Use this Margin of Error Calculator to estimate the plus-or-minus amount around a sample mean or proportion at a selected confidence level.

Calculation Method

For a population mean:

Margin of error = z × σ ÷ √n

For a population proportion:

Margin of error = z × √[p(1 − p) ÷ n]

A confidence interval is then written as:

Estimate ± margin of error

Example

Suppose a survey has 600 responses, uses 95% confidence, and the estimated proportion is 50%.

MoE = 1.96 × √(0.50 × 0.50 ÷ 600)

MoE ≈ 0.040, or 4.0 percentage points

If the survey estimate is 52%, the approximate confidence interval is:

52% ± 4% = 48% to 56%

Important Note

Margin of error describes sampling uncertainty under the selected formula. It does not include errors caused by biased sampling, nonresponse, poor survey questions, measurement problems, data-entry errors, or complex sampling designs.

Source

• Penn State STAT 500 — Confidence Intervals and Margin of Error