StatCalcPro

Margin of Error Calculator

A poll of 1,000 people has a margin of error of about ±3.1% at 95% confidence. Enter your own sample size to see yours.

Margin of error
±3.1%

A result of 50% from 1,000 responses means the true figure is likely between 46.9% and 53.1% (95% confidence).

  1. Critical value for 95%: z = 1.96
  2. Standard error = √(p(1 − p)/n) = √(0.5 × 0.5 / 1000) = 0.01581
  3. E = z × SE = ±3.1%

Margin of error by sample size

p = 50%, large population.

Sample size90%95%99%
100±8.2%±9.8%±12.9%
400±4.1%±4.9%±6.4%
1,000±2.6%±3.1%±4.1%
2,500±1.6%±2%±2.6%
10,000±0.8%±1%±1.3%

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What the margin of error tells you

E = z × √(p(1 − p) / n)   ·   E = z × σ / √n

The margin of error is half the width of a confidence interval. When a poll reports 52% ± 3%, it means that if the poll were repeated many times, about 95% of the intervals built this way would contain the true share.

Because n sits under a square root, precision is expensive: going from ±5% to ±2.5% takes four times as many responses. If you are planning a survey and want the size that gives a chosen margin, use the sample size calculator. Comparing two percentages, such as two candidates in the same poll, has a larger margin than either one alone, so a 2-point lead inside a ±3% margin is not a clear lead.

Frequently asked questions

How do you calculate margin of error?

Margin of error = critical value × standard error. For a proportion: E = z × √(p(1 − p) ÷ n). For a mean with a known or estimated SD: E = z × σ ÷ √n. At 95% confidence z = 1.96; at 90%, 1.645; at 99%, 2.576.

What is the margin of error for a sample of 1,000?

About ±3.1 percentage points at 95% confidence, using p = 50%: 1.96 × √(0.25 ÷ 1000) = 0.031. This is why many national polls survey roughly 1,000 people.

What is a good margin of error?

For opinion polls and most surveys, ±3% to ±5% at 95% confidence is the usual target. Internal or exploratory surveys often accept ±10%. Smaller margins cost more: halving the margin needs four times the sample.

Why use 50% for the proportion?

p(1 − p) is largest at p = 0.5, so 50% gives the widest, most cautious margin. If your result came out at, say, 20%, entering 20 gives the margin for that specific figure, which is smaller.

Does the margin of error cover all survey error?

No. It only describes random sampling error. Non-response, biased question wording and an unrepresentative sampling frame can all add error that no formula shows.

When should I use the finite population correction?

When your sample is more than about 5% of the whole population, for example 200 responses from a company of 1,000 staff. The correction √((N − n) ÷ (N − 1)) shrinks the margin because you have seen a large share of everyone.

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