BYTETOOLS

Margin of Error Calculator

Calculate the margin of error for a survey or sample: z × √(p(1−p)/n) for proportions or z × σ/√n for means, with finite population correction.

± 3.099%
Margin of error

Resulting confidence interval

46.901%
Lower bound
53.099%
Upper bound
1.5811%
Standard error
1.96
z critical value

MoE = z × √(p̂(1−p̂)/n).

What is the Margin of Error Calculator?

The ByteTools Margin of Error Calculator reports how much your survey or sample result could differ from the true population value.

  • Proportion and mean modes with the correct formula for each
  • Finite population correction applied when N is given
  • Shows the resulting confidence interval, not just the ± figure
  • Standard confidence levels plus custom levels
  • Accepts the proportion as a percentage or decimal
  • 100% private — everything computed in your browser

How to use the Margin of Error Calculator

  1. 1

    Choose proportion mode (survey percentages) or mean mode (measured averages).

  2. 2

    Enter your sample size n and the observed proportion or standard deviation.

  3. 3

    Pick a confidence level — 95% is the standard choice.

  4. 4

    Optionally enter the population size for the finite correction.

  5. 5

    Read the margin of error and the resulting confidence interval.

About the Margin of Error Calculator

The ByteTools Margin of Error Calculator reports how much your survey or sample result could differ from the true population value. For proportions it computes MoE = z × √(p̂(1−p̂)/n); for means it computes MoE = z × σ/√n — where z is the critical value for your confidence level and n is your sample size.

If you know the total population size, the finite population correction √((N−n)/(N−1)) is applied automatically, tightening the margin when your sample is a large slice of a small population. The output also shows the resulting confidence interval around your observed result.

It is the exact reverse of our Sample Size Calculator: instead of asking how many responses you need, it tells you how precise the responses you already have actually are. Everything runs 100% locally in your browser — no data is uploaded or stored.

Frequently asked questions

How do you calculate margin of error?

For a proportion, MoE = z × √(p(1−p)/n). A survey of 1,000 people with a 50% result at 95% confidence gives 1.96 × √(0.25/1000) ≈ 0.031, or about ±3.1 percentage points. This tool applies the formula and shows the interval.

What does a margin of error of ±3% mean?

If your survey says 47% with a ±3% margin at 95% confidence, the true population figure plausibly lies between 44% and 50%. It quantifies sampling uncertainty only — it says nothing about biased questions or unrepresentative samples.

How does sample size affect the margin of error?

The margin shrinks with the square root of the sample size: quadrupling n halves the margin of error. Going from 100 to 400 respondents cuts roughly ±9.8% to ±4.9% for a 50% result at 95% confidence.

When does the finite population correction matter?

When your sample is more than about 5% of the population. Surveying 300 people from a company of 600 makes the effective margin noticeably smaller than the uncorrected formula suggests. For large populations the correction is negligible.

Is margin of error the same as standard error?

They are related but not identical. The standard error is the standard deviation of the sampling distribution; the margin of error is the standard error multiplied by the critical value for your confidence level (1.96 at 95%). The tool reports both.

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