Sample Size Calculator

How to use this calculator

The confidence level and expected proportion are pre-filled with the common defaults of 95% and 50%. Enter the margin of error you can tolerate and the required sample size appears, with a rounded-up figure underneath. If you have a pilot estimate of the proportion — say 20% of customers churn — enter it; proportions far from 50% need smaller samples.

Run it backwards to evaluate a survey you already ran: delete the margin of error, enter your sample size, and the achievable margin is calculated. This is how news reports arrive at the "±3 points" quoted for a poll of about 1,000 people.

The formula

n = z² × p̂ (1 − p̂) / E²

E = z × √(p̂ (1 − p̂) / n)

CL: confidence level
z: critical value
p̂: expected proportion
E: margin of error
n: sample size

Worked example

You want to estimate a proportion to within ±5 percentage points at 95% confidence, with no prior estimate of the proportion.

z = 1.96 for 95% confidence.
Use p̂ = 50%, the most conservative choice.
n = 1.96² × 0.5 × 0.5 / 0.05² = 384.1, rounded up to 385.

Survey at least 385 respondents.

Assumptions and limits

Simple random sampling from a large population. For populations under about 20 times the sample size, apply the finite population correction n′ = n / (1 + (n − 1)/N).
Margin of error covers sampling error only, not non-response or question-wording bias.

Frequently asked questions

Why use 50% when I do not know the proportion?

p(1 − p) is largest at 0.5, so it gives the largest, safest sample size. Any other true proportion will then have a smaller margin of error.

Does population size matter?

Barely, unless the population is small. A national poll and a city poll need about the same sample for the same margin of error.

How many responses do I need for ±3% at 95%?

About 1,068 with p̂ = 50%.