How to use the confidence interval for a proportion calculator
Find a confidence interval for a proportion. Enter successes, sample size, confidence level in the fields above; the sample proportion, margin of error, lower bound, upper bound are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- k — Successes
- n — Sample size
- cl — Confidence level (%)
Worked example
With successes = 520, sample size = 1000, confidence level = 95 %, the calculator gives sample proportion ≈ 0.52; margin of error ≈ 0.03096495; lower bound ≈ 0.4890351; upper bound ≈ 0.5509649.
Frequently asked questions
What is the formula for the confidence interval for a proportion calculation?
Sample proportion = k / n. Margin of error = norminv(0.5+cl / 200) × √([Sample proportion] × (1-[Sample proportion]) / n). Lower bound = [Sample proportion]-[Margin of error]. Upper bound = [Sample proportion]+[Margin of error]. Here k is successes, n is sample size, cl is confidence level (%).
What inputs do I need for the confidence interval for a proportion calculator?
You need successes, sample size, confidence level in %. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.