Margin of Error Calculator

The margin of error is the “±” in a poll or survey result. Calculate it for a proportion or a mean at 90%, 95% or 99% confidence, with an optional finite population correction for small populations.

Don’t know the proportion yet? Keep 50%: it gives the largest (most cautious) margin of error.

Margin of error
± 3.1%
z*
1.96
Standard error
0.01581

Step-by-step working

  1. z* for 95% confidencez* = 1.96
  2. Standard error of a proportionSE = √(p(1 − p) ÷ n) = √(0.5 × 0.5 ÷ 1000) = 0.01581
  3. Margin of error = z* × SEME = 0.03099 = ±3.1 percentage points

Formula ME = z* · √(p(1 − p) ÷ n) ME = z* · σ ÷ √n

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

Poll example

A poll of 1,000 voters finds 52% support. At 95% confidence: ME = 1.96 × √(0.52 × 0.48 ÷ 1000) ≈ 0.031, so ±3.1 percentage points. The true support is plausibly anywhere from 48.9% to 55.1%.

Margin of error shrinks with the square root of the sample: to halve it you need four times as many respondents.

What it does not cover

The margin of error only accounts for random sampling variation. It does not cover biased samples, leading questions, non-response or people not telling the truth, which can be much larger sources of error.

Frequently asked questions

Why use 50% when I don’t know the proportion?

p(1 − p) is largest at p = 0.5, so it gives the most conservative (largest) margin of error.

When should I use the finite population correction?

When your sample is more than about 5% of the whole population, for example surveying 200 of a school’s 800 students.