Statistics
Margin of Error Calculator
Enter a sample proportion or mean with the sample size and confidence level to get the margin of error and the resulting confidence interval.
Add a population size for the finite population correction, choose t instead of z for small samples of a mean, or flip to reverse mode to find the sample size that hits a target margin.
Use 50% when unknown; it gives the largest (safest) margin.
Leave 0 for a very large or unknown population. Otherwise the finite population correction shrinks the margin.
Try an example
Result
Result
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- Confidence interval
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- Critical value
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- Standard error
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- Finite population correction
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Study path
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What the margin of error calculator solves
Enter a A smaller group taken from a population, used to estimate facts about the whole group. proportion or mean with the sample size and confidence level to get the margin of error and the resulting A range of values that probably contains the true answer, given your data.. Add a Every member of the group you actually care about, not just the ones measured. size for the finite population correction, choose t instead of z for small samples of a mean, or flip to reverse mode to find the sample size that hits a target margin.
Formula
How to use it
- Choose proportion for percentages (polls, yes/no questions) or mean for measured quantities.
- Enter the sample statistic, the sample size, and the confidence level. Add N only if the population is small enough that sampling a noticeable fraction of it matters.
- For a mean, use t when the A number saying how far, on average, the data values sit from the mean. came from the sample, z when σ is known.
- Reverse mode: enter the margin you want and read the sample size (rounded up).
How to read the answer
A margin of error of ±3% at 95% confidence means the interval statistic ± 3% would capture the true population value in about 95% of repeated samples. Larger samples and lower confidence levels shrink the margin; the margin falls with the square root of n, so quadrupling the sample halves it. The finite population correction only matters when n is a sizeable fraction of N.
Common mistakes and edge cases
- Entering the proportion as a decimal in the percent field (0.5 instead of 50).
- Using z with a small sample and a sample standard deviation; t gives the honest (wider) margin.
- Reporting the margin without the confidence level; ±3% at 90% is a different claim than ±3% at 99%.
- Applying the finite population correction with the wrong N, or when N is unknown; leave it at 0 in that case.
Worked examples
Poll of 1,000 at 95%
Result
±3.10%
Poll with a finite population
Result
±4.80%
Mean with t, n = 25
Result
±4.9534
Mean with z, 99%
Result
±3.091
Sample size for ±3% at 95%
Result
1068
Sample size for a mean (σ = 15, E = 3)
Result
97
Impossible: sample larger than population
Result
Error
Frequently asked questions
What is the margin of error formula for a proportion?+
E = z* × √(p̂(1 - p̂)/n). With p̂ = 0.5, n = 1000, and z* = 1.96 for 95% confidence, E ≈ 0.031, or ±3.1 percentage points.
Why do polls use 50% for the proportion?+
p̂(1 - p̂) is largest at 0.5, so assuming 50% gives the biggest possible margin. It is the conservative choice when the true proportion is unknown.
How does sample size affect the margin of error?+
The margin shrinks with √n. Going from 400 to 1,600 respondents halves the margin; going from 1,000 to 2,000 only cuts it by about 29%.
When should I use the finite population correction?+
When the sample is more than about 5% of the population. Sampling 300 of 1,200 employees is 25%, so the FPC noticeably shrinks the margin; sampling 1,000 of 300 million people does not need it.
Is the margin of error the same as the confidence interval?+
The margin is half the width of the confidence interval. Interval = statistic ± margin. See the confidence interval calculator for the full interval with more options.
How many people do I need for a ±5% margin?+
At 95% confidence with p̂ = 50%: n = 1.96² × 0.25 / 0.05² ≈ 385. Use the sample-size mode for other margins and confidence levels.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026