Margin of Error Calculator

Estimate a normal-approximation margin of error for a mean or proportion at common confidence levels

Your result will appear here.

About the Margin of Error Calculator

Margin of Error Calculator estimates the plus-or-minus distance around a sample estimate for a chosen confidence level. It is commonly used with survey proportions and sample means.

The margin of error describes sampling uncertainty under the statistical model. It does not capture bias from poor sampling, nonresponse, measurement errors or misleading questions.

How to Use the Margin of Error Calculator

  1. Enter the standard error or the inputs needed to calculate it.
  2. Choose the confidence level.
  3. Select the appropriate z or t critical value method when supported.
  4. Calculate the margin of error and combine it with the sample estimate to form an interval.

How the Calculation Works

Margin of error = critical value × standard error.

For a common large-sample 95% normal interval, the critical z value is about 1.96. Other confidence levels or small-sample mean problems can require different critical values.

Worked example

Margin of Error Calculator Worked Example

Standard error 2.5 at 95% confidence

Using z≈1.96, margin of error = 1.96×2.5 = 4.9. An estimate of 60 would therefore have a simple interval of about 55.1 to 64.9.

Result guide

Understanding Your Margin of Error Calculator Result

A larger margin of error means less precision. Raising the confidence level generally widens the margin when sample information stays the same. Sample size is one of the main controllable drivers of margin of error. For many common designs, reducing the margin by half requires roughly four times the sample size when other assumptions stay the same.

Before you rely on the answer

Assumptions and Limitations

  • The selected critical value matches the statistical method.
  • Standard error is calculated correctly.
  • Sampling bias and non-sampling errors are not represented.

Practical tip

Using This Result in Practice

A very small margin of error does not rescue a biased sample. Precision and representativeness must be evaluated separately.

Related calculations

Useful Calculations to Continue With

If you first need the sampling standard error, use the Standard Error Calculator.

If you want the full lower and upper interval rather than only the half-width, use the Confidence Interval Calculator.

Authoritative references

Useful Official Sources

For standards, definitions or real-world guidance related to this calculation, these primary sources may be useful:

Common questions

Margin of Error Calculator FAQ

What is margin of error?

The critical value multiplied by standard error, giving the plus-or-minus width around an estimate.

Does higher confidence increase margin of error?

Yes, with the same sample data, a higher confidence level uses a larger critical value.

Does margin of error include survey bias?

No. It mainly reflects sampling variability under the chosen model.