How wide is your confidence interval?
Your sample gives you an estimate. This calculator tells you the ± window around it, the range any honest report has to publish alongside the headline number.
Your survey
Confidence level
At 95% confidence, your true value sits between 45.1% and 54.9%.
Lower bound
Estimate
Upper bound
How it works
Margins don't disappear, they just get hidden
Every survey estimate is wrong. The useful question is how wrong, and in which direction could it be wrong. The margin of error answers both: it's the ± radius around your estimate at a chosen confidence level.
If 62% of 500 respondents say yes, the margin at 95% confidence is roughly ±4.3%. The true proportion is somewhere between 57.7% and 66.3%, not the clean "62%" you'd prefer to put on a slide.
Methodology
The standard-error formula
Formula
MoE = z · √(p(1 − p) / n) · √((N − n) / (N − 1))
- z
- Z-score for your confidence level (1.96 for 95%).
- p
- Observed proportion, as a decimal.
- n
- Sample size, the respondents you actually have.
- N
- Population size. The second √ term is the finite-population correction; it only matters when your sample is a big slice of the population.
Reporting tips
What to print, what to skip
- 1
A ±5% margin is the newsroom default. Enterprise research teams target ±3% or tighter.
- 2
Report the margin next to every survey stat you share. A 62% approval with no margin is marketing copy, not data.
- 3
Margin shrinks with the square root of the sample. To halve your margin, you need 4× the responses.
- 4
At p = 0.5 the margin is maximized. If your actual proportion is 80/20 or 90/10, the real margin is smaller than the worst-case figure.
- 5
Small subgroups in your survey have their own (much wider) margins. "Women 18 to 24" in a 500 person survey is a footnote, not a conclusion.
Run the math once. Run the form forever.
Try WittyForm freeMore calculators