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Sample Size Calculator: How Many Responses Do You Need?

This free sample size calculator tells you how many people you need to survey for a given confidence level and margin of error. It uses Cochran’s formula and corrects for a small population.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A sample size calculator tells you how many responses make your survey reliable. Too few answers give a wide margin of error, and too many waste time and money. The right number depends on your confidence level, your margin of error and, for small groups, the population size.

Fill in the boxes and read the number of responses to collect.

How to Use This Tool

  1. Choose the confidence level.
  2. Enter the margin of error you can accept.
  3. Leave the proportion at 50% unless you know better.
  4. Optionally enter the population size and press Calculate.

How the Calculation Works

The z-score for the confidence level (1.96 for 95%) is squared and multiplied by p × (1 − p), then divided by the square of the margin of error. This gives the sample for an infinite population. With a population N, the correction n = n0 ÷ (1 + (n0 − 1) ÷ N) reduces it. The result is rounded up.

Worked Example

At 95% confidence with a 5% margin of error and p = 50%, n0 = 384.16, so you need 385 responses. For a population of 1,000, the corrected size is 278.

Common Uses

  • Customer and staff surveys.
  • Market research.
  • School and academic projects.
  • Polls and quality checks.

Tips and Common Mistakes

  • Round up, and add 10 to 20 percent for people who do not respond.
  • A smaller margin of error needs a much bigger sample.
  • Random selection matters as much as the number.

Next, you may need the margin of error calculator, confidence interval calculator, normal distribution calculator, probability calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Cochran’s formula: n = z² × p × (1 − p) ÷ e², where z is the z-score for the confidence level, p the expected proportion and e the margin of error.
It gives the largest sample size, so it is the safe choice when you do not know the real share.
Only when the population is small. For a population over about 20,000 the sample size barely changes. The tool applies a finite population correction when you enter it.
About 385 responses for a large population.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.