Free margin of error calculator for surveys and polls. Enter sample size, confidence level, and response percentage to get your margin of error and confidence interval.
Your results will appear here.
Enter your values and press Calculate.
The calculator looks up the z critical value for your confidence level (1.96 for 95%), computes the standard error as the square root of p times (1 minus p) divided by the sample size, and multiplies the two to get the margin of error in percentage points. If you enter a population size larger than your sample, it applies the finite population correction factor, which shrinks the margin when your sample is a large slice of a known group. It then adds and subtracts the margin from your response percentage to show the confidence interval bounds.
The margin of error for a survey proportion comes from one compact formula: MOE = Z * sqrt(p(1-p)/n). Z is the critical value for your confidence level (the z score for 95% confidence is 1.96, for 90% it is 1.645, and for 99% it is 2.576). The value p is your response proportion as a decimal (50% becomes 0.5), and n is the number of completed responses in your sample.
Inside the square root, p(1-p)/n is the variance of your sample proportion, and its square root is the standard error. Multiplying the standard error by Z stretches it to the chosen confidence level. Worked example: 1,000 respondents, 50% say yes, 95% confidence. The standard error is sqrt(0.25/1000), about 0.0158, and times 1.96 gives 0.031, a margin of error of about +/-3.1 percentage points.
If your sample is a substantial slice of a known population, multiply by the finite population correction factor sqrt((N-n)/(N-1)), where N is the population size. This correction only helps when you are sampling a meaningful fraction of the group, such as employees of one company or students of one school.
Pick your confidence level first. Most surveys use 95%, which is the standard in market research and social science; choose 99% only when the cost of being wrong is high, and 90% for quick directional polls. Then enter your sample size, which is the number of completed responses, not the number of people you invited.
Enter the response percentage for the answer you are analyzing. If you are still planning the survey and do not have results yet, leave it at 50%, which gives the most conservative, widest margin. Optionally enter your population size. When your sample is more than about 5% of a known population, the calculator applies the finite population correction and your margin shrinks. Click Calculate to see the margin of error, the standard error, the z value used, and the confidence interval bounds.
The margin of error is half the width of your confidence interval. A poll reporting 52% with a margin of error of +/-3 percentage points means the true population value is plausibly anywhere from 49% to 55%. Saying you are 95% confident means that if you repeated the same survey 100 times, about 95 of the resulting intervals would contain the true value; it does not mean there is a 95% chance this specific interval is right.
The interval also settles arguments about poll differences. If one candidate polls 55% with an interval of 49.3% to 60.2% and another polls 40% with an interval of 34.3% to 45.7%, the difference is statistically meaningful because the two intervals do not overlap. If they did overlap, the apparent lead could just be sampling noise.
One caveat: the margin of error only covers random sampling error. Non-response bias, leading questions, a non-representative sample, and data entry mistakes are separate problems that no sample-size math can fix.
The honest lever is sample size: more respondents means a smaller margin. Because the margin shrinks with the square root of the sample size, cutting it in half requires roughly four times as many responses, so gains get expensive fast once you are already at a few thousand.
Lowering the confidence level also shrinks the margin, since a 90% confidence level uses a smaller z value (1.645) than 95% (1.96). But that is a trade-off, not a free lunch: you are now less certain the interval contains the true value. Reducing variability in responses helps too; if nearly everyone answers the same way, the estimate is inherently tighter, which is why results near 0% or 100% have smaller margins than fifty-fifty splits.
For bounded groups, survey a larger fraction of the population so the finite population correction applies. And improve the survey itself: clear unbiased questions and a high response rate reduce the non-sampling errors that the margin of error cannot see.
Conversely, a higher confidence level increases the margin of error, because it uses a larger z value: moving from 90% (z = 1.645) to 95% (z = 1.96) widens the margin by about 19% for the same sample.
The relationship is an inverse square root: margin of error is proportional to 1/sqrt(n). Doubling your sample does not halve the margin; it cuts it by about 30%. This is why tiny polls are so noisy and why huge polls stop improving much after a point.
