Margin of Error Calculator: Surveys and Polls
This margin of error calculator tells you how far a survey or poll result could be from the true value. Enter the sample size, the result percentage (use 50% if you do not know it, which gives the largest margin) and the confidence level. Add the population size if you surveyed a big share of a small group, such as 300 of 1,200 employees, to apply the finite population correction. You can also find the margin of error for a mean from the standard deviation. Results show the ± margin, the confidence interval and how the margin changes with other sample sizes.
Margin of Error Calculator
Find the margin of error for a survey proportion or a mean, with an optional population size correction.
How to use the Margin of Error Calculator
- Choose proportion (survey %) or mean.
- Enter the sample size and the result.
- Pick the confidence level and, optionally, the population size.
- Read the ± margin of error and the confidence interval.
Margin of error formula
MOE = z × √(p(1 − p) ÷ n) · for a mean, MOE = z × ฯ ÷ √n · with FPC, multiply by √((N − n) ÷ (N − 1))
Features
- Survey proportion or mean
- 90%, 95%, 98% and 99% confidence
- Finite population correction
- Confidence interval
- Table of margins for other sample sizes
Frequently asked questions
What is the margin of error?
It is the range above and below a survey result that likely contains the true population value. A poll at 52% ± 3% suggests the true value is between 49% and 55%.
How do you calculate margin of error?
For a proportion, MOE = z × √(p(1 − p) ÷ n). At 95% confidence z = 1.96, so 1,000 people at 50% give 1.96 × √(0.25 ÷ 1,000) = 3.1%.
What sample size gives a 5% margin of error?
About 385 responses at 95% confidence for a large population, assuming 50%. For ±3% you need about 1,068.
Why use 50% when the result is unknown?
p(1 − p) is largest at p = 0.5, so 50% gives the most conservative, widest margin of error.
What is the finite population correction?
When the sample is more than about 5% of the population, multiply the margin by √((N − n) ÷ (N − 1)). It makes the margin smaller.