What is margin of error in a survey? It is the plus-or-minus range that describes how much a survey result may differ from the true population value because you asked a sample instead of everyone. If 60% of respondents support a policy, a margin of error of 5% means the real figure is probably somewhere between 55% and 65%. Last reviewed October 2026.
That sounds simple, and mostly it is. The trouble starts when a survey reports a bare percentage with no range attached, or attaches a range that came from a method where the math doesn’t actually apply. This guide walks through what the number means, how it is calculated, and how to tell whether a survey that quotes one has earned the right to.
Table of Contents
- What Is Margin of Error in a Survey?
- What is margin of error in a survey, key concepts
- How Is Margin of Error Calculated?
- A worked example
- What Does a 95% Confidence Level Mean?
- Why Does Sample Size Affect Margin of Error?
- How Do You Read a Survey Result?
- What Is the Difference Between Margin of Error and Error?
- How Can You Reduce a Survey’s Margin of Error?
- How Should You Report the Margin of Error?
- Frequently Asked Questions
- What is a good margin of error for a survey?
- What does a 95% margin of error mean?
- What does a 2% margin of error mean?
- Is 5% margin of error acceptable?
- Why is 5% the margin of error?
- Does margin of error apply to online surveys and social media polls?
- What to Do First
What Is Margin of Error in a Survey?
Margin of error is a statistical expression of the random sampling error in survey results. It gives the range within which the true population value is expected to fall, based on the sample size and the confidence level chosen by the researcher. It is not a measure of how wrong the survey could be for other reasons, which is the part most readers take for granted.
What is margin of error in a survey, key concepts
- The plus-or-minus range. A reported result of 60% with a margin of error of 5% becomes 55% to 65%.
- Confidence level. The odds that the interval captures the true value across repeated random samples. 95% is the standard used in most published polling.
- Sample size. The number of people who answered. More answers, tighter range.
- Probability samples only. The calculation assumes every person had a known, non-zero chance of being asked. Opt-in panels and social media polls do not qualify, so their margin of error is decoration rather than math.
Two survey results can share an identical percentage and mean completely different things. One comes from 400 randomly selected people, the other from 40 volunteers who followed a link. The first has a defensible range. The second has a number that describes only the people who clicked.
It also has nothing to do with profit. The phrase gets tangled with margin of profit and general business slack constantly, especially in nonprofit and community settings where people talk about having less room for error. Those are budgeting concepts. Margin of error describes arithmetic, nothing else.
How Is Margin of Error Calculated?
For a survey measuring a proportion, the formula is short enough to write out:
MoE = Z × √( p(1 − p) ÷ n )
- Z is the critical value tied to your confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
- p is the sample proportion, written as a decimal. At 60% support, p = 0.60.
- n is the number of completed responses.
That square root term is the standard error. It measures how much a proportion bounces around between one random sample and the next, and it shrinks as the sample grows.
A worked example
Say you survey 400 people and 240 say yes. Work it out in four steps.
- Convert the proportion: p = 240 ÷ 400 = 0.60.
- Multiply p by its complement: 0.60 × 0.40 = 0.24.
- Divide by the sample size: 0.24 ÷ 400 = 0.0006. The square root of that is about 0.0245.
- Multiply by 1.96 for 95% confidence: 1.96 × 0.0245 = 0.048, or roughly 4.8%.
So the reportable result is 60% plus or minus 4.8%, which puts the true population value somewhere between 55.2% and 64.8%.
Note where the biggest wiggle room sits. When p is 0.50, the term p(1 − p) is at its maximum, so a 50/50 split produces the widest margin of error for any given sample size. A survey that lands at 12% or 88% has a narrower range than one landing at 50%, with the same number of responses.
For means rather than percentages, such as average satisfaction on a ten-point scale, the calculation uses the standard deviation of responses instead of p(1 − p). The logic and the sample-size effect stay the same.
What Does a 95% Confidence Level Mean?
Here is where the standard explanation usually goes wrong, and getting it right matters if you are going to publish or defend a survey result.
The popular version says there is a 95% chance the true value falls inside the interval. Statisticians push back on this constantly, and the correction has been made publicly and at length by researchers such as Andrew Gelman writing on statmodeling.stat.columbia.edu. A frequentist confidence level describes the method, not the odds for any single result. The accurate phrasing is that if you drew many random samples of this size and built an interval from each one using the same procedure, about 95% of those intervals would contain the true population value. Your specific interval is one of those intervals, and you do not know which kind you got.
