The margin of error at 90, 95 or 99% confidence, the margin on the gap between two candidates, subgroup margins and the design effect from weighting
Updated October 2026
A poll interviews a sample instead of everyone, so its percentages wobble from sample to sample. The margin of error says how far a result is likely to sit from the value you would get by asking the whole population, at a stated confidence level, usually 95%. It covers sampling error only, and only for probability samples where everyone has a known chance of selection, as AAPOR’s explainer stresses.
The margin is in percentage points, not percent: a 48% result ±3 points means 45% to 51%.
| Sample size | 90% | 95% | 99% | 95%, design effect 1.5 |
|---|---|---|---|---|
| 100 | ±8.2 | ±9.8 | ±12.9 | ±12.0 |
| 200 | ±5.8 | ±6.9 | ±9.1 | ±8.5 |
| 400 | ±4.1 | ±4.9 | ±6.4 | ±6.0 |
| 600 | ±3.4 | ±4.0 | ±5.3 | ±4.9 |
| 800 | ±2.9 | ±3.5 | ±4.6 | ±4.2 |
| 1,000 | ±2.6 | ±3.1 | ±4.1 | ±3.8 |
| 1,067 | ±2.5 | ±3.0 | ±3.9 | ±3.7 |
| 1,500 | ±2.1 | ±2.5 | ±3.3 | ±3.1 |
| 2,000 | ±1.8 | ±2.2 | ±2.9 | ±2.7 |
| 3,000 | ±1.5 | ±1.8 | ±2.4 | ±2.2 |
| 5,000 | ±1.2 | ±1.4 | ±1.8 | ±1.7 |
| 10,000 | ±0.8 | ±1.0 | ±1.3 | ±1.2 |
The margin shrinks with the square root of the sample size, so quadrupling the sample only halves it. That is why most national polls stop around 1,000 to 1,500 interviews. Pew Research Center’s Andrew Mercer uses 1,067 as the sample that gives ±3 points; AAPOR notes that doubling from 1,000 to 2,000 cuts the margin by only about one point.
| Reported percentage | n = 1,000 | n = 400 |
|---|---|---|
| 50% | ±3.1 | ±4.9 |
| 40% | ±3.0 | ±4.8 |
| 30% | ±2.8 | ±4.5 |
| 20% | ±2.5 | ±3.9 |
| 10% | ±1.9 | ±2.9 |
| 5% | ±1.4 | ±2.1 |
Pollsters quote the margin at 50%, its largest value, so results near 10% or 90% are a little more precise than the headline margin suggests.
When one candidate gains a point in a sample, the other usually loses one, so the gap moves twice as much as either share. The margin on the difference between two candidates in the same poll is z × √((p₁ + p₂ − (p₁ − p₂)²) ÷ n). Pew’s example: a candidate ahead 48% to 43% in a poll with a ±3-point margin has a margin of about 6 points on the 5-point lead, so the true lead could be anywhere from about −1 to +11.
| Poll of 1,000 | Lead | Margin on each share | Margin on the lead | Lead outside the margin? |
|---|---|---|---|---|
| 48% vs 43% | 5 | ±3.1 | ±5.9 | No |
| 50% vs 45% | 5 | ±3.1 | ±6.0 | No |
| 46% vs 44% | 2 | ±3.1 | ±5.9 | No |
| 40% vs 30% | 10 | ±3.0 | ±5.1 | Yes |
| 52% vs 40% | 12 | ±3.1 | ±5.9 | Yes |
Comparing the lead with the headline margin (“5 points, more than the ±3-point margin”) is the most common misreading of polls. Comparing two polls is noisier still: Pew calculates that a 3-point change in a lead between two such polls has a margin of about ±8 points.
The headline margin applies to the full sample only. AAPOR’s example: in a poll of 1,000 adults with a ±3-point margin, results for a subgroup of 200 carry ±6.9 points. Pew’s: a group that makes up 15% of adults is about 160 interviews, ±8 points on each candidate and ±16 on the gap between them. Enter the subgroup’s share to see its margin.
Pollsters weight their samples to match the population on age, education, region and other traits. Weighting fixes bias but costs precision. The design effect measures that cost: the margin is multiplied by its square root, and the poll behaves like a simple random sample of n ÷ design effect people. A Pew Research Center survey of 6,224 people with a design effect of 1.25 reported a ±1.4-point margin, which the calculator reproduces. Good pollsters say whether their published margin includes the design effect.
It uses the normal approximation for a simple random sample, adjusted by the design effect you enter. It does not compute exact margins from survey weights, handle stratified or clustered designs directly, or model non-sampling error. For planning a survey’s size, use the sample size calculator.