Margin of Error Calculator
Enter your sample size and confidence level. Get the margin of error for your survey results, with the range around any percentage.
Completed responses to the question you are reporting.
Leave at 50% for the margin usually quoted for a whole survey.
Only matters when your sample is a large share of the population.
Margin of error
At 95% confidence, a result of 50% is likely between 45.1% and 54.9%.
Three inputs, one number:
Sample size
How many completed responses you have. Count only the people who answered the question you are reporting, not everyone you invited.
Confidence level
How sure you want to be that the true value falls inside the range. 95% is the research standard. Use 99% for high-stakes decisions and 90% for exploratory work.
Your result
The percentage you want to check, such as 60% said yes. Leave it at 50% for the widest, safest margin, which is the one usually quoted for a whole survey.
The margin of error formula
Margin of error = z × √(p × (1 − p) ÷ n)
z is the score for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is your result as a decimal and n is the sample size. Worked example at 95% with 400 responses and a result of 50%: 1.96 × √(0.5 × 0.5 ÷ 400) = 0.049, or 4.9 points.
For a small population of N people, multiply by √((N − n) ÷ (N − 1)). With 400 responses from a population of 2,000, the 4.9 points become 4.4.
Margin of error by sample size
For a result of 50% and a large population.
| Sample size | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| 100 | ±8.2 | ±9.8 | ±12.9 |
| 200 | ±5.8 | ±6.9 | ±9.1 |
| 400 | ±4.1 | ±4.9 | ±6.4 |
| 600 | ±3.4 | ±4.0 | ±5.3 |
| 1,000 | ±2.6 | ±3.1 | ±4.1 |
| 2,000 | ±1.8 | ±2.2 | ±2.9 |
Common questions
How do you calculate margin of error?
Multiply the z-score for your confidence level by the square root of p × (1 − p) ÷ n, where p is your result as a decimal and n is the sample size. At 95% confidence with 400 responses and a result of 50%, that is 1.96 × 0.025, or 4.9 points.
What is a good margin of error for a survey?
Plus or minus 5 points at 95% confidence is the common standard, and it takes about 385 responses. Plus or minus 3 points is used when a decision is expensive to get wrong, and it takes about 1,068.
Why use 50% if my result is different?
A result of 50% gives the widest margin, so it is the safe figure to quote for a whole survey. Results closer to 0% or 100% have smaller margins. Enter your actual percentage to see the margin for one specific result.
Does population size change the margin of error?
Only when your sample is a large share of the population. If you surveyed 400 of 2,000 people, the margin shrinks from 4.9 to 4.4 points. For a population in the tens of thousands or more, it makes almost no difference.
What is the difference between margin of error and confidence interval?
The margin of error is the plus-or-minus figure. The confidence interval is the range you get when you apply it: a result of 60% with a margin of 5 points has a confidence interval of 55% to 65%.
How do I get a smaller margin of error?
Collect more responses. The margin falls with the square root of the sample size, so you need four times the responses to halve it. Use the sample size calculator to find how many you need for a target margin.