Polls report a margin of error so readers know how much the result could differ from the true population value.
How to use the Margin of Error Calculator
- Observed percentage
- Sample size
- Population size (0 = very large)
- Confidence level
Results update as you type, and every field accepts the units shown in its menu.
How it works
Multiply the z value for the confidence level by the standard error of the proportion, then correct for finite populations.
Inputs explained
| Field | What to enter |
|---|---|
| Observed percentage | In % |
| Sample size | A number |
| Population size (0 = very large) | A number |
| Confidence level | Choose one: 90%, 95%, 99% |
What each result means
- z value = ninv(1 – (1 – [Confidence level])÷2)
- Margin of error = [z value]×sqrt([Observed percentage]÷100×(1 – [Observed percentage]÷100)÷[Sample size])×[Finite population correction]×100
- Range from = [Observed percentage] – [Margin of error]
- Range to = [Observed percentage] + [Margin of error]
Example values
How the main result changes when Observed percentage changes and everything else stays at the example values above:
| Observed percentage (%) | Margin of error (± percentage points) |
|---|---|
| 25 | 2.68 |
| 37.5 | 3 |
| 50 | 3.1 |
| 62.5 | 3 |
| 75 | 2.68 |
| 100 | 0 |
Formula
MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))Worked example
Inputs — Observed percentage: 50 %; Sample size: 1,000; Population size (0 = very large): 0; Confidence level: 95%.
Results — z value = 1.96; Margin of error = 3.1 ± percentage points; Range from = 46.9 %; Range to = 53.1 %.
Frequently asked questions
Why do polls of 1,000 people have about ±3%?
At 95% confidence and p = 50%, MOE ≈ 1.96 × √(0.25/1000) ≈ 3.1%.
Does population size matter?
Only when the sample is a sizeable share of the population.
What formula does the Margin of Error Calculator use?
MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1)).