Margin of Error Calculator: SurveyMonkey Guide

The SurveyMonkey margin of error calculator tells you how much the results from a sample survey could differ from the true population value, based on your sample size, population size, and confidence level. You enter your sample size, population size, and choose a confidence level, and it returns the margin of error as a percentage (e.g., ±4%). This article explains the formula, how to use it, and what the result really means for your survey.

Formula

The margin of error (E) for a proportion is calculated as:

E = Z * sqrt( pÌ‚(1 – pÌ‚) / n ) * sqrt( (N – n) / (N – 1) )

• Z = Z-score corresponding to the confidence level (1.96 for 95%, 2.576 for 99%, 1.645 for 90%)
• pÌ‚ = sample proportion (the percentage of respondents who give a particular answer). When unknown, use 0.5 (50%) to get the maximum possible margin of error.
• n = sample size (number of completed responses)
• N = population size (total number of people in the group you’re studying)

The first factor accounts for sampling variability; the second is the finite population correction (FPC), which adjusts for when the sample is a large fraction of the population. For very large populations, the FPC approaches 1 and can be ignored.

Worked Example

Using the default values from the calculator above: sample size = 400, population size = 10,000, confidence level = 95% (Z = 1.96).

1. Assume pÌ‚ = 0.5 (worst-case variability). Then pÌ‚(1 – pÌ‚) = 0.25.
2. Divide by n: 0.25 / 400 = 0.000625.
3. Take the square root: sqrt(0.000625) = 0.025.
4. Compute the FPC: (10,000 – 400) / (10,000 – 1) = 9600 / 9999 ≈ 0.9601. Square root: sqrt(0.9601) ≈ 0.9798.
5. Multiply: 1.96 * 0.025 * 0.9798 ≈ 0.0480.
6. Convert to percentage: 0.0480 * 100 = 4.80%.

The calculator shows a margin of error of ±4.80% for these inputs. That means if 60% of your sample chose a particular answer, the true population percentage is likely between 55.2% and 64.8% (60% ± 4.8%).

What the Margin of Error Means

The margin of error quantifies sampling error—the random difference between a sample result and the true population value. It does not include other errors like non-response bias, question wording, or data entry mistakes. A 95% confidence level means that if you repeated the survey 100 times with fresh random samples, the confidence interval (your result ± margin of error) would contain the true population value about 95 times.

For example, if your survey finds that 70% of respondents prefer Product A, with a margin of error of ±5% at 95% confidence, you can say: “We are 95% confident that the true percentage of the population who prefer Product A is between 65% and 75%.”

How to Choose Your Sample Size

To get a smaller margin of error, you need a larger sample size. The relationship is not linear: to halve the margin of error, you must quadruple the sample size (because n appears under a square root). Here are some common targets:

• For a margin of error of ±5% at 95% confidence, you need about 385 responses (for a large population).
• For ±3%, you need about 1,067 responses.
• For ±2%, you need about 2,401 responses.

These numbers assume a 50/50 split (p̂ = 0.5), which gives the largest margin of error. If you expect the proportion to be closer to 10% or 90%, the required sample size is smaller.

Common Mistakes and Misconceptions

• Using the wrong population size: The population size should be the total number of people your sample represents. If you surveyed customers of a small business, N is the total customer base, not the general public.
• Ignoring the finite population correction: When your sample is more than 5% of the population, the FPC matters. For a population of 1,000 and a sample of 300, the FPC reduces the margin of error noticeably.
• Interpreting the margin of error as a maximum error: The margin of error is a range at a given confidence level—it’s not a hard cap. There is always a small chance (e.g., 5% at 95% confidence) that the true value lies outside the interval.
• Applying the margin of error to subgroups: If you analyze a subgroup (e.g., women only), the effective sample size is smaller, so the margin of error for that subgroup is larger. The overall margin of error does not apply to subgroup results.

Limitations of the Formula

The margin of error formula assumes a simple random sample, which is rarely how real surveys are conducted. SurveyMonkey and other platforms often use convenience samples (e.g., people who click your link), which can introduce selection bias. The formula also assumes that every respondent’s answer is independent and that the sample proportion is not extremely close to 0% or 100% (where the normal approximation breaks down). For proportions below about 10% or above 90%, consider using the Wilson score interval instead.

Additionally, the margin of error only accounts for random sampling error. Non-response bias, question order effects, and respondent dishonesty are not captured. So a low margin of error does not guarantee an accurate survey—it only tells you about sampling variability.

Alternatives and Related Calculators

If you need to determine how many responses you need to achieve a target margin of error, use a sample size calculator (the inverse calculation). If you’re comparing two groups or two time periods, you need a confidence interval for the difference in proportions, which has a different formula. For small samples (n < 30) or extreme proportions, use the exact binomial confidence interval (Clopper-Pearson) instead of the normal approximation.

Frequently Asked Questions

What is a good margin of error?

A margin of error of ±5% or less is commonly considered acceptable for most surveys. For high-stakes decisions (e.g., medical research or political polling), ±3% or even ±2% may be required. The acceptable level depends on how much precision you need and the cost of collecting more responses.

How many responses do I need for a margin of error of ±5%?

For a large population (over 20,000), you need about 385 completed responses at 95% confidence. If your population is smaller, the required sample size is slightly less—for example, for a population of 1,000, you need 278 responses to achieve ±5%.

Does population size matter?

Yes, but only when the sample is a significant fraction of the population. For populations larger than about 20,000, the margin of error barely changes with population size. For example, a sample of 400 from a population of 10,000 gives a margin of error of ±4.8%, while the same sample from a population of 1,000,000 gives ±4.9%.

Why does the calculator use 50% for the sample proportion?

Because 0.5 (50%) maximizes the product pÌ‚(1 – pÌ‚), giving the largest possible margin of error. This is a conservative approach—it ensures your margin of error is at least as large as the true value, regardless of what the actual proportion turns out to be.

Can I use the margin of error for non-binary questions (e.g., averages)?

No, this calculator is for proportions (percentages). For averages (e.g., mean age or rating), you need a different formula that uses the standard deviation of the responses: E = Z * (σ / sqrt(n)), where σ is the sample standard deviation.

How do I report the margin of error in my results?

State it alongside your main findings, e.g., “The survey of 400 customers has a margin of error of ±4.8% at the 95% confidence level.” When presenting a specific percentage, include the interval: “62% ± 4.8%, or between 57.2% and 66.8%.”

Related

• Average Hours Calculator: Work Out Your Mean Hours
• Long Jump Run Up Distance: How to Calculate
• Gross Up Distribution Calculator: How It Works

in n | Sample size | responses | 400 | 1
in N | Population size | people | 10000 | 1
sel cl | Confidence level | 95%=1.96, 99%=2.576, 90%=1.645
out moe | Margin of error | % | (cl * sqrt(0.25 / n) * sqrt((N - n) / (N - 1))) * 100 | 2
out ci | Confidence interval lower bound | % | 50 - moe | 2
out ciu | Confidence interval upper bound | % | 50 + moe | 2