Margin of Error Calculator

What is a margin of error?

A margin of error estimates how much a survey percentage may differ from the true percentage in the population because only a sample was asked. It is usually shown as a plus-or-minus amount around the survey result.

This margin of error calculator uses the confidence level, sample size, and result being measured. It applies the formula MOE = z x square root of (p (1 - p) / n), with a finite population correction if you enter a population size. Here, p is the measured proportion and n is the number of responses. The result is most useful when the survey uses a sound sampling method.

Why margin of error matters

A survey estimate can influence decisions about pricing, hiring, product changes, or where to spend a budget. The margin helps you judge how much confidence to place in a reported percentage before acting on it.

A smaller margin means a narrower range around the estimate, but it does not guarantee the survey is accurate. The calculation does not account for biased questions, people who do not respond, or a sample that leaves out part of the population. Review how the survey was collected as well as its margin.

How to use this margin of error and sample size calculator

1. Enter the number of completed responses, not the number of people invited.
2. Choose the confidence level. The calculator offers 90%, 95%, or 99%. A higher confidence level generally produces a wider margin when the other inputs stay the same.
3. Enter the result being measured as a percentage. For example, use 50 for a survey result of 50%.
4. Enter the population size if you know it and the survey covers a defined group. Leave it at 0 when treating the population as very large.
5. Enter your target margin to estimate the sample size needed. Use the result to plan how many completed responses to seek.

Margin of error calculator example

How to read your results

The margin is the amount to add to and subtract from your measured result to form the displayed range. In the example, the result is 50% and the margin is ±3.1%, so the range runs from 46.9% to 53.1%.

The confidence level describes the method, not the chance that a particular survey result is correct. If the same sampling process were repeated many times, the stated confidence level refers to how often the resulting ranges would contain the population value. A margin of error does not cover other sources of survey error.

How to reduce your margin of error

1. 01

   Collect more completed responses

   A larger sample generally narrows the margin when the confidence level and other inputs stay the same. Use the calculator’s sample-size result to plan outreach, then track completed responses rather than invitations.

2. 02

   Set a realistic target

   Enter the margin you need before collecting responses. If the required sample is hard to reach, consider whether a wider margin still supports the decision, or whether you can extend the survey period.

3. 03

   Use a representative sampling process

   Invite people from the population you want to understand, and make the question clear and neutral. A bigger sample cannot fix a survey that systematically misses customers, employees, or other groups.

4. 04

   Choose the confidence level deliberately

   A lower confidence level can produce a narrower margin, while giving less confidence in the range. Compare the available levels and choose one that fits the decision rather than selecting a level just to make the result look more precise.

Common margin of error mistakes

• Counting invitations instead of responses

  The formula uses the sample size that actually answered. Invitations that receive no response do not count toward that total.

• Treating the range as a guarantee

  The range describes sampling uncertainty under the method’s assumptions. It does not account for a biased sample, unclear wording, or inaccurate answers.

• Entering the wrong result format

  Enter a percentage such as 50 for a 50% result. The formula uses the corresponding proportion.

• Ignoring population size when it is known

  For a survey of a defined, limited population, enter its size so the calculator can apply a finite population correction. Use 0 when treating the population as very large.

The margin of error formula

Key terms

Margin of error

The plus-or-minus amount around a survey estimate that represents sampling uncertainty under the calculation’s assumptions.

Confidence level

The stated confidence associated with a method for producing ranges across repeated samples.

Finite population correction

An adjustment to the margin when the survey draws responses from a known, limited population.

Sample size

The number of completed responses included in the survey calculation.