At 95% confidence with a 50% response, the margins look like this: 50 respondents give about +/-13.9 percentage points, 100 give +/-9.8, 200 give +/-6.9, 500 give +/-4.4, 1,000 give +/-3.1, and 5,000 give +/-1.4. Notice that the first jump, from 50 to 500 responses, buys far more precision than the second, from 1,000 to 5,000.
For very large populations, the population size itself barely matters. A national poll of 1,000 adults has roughly the same margin of error whether the country has 5 million or 300 million people; what matters is the sample size and the confidence level, not the population you are generalizing to.
The standard formula assumes an infinitely large population. That is fine for national polls, but if you survey 200 employees out of a 1,000-person company, you have measured a fifth of the whole group, and the uncertainty is genuinely smaller. The finite population correction (FPC) captures this.
The correction factor is sqrt((N-n)/(N-1)). Multiply your margin of error by it. When n is tiny next to N, the factor is essentially 1 and changes nothing. As n approaches N, the factor approaches 0, reflecting that a full census has no sampling error. Example: 200 of 1,000 employees, 65% satisfied, 99% confidence gives about +/-7.8 percentage points with the correction, versus about +/-8.7 without it.
A practical rule: use the correction when your sample is more than about 5% of a known population (some guides say 1%). This calculator applies it automatically whenever you enter a population size larger than your sample size.
It means the true population value is likely within 3 percentage points of your survey result, at the stated confidence level. If a poll reports 52% with a +/-3 percentage point margin at 95% confidence, the real figure is plausibly between 49% and 55%. Intervals built this way capture the true value about 95% of the time.
There is no universal standard, but a margin of 3% to 8% is considered good in most survey practice, and +/-5 percentage points is the most common benchmark. The right target depends on how the result will be used: a quick internal pulse survey can live with +/-8 points, while published polling or academic research usually aims for +/-3 to +/-5.
For most surveys, yes. A +/-5 percentage point margin at 95% confidence is the classic planning target and needs about 385 respondents for an unknown fifty-fifty split. Treat it as a starting benchmark, not a law: tighten it if small differences decide your outcome, and accept a wider margin if you only need a directional read.
Increase your sample size. Because the margin falls with the square root of n, you need roughly four times as many respondents to halve it. You can also lower the confidence level (90% instead of 95% shrinks the margin but reduces certainty), apply the finite population correction when sampling a large share of a known group, and reduce response variability with clear, unbiased questions.
The quantity p(1-p) reaches its maximum exactly when p is 0.5, so a fifty-fifty result produces the widest possible margin of error for a given sample size. Using 50% while planning gives the most conservative estimate: it guarantees the real margin for any actual result will be no larger than the figure you calculate. Results near 0% or 100% are estimated more precisely.
Use it when your sample is a substantial fraction of a known, bounded population, roughly 5% or more (some guides use 1%). Surveying 200 employees at a 1,000-person company qualifies, and the correction shrinks the margin. For national polls of millions of people, the correction factor is essentially 1 and is usually omitted.
Use 95% for most surveys; it is the standard in market research, social science, and academic work, and means about 1 in 20 intervals will miss the true value. Use 90% for quick, low-stakes polls where a smaller sample matters more than certainty. Reserve 99% for high-stakes decisions, since it needs a substantially larger sample for the same precision.
Standard error measures how much a sample statistic would vary across repeated samples; it is the square root of p(1-p)/n. The margin of error adds your confidence level on top: margin of error equals the critical z value times the standard error. In short, the standard error is the raw variability, and the margin of error is that variability scaled to your chosen confidence.
For large populations, practically no. A poll of 1,000 people has nearly the same margin of error whether the population is 5 million or 300 million. Population size only matters when the sample is a large fraction of a finite group, in which case the finite population correction reduces the margin.
Flip the formula around: n = Z² * p(1-p) / E², where E is your target margin as a decimal, then round up to the next whole respondent. For 95% confidence (Z = 1.96), a +/-3 percentage point margin, and p = 0.5, this gives about 1,068 respondents. With a known population, the finite-population version n = n0 * N / (n0 + N - 1) gives a smaller required sample.