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Margin of error calculator

Find the margin of error and confidence interval for any survey result. Enter your sample size, confidence level and, if you know it, the population size.

Enter the share of respondents who gave an answer (for example 62% said “Yes”). Leave it at 50% for the most conservative, worst-case margin of error. Everything runs in your browser; nothing is sent or stored.

Margin of error

±4.9%

at 95% confidence (z = 1.96) with n = 400.

95% confidence interval

45.1% to 54.9%

An observed result of 50.0% means the true population value is likely between 45.1% and 54.9%.

Exact value
±4.90%

The margin of error is the range, above and below a survey result, within which the true population value is likely to fall at a chosen confidence level. It shrinks as your sample grows and is the “±” you see next to poll results. A confidence interval is that range written out, and its two ends are the confidence limits.

How to use the margin of error calculator

  1. Enter your sample size: Type the number of completed responses (n) you collected or plan to collect.
  2. Pick a confidence level: Choose 90%, 95% or 99%. 95% is the standard choice for most surveys and polls.
  3. Add the population size (optional): If you surveyed a known, limited group such as 2,000 customers or 300 employees, enter it to apply the finite population correction. Leave it blank for large or unknown populations.
  4. Enter the observed percentage: Type the share of respondents who chose an answer, or keep 50% for the worst-case margin of error.
  5. Read the margin and interval: The calculator shows the margin of error (±%) and the confidence interval, the range where the true value most likely falls.
Hand-drawn line chart on grid paper next to a steel ruler and pens

The margin of error formula

MOE = z × √(p × (1 − p) ÷ n)

  • z is the z-score for your confidence level: 1.645 for 90%, 1.96 for 95% and 2.576 for 99%.
  • p is the observed (or expected) proportion as a decimal, for example 0.62 for 62%. Use 0.5 if you don’t know it yet.
  • n is the number of completed responses.

The square-root part, √(p × (1 − p) ÷ n), is the standard error of a proportion. When you survey a known, limited population of size N, multiply the result by the finite population correction √((N − n) ÷ (N − 1)). It matters when your sample is a meaningful share of the group, such as 150 out of 400 employees.

The confidence interval is then p − MOE to p + MOE. This is the standard normal-approximation (Wald) interval used for survey percentages; it works well when you have at least 10 responses on each side of the answer.

Worked example

You survey 400 customers and 62% answer “Yes” to “Would you buy from us again?”. At 95% confidence:

  1. Standard error: √(0.62 × 0.38 ÷ 400) = √0.000589 ≈ 0.0243.
  2. Margin of error: 1.96 × 0.0243 ≈ 0.0476, so ±4.8%.
  3. Confidence interval: 62% − 4.8% to 62% + 4.8%, so 57.2% to 66.8%.

If those 400 customers came from a customer base of only 2,000, the finite population correction is √(1,600 ÷ 1,999) ≈ 0.895, and the margin of error drops to about ±4.3%.

Margin of error by sample size

Worst-case margin of error (p = 50%) for a large population:

Margin of error by sample size and confidence level, p = 50%
Responses (n)90%95%99%
100±8.2%±9.8%±12.9%
200±5.8%±6.9%±9.1%
300±4.7%±5.7%±7.4%
400±4.1%±4.9%±6.4%
500±3.7%±4.4%±5.8%
1,000±2.6%±3.1%±4.1%
1,500±2.1%±2.5%±3.3%
2,000±1.8%±2.2%±2.9%
5,000±1.2%±1.4%±1.8%

How sample size relates to the margin of error

The margin of error falls with the square root of the sample size. Doubling your responses does not halve the margin; you need about four times as many responses to cut it in half. Going from 100 to 400 responses takes you from roughly ±9.8% to ±4.9%, but getting to ±2.5% takes about 1,500.

That is why most surveys aim for a practical target, often ±5% at 95% confidence, which needs about 385 completed responses from a large population. To work backward from the margin you want to the number of responses you need, use the survey sample size calculator.

Choosing a confidence level

The confidence level is how sure you want to be that the interval contains the true value. 95% is the convention for most surveys and polls. 90% gives a narrower interval and suits quick internal pulse checks. 99% gives a wider interval and suits decisions where being wrong is costly. Pick the level before you look at the results, and report it next to the margin of error.

Margin of error for subgroups

The margin of error applies to the group you are describing. If 400 people answered overall but only 120 of them are on the Sales team, results for Sales carry a margin of about ±8.9% (95%, p = 50%), not ±4.9%. Plan subgroup sample sizes separately if you need to compare segments.

What the margin of error doesn’t tell you

  • Question wording: leading or double-barreled questions bias answers no matter how many people respond.
  • Non-response: if the people who skip your survey differ from those who answer, the result is skewed. Florm’s partial responses show where respondents drop off so you can shorten the survey.
  • Coverage: a survey sent only to newsletter subscribers describes subscribers, not all customers.

Scoring Net Promoter Score? NPS is a difference of two percentages, so its margin is wider than a single percentage. The NPS calculator shows the NPS-specific margin of error in points.

Collect responses with Florm

Florm’s online survey maker shows views, completions and drop-off for every survey, so you can see how close you are to your target sample size while responses come in. Export the results to Excel or PDF and plug the counts into this calculator.

Margin of error calculator FAQ

What is the margin of error in a survey?

The margin of error tells you how far a survey result may be from the true value in the whole population because you only asked a sample. A result of 62% with a ±4.8% margin of error at 95% confidence means the true share is likely between 57.2% and 66.8%.

How do you calculate the margin of error?

Multiply the z-score for your confidence level by the standard error of the proportion: MOE = z × √(p × (1 − p) ÷ n). For a known, limited population N, multiply the result by the finite population correction √((N − n) ÷ (N − 1)).

What is the margin of error for 400 responses?

About ±4.9% at 95% confidence, assuming a 50% result and a large population: 1.96 × √(0.5 × 0.5 ÷ 400) = 0.049. At 90% confidence it is ±4.1%, and at 99% it is ±6.4%.

What is the difference between a margin of error and a confidence interval?

The margin of error is the ± amount. The confidence interval is the range it creates around your result: observed percentage minus the margin of error to observed percentage plus the margin of error. The lower and upper ends are called confidence limits.

Why does the calculator use 50% by default?

p × (1 − p) is largest when p is 50%, so 50% gives the widest, most conservative margin of error. Polls usually report this worst-case figure. If you know the observed percentage, enter it to get the exact interval for that answer.

Does a bigger population need a bigger sample?

Only up to a point. Once the population is much larger than the sample, its size barely matters: 400 responses give about ±4.9% whether the population is 100,000 or 100 million. The finite population correction only makes a noticeable difference when you survey a sizable share of a small group.

What does the margin of error not cover?

It only covers random sampling error. It does not account for biased question wording, people who chose not to respond, or a sample that doesn’t represent the population. A well-designed questionnaire matters as much as the number of responses.

Does this calculator store my data?

No. All calculations run in your browser. Nothing you enter is sent to Florm or stored.

Related

Sample size calculatorHow many responses you need for a target margin.NPS calculatorScore, breakdown and NPS margin of error.Online survey makerCreate and share surveys with Florm.

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