Margin of Error Calculator

MOE = z × √[p(1−p)/n] for a simple proportion. Click any i for detail.

Sample & confidence

Sample size n i n Number of respondents.
Proportion p̂ (0–1) i p Sample proportion as a decimal (0.5 = 50%).
Confidence level i Conf Maps to z: 90→1.645, 95→1.96, 99→2.576.

How to use this calculator

Enter sample size n.
Enter proportion p as a decimal 0–1.
Choose confidence level.
Read MOE and percentage-point form.

Results explained

For a simple random sample proportion, approximate MOE is z times the standard error √[p(1−p)/n]. Design effects, finite populations, and clustering are ignored.

Quick reference: proportion MOE

MOE = z √[p(1−p)/n].

Item	Detail
95% z	1.96
99% z	2.576
p=0.5	Largest SE for fixed n
Larger n	Smaller MOE

SRS assumption — polls with weighting differ.

How the estimate is built

MOE = z × sqrt(p×(1−p)/n).

Example scenario

n=1000, p=0.5, 95% → MOE ≈ 0.031 (±3.1 pp).

FAQ

Enter 50% as p?

Use 0.5, not 50 — the field is 0–1.

Means, not proportions?

Different SE — see sample-size tools.

Finite population?

Apply FPC separately if n is large vs N.

See sample size?

Yes — solves for n given E.