Practically, that means a 95% confidence level leaves a real chance, about one in twenty, that your interval misses the true value entirely. That is a small risk, and it is why 95% is the default for published polling and research.
| Confidence level | Z-score | Margin of error at 400 responses (p = 0.50) |
|---|---|---|
| 90% | 1.645 | plus or minus 4.1% |
| 95% | 1.96 | plus or minus 4.9% |
| 99% | 2.576 | plus or minus 6.4% |
The table shows why 95% became the default. Going from 90% to 95% costs about 0.8 points of extra width. Going from 95% to 99% costs another 1.5 points, and buys protection against a rarer and generally more theoretical failure. Most practitioners take the middle.
One clarification that causes endless confusion: the 5% in a 95% confidence level is not the same 5% as a 5% margin of error. The first is the remaining probability that the interval misses the truth. The second is the width of the interval itself, and it depends entirely on your sample size. Surveys reporting a 5% margin of error often use a 95% confidence level, but the two numbers answer completely different questions.
Why Does Sample Size Affect Margin of Error?
Margin of error scales with the square root of the sample size, which means gains get harder as you go. Quadrupling your responses cuts the margin in half. Doubling it shaves the margin by about 29%, not 50%.
For a question where responses split roughly evenly, at 95% confidence:
| Completed responses | Margin of error |
|---|---|
| 100 | plus or minus 9.8% |
| 400 | plus or minus 4.9% |
| 1,000 | plus or minus 3.1% |
| 2,000 | plus or minus 2.2% |
| 5,000 | plus or minus 1.4% |
Going the other way, this is roughly what you need to hit a target margin of error at 95% confidence. It assumes the worst-case split, so real response patterns sometimes land a little tighter.
| Target margin of error | Responses needed |
|---|---|
| plus or minus 5% | about 385 |
| plus or minus 4% | about 600 |
| plus or minus 3% | about 1,067 |
| plus or minus 2% | about 2,400 |
| plus or minus 1% | about 9,600 |
That last row explains why national polling runs into the thousands. A plus or minus 2% margin of error, which is the precision most election coverage implies, needs a sample a small community project will rarely reach.
Sample size also hides inside every subgroup you report. If 400 people answer but only 60 are under 25, that slice carries a margin of error near 12% rather than 5%. Analysts call this the sample size penalty, and it is the most commonly dropped number in published breakdowns. If you report a cross-tabulation, report the sample size behind each cell.
How Do You Read a Survey Result?
Start by converting the headline into a range before you decide anything about it. A result of 42% with a margin of error of 2% tells you the true value sits between 40% and 44%, which is a narrower claim than 42% and worth more than 42% on its own. That single conversion is where what is margin of error in a survey turns from a definition into a tool.
Then compare intervals rather than point estimates. If two options sit at 48% and 52% with a 4-point margin of error, their ranges overlap almost completely. That is a statistical tie, whatever the numbers say on the night. The famous election headline where one candidate leads by two points against a three-point margin of error describes a race nobody can call.
When intervals overlap substantially, treat the difference as unresolved. When they do not overlap at all, you have a much stronger case that the difference is real. Two figures whose intervals are just barely apart are weaker evidence than two figures with a clear gap, so a “leader by 1 point” story rarely deserves the headline it gets.
Two more checks before you lean on a result. Look at whether the survey named its sampling method, and look at the response rate. A random-digit poll that reaches 12% of contacted households and a posted Facebook poll that gathers 300 replies can produce identical percentages with completely different standing.
What Is the Difference Between Margin of Error and Error?
Margin of error covers one narrow category of mistake. Surveys have several others, and they are usually larger.
| Term | What it means |
|---|---|
| Margin of error | The plus-or-minus range reflecting random sampling error at a stated confidence level |
| Confidence interval | The full range itself, which is the estimate plus and minus the margin |
| Standard error | The underlying measure of how much a sample proportion varies, before any confidence multiplier |
| Non-sampling error | Anything caused by question wording, mode, non-response or record-keeping, none of it captured by the margin |
| Statistical significance | A test result indicating the observed difference is unlikely under random sampling alone, with no threshold fixed in advance |
Non-sampling error is where community and advocacy research most often gets burned. Five things a margin of error cannot touch:
- Wording that leads. Ask “Do you support the new program?” and “Do you oppose wasteful spending?” and you will get different numbers from the same people. The margin of error will be identical and equally meaningless.
