Estimate the margin of error and confidence interval for a sample proportion in a survey or poll.
Sample Size (n) — Value for sample size (n). Provide accurate numbers for a reliable Margin of Error (±). Example: 100.
Observed Proportion (p̂) (%) — Value for observed proportion (p̂) in %. Provide accurate numbers for a reliable Margin of Error (±). Example: 50 %.
Confidence Level (%) — Value for confidence level in %. Provide accurate numbers for a reliable Margin of Error (±). Example: 95 %.
Margin of Error (±)
9.8%
Margin of Error (±) — Percentage %. Above 0 increases with input; compare to benchmarks or goals.
Lower Bound
40.2%
Lower Bound — Percentage %. Above 0 increases with input; compare to benchmarks or goals.
Upper Bound
59.8%
Upper Bound — Percentage %. Above 0 increases with input; compare to benchmarks or goals.
Standard Error
5%
Standard Error — Percentage %. Above 0 increases with input; compare to benchmarks or goals.
Critical Value (z)
1.9600
Critical Value (z) — Calculated outcome. Derived from your inputs via the displayed formula; use to plan.
What this means
Use the observed proportion p̂ and the sample size n to compute the standard error, then multiply by the critical z-value for the confidence level (e.g. 1.96 for 95%). The confidence interval is p̂ minus and plus the margin of error, clipped to stay within 0–100%.
The margin of error expresses how much a sample proportion could differ from the true population proportion. It is the half-width of the confidence interval at your chosen confidence level.
Formula
MOE = z · √(p̂(1 − p̂) ÷ n); CI = p̂ ± MOE
Worked examples
FAQ
What is the "rule of 1000" in polling?
A sample of roughly 1,000 respondents at 95% confidence typically yields a margin of error around ±3%, which is the standard reported in national surveys.
Why do I multiply p̂ by 100?
p̂ is entered as a percentage; internally the tool uses the decimal form 0–1 for the formula and converts the margin of error back to percentage points.