How is margin of error calculated?

Margin of error uses the formula MOE = Z × √(p(1−p)/n), where Z is the Z-score for your confidence level (1.96 for 95%), p is the response proportion (0.5 for maximum uncertainty), and n is your sample size. A free online calculator applies this formula instantly from your inputs.

What is a good margin of error for a survey?

A margin of error of ±5% at 95% confidence is the standard for most surveys. For high-stakes decisions, aim for ±2–3%. For informal or exploratory research, ±10% is often acceptable. The right margin of error depends on how consequential your decisions are and how precise your data needs to be.

What is the relationship between sample size and margin of error?

Sample size and margin of error are inversely related — more responses mean less uncertainty. However, the relationship is not linear: halving your margin of error requires quadrupling your sample size. Increasing from 400 to 1,600 responses reduces margin of error from roughly ±5% to ±2.5% at 95% confidence.

Does margin of error account for survey bias?

No. Margin of error only measures random sampling error — it does not account for non-sampling errors like biased questions, low response rates, or selection bias. A small margin of error does not guarantee accurate results if the survey design or respondent selection process is flawed. Good survey design is equally as important as a sufficient sample size.

Tools / CALCULATOR

Free Margin of Error Calculator — How Reliable Are Your Survey Results?

Enter your sample size and confidence level. See exactly how accurate your survey data is — instantly and for free.

Calculate My Margin of Error

Sample size (responses)

Population size (optional)

Confidence level95%

Result

±4.9%

margin of error

n = 400 · 95% confidence

Standard precision

A 60% result is likely between 55.1% and 64.9%

How precise that is

PreciseStandardDirectionalLow

About this tool

You’ve collected your survey responses — but how much should you trust the results? That depends on your margin of error. The margin of error tells you how far your survey results might deviate from the true value in the overall population. Our free Margin of Error Calculator gives you an instant answer: enter your sample size, population size, and confidence level, and you’ll know exactly how precise your data is.

A smaller margin of error means more reliable results — but it requires a larger sample. A larger margin of error is acceptable for informal surveys or early-stage research, but can be dangerous for decisions with major business, financial, or public-policy implications. Understanding your margin of error before presenting results protects you from overstating the confidence of your data and making costly decisions on uncertain findings.

Use this tool immediately after your survey closes to validate your results, or before you launch to set response targets that will give you the precision level you need. For best results, pair this calculator with our Sample Size Calculator — use that tool before your survey to plan your target, and this tool after to verify your results.

Key benefits

Know exactly how reliable your survey results are before sharing or acting on them

Instantly calculate margin of error from sample size and confidence level

Supports 90%, 95%, and 99% confidence levels — the three standard research thresholds

Understand when your sample is large enough — and when you need more responses

Completely free to use — no sign-up required

Pair with the Sample Size Calculator for full end-to-end survey validation

How it works

Enter your inputs

Input your sample size (number of responses collected), your population size if known, and your desired confidence level.

Get your margin of error

See your margin of error displayed as a ± percentage, calculated instantly.

Interpret and decide

Use the result to determine whether your sample is large enough to support your conclusions — or whether you need more responses before acting on the data.

Quick answer

Margin of error in a survey measures how far your results might deviate from the true population value. It is calculated using the formula MOE = Z × √(p(1−p)/n), where Z is the confidence-level Z-score (1.96 for 95% confidence), p is the response proportion, and n is the sample size. A survey of 400 people typically yields a ±5% margin of error at 95% confidence. Use a free margin of error calculator to check the reliability of your results after any survey.

Margin of Error Calculator — FAQ

Margin of error is the range of values within which the true population value is likely to fall, given your sample size and confidence level. For example, a survey result of 60% with a ±5% margin of error means the true population value is likely between 55% and 65%. It quantifies the uncertainty inherent in any survey that doesn’t capture every person in the target population.

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