What is the margin of error?
The margin of error is the plus-or-minus range around a survey result, such as 62% ±5%, within which the true value for your whole audience likely falls. It shrinks as more people answer, and it is usually given at 95% confidence.
Margin of error in plain terms
A survey asks some of your customers and uses their answers to describe all of them. Chance decides who happens to answer, so the result can land a little above or below the true value. The margin of error puts a size on that uncertainty. If 62% of the people who answer say yes, with a margin of ±5%, the true share for your whole audience likely sits between 57% and 67%.
The word likely carries a number, the confidence level. At 95% confidence, if you ran the same survey many times with new samples, about 95 of every 100 ranges would contain the true value. A higher confidence level gives a wider range for the same answers.
The margin of error matters most when you compare. A share that moved from 60% to 63% with a margin of ±5% may not have moved at all. Knowing the margin keeps your team from reacting to noise.
- Written as
- ± a number of points, such as ±4.9%
- Depends on
- The number of answers, the result itself and the confidence level
- Usual level
- 95% confidence
- Covers
- Random sampling error only
- Shrinks with
- More answers: four times the sample halves it
How to calculate the margin of error
For a share of answers, such as the share who said yes, multiply the z value for your confidence level by the standard error of that share. At 95% confidence, z is 1.96, at 90% it is 1.645 and at 99% it is 2.576.
The margin is largest when the share is 50%, so many surveys quote that worst case. When your audience is small and a large part of it answered, the second line, the finite population correction, makes the margin smaller.
MOE = z × √(p × (1 − p) ÷ n)
Small population: MOE × √((N − n) ÷ (N − 1))
z is 1.96 at 95% confidence, p is the share as a decimal, n is the number of answers and N is the population size.
A margin of error example
Say 400 customers answer “Would you pay for same-day delivery?” and 240 of them, 60%, say yes. The standard error is the square root of 0.6 × 0.4 ÷ 400, about 0.0245. Multiplied by 1.96, that gives a margin of about ±4.8%.
So between 55.2% and 64.8% of your customers would likely pay for it, at 95% confidence. To get the margin down to ±2.4%, you would need four times as many answers, about 1,600.
- Answers
- 400
- Said yes
- 240, which is 60%
- Standard error
- √(0.6 × 0.4 ÷ 400) ≈ 0.0245
- Margin at 95%
- 1.96 × 0.0245 ≈ ±4.8%
- Likely range
- 55.2% to 64.8%
What is a good margin of error?
For most business surveys, ±5% at 95% confidence is a common target, and it takes about 385 answers from a large audience. ±3% suits decisions where a few points matter, such as pricing, and needs about 1,068 answers. ±10% needs only 97 answers and is enough to see which way a large group leans.
Pick the margin before the survey, from the smallest change you need to see. If a 3-point drop in satisfaction would change what your team does, a margin of ±5% can't show it.
Margin of error when comparing two results
When you compare two results, such as this month and last month or mobile and desktop, each one has its own margin, and the difference between them is less certain than either result alone. Ranges that don't overlap point to a real difference. Ranges that overlap a little may still hide one, so run a significance test before you decide.
Filtering to one device or one country also leaves fewer answers behind each number, so the margin for that group is wider than the margin for everyone.
What the margin of error doesn't cover
The margin of error measures only the chance of who happened to answer. It says nothing about a leading question, a survey shown only to happy customers or people who skip a question, and those errors don't shrink with more answers.
- Leading or loaded question wording
- Asking only one kind of customer, such as the ones who stayed
- A low response rate where the people who answer differ from the rest
- Answers given in a hurry to get past the survey
Margin of error in Usertick
Every number on Results comes with the answers behind it. Each question card shows its answer count, and a score that rests on fewer than 30 answers says how many it has. Enter the count and the share into the margin of error calculator to see the range around any result.
When Usertick compares results, it accounts for chance itself. The variant comparison names a difference only when it is clear at 95% confidence with at least 30 answers on each side. The Audience tab shows a group's score from 5 answers, and flags a group as clearly lower only when it has at least 20 answers and sits 8 NPS points, or 8% of the scale, below the overall score.
Filters by date, country, device, language, page and answers narrow Results to one group, so you can check how many answers that group has before you read its score.
Mistakes to avoid with the margin of error
Small choices that keep the results useful.
- 01
Quoting one margin for every group
The margin for all answers is far smaller than the margin for one country or one plan. Work out the margin for each group you report.
- 02
Treating small moves as real change
A 2-point change inside a ±5% margin is most likely noise. Wait for more answers or a larger move before you act.
- 03
Leaving out the confidence level
A margin means little without its confidence level. Say ±4.9% at 95% confidence, and use the same level every time.
- 04
Expecting it to catch bias
A biased question or a skewed audience stays wrong however many people answer. Fix the wording and who you ask first.
Frequently asked questions
Answers vary most when the split is even, so chance moves the result most there. Quoting the margin at 50% gives the worst case for any question in the survey.
About 385 from a large audience at 95% confidence. A smaller audience needs fewer, such as 323 when you have 2,000 customers.
Yes, and it is wider than for a single share, because NPS subtracts one share from another. Say 400 customers answer with 55% promoters and 20% detractors: the score of 35 carries a margin of about ±8 points at 95% confidence.
The confidence interval is the full range, such as 55.2% to 64.8%. The margin of error is half its width, the ±4.8% you add to and subtract from the result.
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