- Double-barreled questions. “How satisfied are you with pay and scheduling?” cannot be answered cleanly, and the answer that lands is arbitrary.
- Non-response bias. People who skip a survey differ systematically from people who finish it. Weighting can help; it cannot fully repair the gap.
- Coverage error. A frame that misses renters, night-shift workers, or people without stable internet produces a sample that is not the population, whatever the sample size.
- Opt-in panels and snowball samples. Nobody can state the selection probability, so the formula has no valid input. This is the single biggest gap between published margin of error and actual survey quality.
A useful habit: treat the margin of error as the floor of a survey’s uncertainty, not the whole of it. Reporters and readers who quote the plus-or-minus figure as the complete error budget are reading only the easiest part.
How Can You Reduce a Survey’s Margin of Error?
Four moves improve precision, and only the first two are usually available to you.
- Collect more completed responses. This is the only lever that touches the margin directly. Budget for it in advance, since chasing responses after a weak response rate is expensive and often unsuccessful.
- Use a probability-based sample. Random digit dialing, address-based sampling, or a panel built with known selection probabilities. A proper sample with fewer responses beats an opt-in sample with thousands.
- Keep the response distribution away from the middle. Nothing you do here matters much, but a 10% or 90% split already carries a tighter range than 50/50.
- Trim the questions that add error without adding knowledge. Long matrices raise fatigue and straight-lining. Neither shows up in the margin of error, and both damage the result.
One warning. A larger sample does not fix a biased one. Ten thousand responses collected from a self-selected audience produce a very precise measurement of the wrong population, which is more dangerous than a small honest survey because the precision discourages scrutiny.
How Should You Report the Margin of Error?
Publish the estimate with its context, in one sentence, every time. A workable template:
Among 1,050 randomly selected adults surveyed between [dates], 62% reported [finding], plus or minus 2.9% at a 95% confidence level. Full methodology is available on request.
Alongside it, publish the fields that make the number checkable:
- The estimate and the margin of error, together rather than apart.
- The confidence level you used.
- The total completed sample size, and the size behind any subgroup you report.
- The population the sample was drawn from and the sampling method used to reach it.
- The response rate, defined as completed interviews over eligible people contacted.
- Field dates and any weighting applied.
- Full question wording, since wording is part of the finding.
If the sample is opt-in or recruited through social media, say so plainly and omit the margin of error entirely. Reporting a number you cannot justify is worse than reporting none.
Frequently Asked Questions
What is a good margin of error for a survey?
It depends on what you plan to do with the result. Plus or minus 5% is fine for directional insight and early exploration. Plus or minus 3% or tighter suits decisions with real cost attached. Anything above 10% is too wide to act on. Remember the threshold only means something if the sample was random and representative in the first place.
What does a 95% margin of error mean?
It is two separate ideas joined together. The 95% is the confidence level, describing how often a repeated random sample of this size would produce an interval containing the true value. The plus-or-minus percentage is the width of the interval, which depends on sample size and response distribution. A 95% confidence interval with a 3% margin of error is not a 95% margin of error.
What does a 2% margin of error mean?
It means your true population value is estimated to sit within two percentage points of the reported figure. A result of 42% with a 2% margin of error points to a true value between 40% and 44%, at your chosen confidence level. Reaching that precision at 95% confidence usually takes around 2,400 responses from a sample where answers split roughly evenly.
Is 5% margin of error acceptable?
For exploring a question, yes. Five points is the conventional threshold most researchers use for directional work, and roughly 385 completed responses will produce it at 95% confidence. It is not enough for decisions that carry real money or real consequences, where a difference between options may be smaller than the range itself.
Why is 5% the margin of error?
The number 5 comes from the 95% confidence level, not from the width of the interval. Confidence levels of 95% became conventional through long practice because the interval stays reasonably tight while the risk of missing the true value stays low. The leftover 5% is the long-run share of random samples whose interval misses, and it is a property of the method rather than your particular result.
Does margin of error apply to online surveys and social media polls?
Only when participants were selected through a method where everyone had a known chance of being asked. A large online panel recruited through probability sampling can support a valid margin of error. A poll posted to social media, a signup link shared in a newsletter, or a convenience sample recruited by volunteers cannot, because there is no selection probability to put into the formula.
What to Do First
Take any survey result you plan to use and write down four things: the percentage, the margin of error, the confidence level, and how the people were selected. If the fourth one is not a genuine random process, the first three tell you nothing, and the survey is a signal of interest rather than a measurement of opinion.
