Free tool
Margin of error calculator
A free margin of error calculator for surveys. Enter your number of responses and confidence level to see how far a result could be from the true figure.
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What the margin of error tells you
When 62% of the people who answered your survey say yes, the true figure for everyone you could have asked is probably not exactly 62%. The margin of error says how far from it the true figure is likely to be. "62%, ±4%" means the real answer is probably between 58% and 66%.
It depends on:
- How many responses you have. More responses mean a smaller margin.
- The confidence level. At 95%, the true figure falls inside the margin 95 times in 100.
- The result itself. Results near 50% have the widest margin. Results near 0% or 100% have narrower ones. Leave it at 50% for the most cautious figure.
- The population size, if you surveyed a large share of a small group.
How it's calculated
The margin of error is z × √(p(1 − p) ÷ n), where z is 1.645, 1.96 or 2.576 for 90%, 95% or 99% confidence, p is the result as a fraction and n is the number of responses. When you know the population N and your sample is a large part of it, multiply by √((N − n) ÷ (N − 1)).
A worked example
With 400 responses, a result of 50% and 95% confidence, the margin of error is 1.96 × √(0.25 ÷ 400) = ±4.9%. With 1,600 responses it halves, to about ±2.5%. To halve the margin, you need four times the responses.
In Excel or Google Sheets
With the number of responses in B1, the z-score in B2 and the result as a decimal in B3:
=ROUND(B2 * SQRT(B3 * (1 - B3) / B1) * 100, 1)
Collect the responses first
Free survey templates
Free survey templates for customer feedback, NPS, CSAT, employee pulse checks, events and research. Each runs live on its page, with unlimited responses.
Questions people ask
Is a ±5% margin of error good enough?
For most decisions, yes. It's the most common target for surveys. If two options are within a few points of each other, you'll need a smaller margin to tell them apart.
Does the margin of error cover every kind of error?
No. It only covers the chance of drawing an unlucky sample. It can't account for a biased sample, a leading question, or people who chose not to answer.
How many responses do I need for a given margin?
Work backwards with the sample size calculator. It tells you how many responses a margin needs, and how many people to invite.
Where can I run a survey for free?
hootform's survey templates ask one question at a time, which helps more people finish, with unlimited responses on the free plan.
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- CES calculator A free customer effort score (CES) calculator. Enter counts for each score from 1 to 7, or paste raw scores, for your average and the share who found it easy.
- Survey sample size calculator A free survey sample size calculator. Enter population, confidence level and margin of error to see how many responses you need and how many to invite.
- Response rate calculator A free survey response rate calculator. Enter how many people you invited, started and finished to get your response, completion and start rates.