studies based on confidence level, margin of error, and population size.

## What this calculates

Calculate the minimum sample size required for your survey or research study. Enter your desired confidence level, margin of error, and expected proportion to find out how many respondents you need.

## Inputs

- **Confidence Level** — options: 90%, 95%, 99% — How confident you want to be that the true value falls within the margin of error.
- **Margin of Error (%)** — min 0.01, max 50 — The maximum acceptable difference between sample and population values.
- **Expected Proportion (%)** — min 1, max 99 — Estimated proportion of the population with the attribute. Use 50% if unknown (most conservative).
- **Population Size (optional)** — min 0 — Total population size. Leave as 0 for very large or unknown populations.

## Outputs

- **Required Sample Size** — The minimum number of respondents needed.
- **Sample Size (Infinite Population)** — Sample size before finite population correction.
- **Formula** — formatted as text — The formula and values used.

## Details

The sample size formula for estimating a population proportion is:

n = (z² × p × (1-p)) / e²

Where:

- z = z-score for the confidence level

- p = expected proportion (use 0.5 if unknown)

- e = margin of error (as a decimal)

Finite Population Correction

If your population is small, apply: n_adj = n / (1 + (n-1)/N)

Using p = 0.5 gives the largest (most conservative) sample size because p(1-p) is maximized at 0.25.

## Frequently Asked Questions

**Q: Why is 50% the most conservative proportion?**

A: When p = 50%, the product p × (1-p) = 0.25, which is its maximum value. Any other proportion produces a smaller product and thus a smaller required sample size. Using 50% ensures your sample is large enough regardless of the true proportion.

**Q: What margin of error should I use?**

A: A 5% margin of error is common for general surveys. For more precise results, use 3% or lower. Medical or scientific studies often require 1-2%. Smaller margins of error require larger sample sizes.

**Q: When should I use the finite population correction?**

A: Apply the finite population correction when your sample is more than about 5% of the total population. For very large populations (over 100,000), the correction has negligible effect.

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Source: https://vastcalc.com/calculators/statistics/sample-size
Category: Statistics
Last updated: 2026-04-21