What margin of error should I target?

±5% is standard for most surveys (meaning the true value is within 5 percentage points of your measured value). ±3% is used for higher-stakes decisions. ±2% requires substantially larger samples and is typical of major political polling. For academic research, ±5% is often acceptable; for precision testing, ±1–2% may be required.

Does population size matter much?

Only for small populations. For populations over ~10,000, the required sample size stabilizes near the 'infinite population' formula: n = Z² × p(1−p) / e². The finite population correction factor reduces required sample size for small populations. For a population of 500, a ±5% margin of error at 95% confidence requires 217 responses (44% of the population) rather than 384.

What is the assumed proportion and why does it affect sample size?

The proportion (p) represents the expected percentage answering 'yes' to your key question. When p = 50%, the sample size requirement is at its maximum — this is the most conservative assumption used when you don't know the true proportion. If your proportion is expected to be more extreme (20% or 80%), the required sample is smaller.

📐Math Tools

How Many People Do You Need to Survey for Statistically Valid Results?

How many people do you need to survey?

What This Does

Sample size is the most consequential decision in survey design and research — yet it's one that many people make by guessing. Too small a sample produces unreliable results that can't be trusted. Too large a sample wastes time and money collecting data beyond what's needed for the precision required. The right sample size depends on three key inputs: confidence level (how certain you want to be that your result is correct), margin of error (how precisely you need to know the true answer), and population size (how many people exist in the group you're studying). For large populations, the formula stabilizes quickly — a sample of 1,067 gives you ±3% margin of error at 95% confidence whether your population is 100,000 or 100 million. This counterintuitive result surprises most people: national polls of 1,000 people can represent 330 million Americans with only ±3% margin of error — because accuracy depends on sample size, not the ratio of sample to population. This calculator computes required sample size from your confidence level, margin of error, and estimated proportion. It also works in reverse: given your actual sample size, it shows your margin of error and what confidence level you've achieved — critical for evaluating the reliability of existing research.

When Should You Use This?

→Planning a survey and needing to know how many responses are required
→Designing an experiment or A/B test and determining the minimum sample size
→Evaluating whether an existing study's sample size supports its claimed conclusions
→Business research, market research, or academic study design
→Understanding the margin of error for polls and surveys you're reading

Example Scenario

A startup is surveying customer satisfaction before a product launch. They want 95% confidence and a ±5% margin of error — sufficient for directional business decisions. Population: 50,000 customers. Required sample size: 381 responses. If they can only collect 200 responses, their margin of error widens to ±6.9% at 95% confidence. The calculator shows the exact trade-off between sample size and precision, letting them decide whether the extra effort to gather 381 responses is worth the improvement in result reliability.

📊

Sample Size Calculator

Find required survey size · calculate margin of error · compare confidence levels

Determine how many respondents you need for statistically valid survey results, or find the margin of error for a sample you already have. Uses the standard formula n = Z²p(1−p)/e² with optional finite population correction.

Confidence Level

Desired Margin of Error (%)

±5% is standard for most surveys

Expected Proportion (%)

50% = most conservative (largest sample)

Population Size (optional)

Leave blank if population > 100,000

About the Sample Size Calculator

Sample size is one of the most critical decisions in survey research, academic studies, and market research. Too small a sample produces unreliable results; too large a sample wastes time and budget. This calculator uses the standard statistical formula to find the minimum number of respondents needed to achieve a desired level of precision at a given confidence level.

The two core parameters are confidence level and margin of error. Confidence level (typically 95%) describes how often your results would fall within the margin of error if you repeated the survey many times. Margin of error (typically ±5%) describes how far your sample result may be from the true population value. Together, they define the precision and reliability of your findings.

For most surveys of large populations, a 95% confidence level with a ±5% margin of error requires approximately 385 respondents. This number is surprisingly constant regardless of how large the population is — a fact that surprises most first-time researchers. Population size only significantly affects the required sample when studying small, finite groups like employees at a specific company or students in a single school.

How the Formula Works

The core formula is n = Z²p(1−p)/e², where Z is the critical value from the standard normal distribution (1.96 for 95% confidence), p is the expected proportion (use 0.5 if unknown), and e is the desired margin of error as a decimal. The product p(1−p) is maximized at p = 0.5, which is why 50% produces the largest — and most conservative — sample size estimate. For finite populations, a correction factor n_adj = n₀/(1 + (n₀−1)/N) reduces the requirement, since a sample of 100 from a town of 500 is proportionally much more representative than 100 from a city of 5 million.

Example: Planning a Customer Survey

You want to survey customers of a software product to measure satisfaction, and you want to be 95% confident your results are within ±5%. You have approximately 8,000 customers. Using the infinite-population formula, you'd need 385 responses. Applying the finite population correction for N=8,000 reduces this to 366 responses. If you want tighter precision at ±3% MOE, the requirement jumps to about 966 responses — more than 2.5× as many, illustrating the cost of precision.

Common Mistakes in Sample Size Planning

Confusing sample size with response rate — if you need 385 completed surveys and expect a 20% response rate, you need to contact ~1,925 people
Using a non-conservative proportion when the true value is unknown — always use 50% unless you have strong prior evidence
Assuming a larger population always requires a larger sample — for populations over 10,000, sample size requirements are nearly identical
Treating the result as a minimum rather than a target — real surveys have dropouts, invalid responses, and incomplete data, so pad your sample by 10–20%

Frequently Asked Questions

What is margin of error and what does ±5% actually mean?

Margin of error defines the range within which the true population value likely falls. If 60% of your sample says 'yes' with a ±5% margin of error at 95% confidence, you can say with 95% certainty that the true population percentage is between 55% and 65%. The margin of error applies to each percentage result, not to the total count of respondents.

Why does sample size barely change for very large populations?

The standard formula assumes an infinite population, and the finite population correction only significantly changes the result when your sample is a meaningful fraction of the population. For a population of 1 million, a required sample of 385 represents only 0.04% of the population — so the correction is negligible. This counterintuitive fact means a national poll of 1,000 people can be as statistically valid as a smaller regional poll of the same size.

What confidence level should I use for my survey?

95% confidence is the accepted standard for most academic, market research, and business surveys. It means that if you ran the same survey 100 times, 95 of those surveys would produce results within the stated margin of error. Use 99% for medical, legal, or high-stakes research. Use 90% only when budget is severely constrained and the research is exploratory rather than definitive.

What is the expected proportion and when should I use 50%?

Expected proportion is your best estimate of the percentage of respondents who will answer 'yes' to your key question. If you expect about 30% to prefer Option A, enter 30%. If you have no prior estimate, always use 50% — this produces the largest (most conservative) required sample size. Using a non-50% proportion is only appropriate when you have reliable prior data, since a wrong assumption can lead to an underpowered study.

What is the difference between sample size and survey response count?

The sample size from this calculator is the number of completed, valid responses you need to analyze. It is not the number of people you invite to take the survey. You must account for your expected response rate: divide the required sample size by your expected response rate to find how many invitations to send. For example, if you need 385 responses and expect a 25% response rate, send invitations to at least 1,540 people.

How does the finite population correction work?

When your population is small and your sample represents a significant portion of it, the standard formula over-estimates the required sample size. The correction formula is n_adj = n₀ / (1 + (n₀−1)/N), where n₀ is the uncorrected sample size and N is the total population. The correction becomes meaningful when n₀/N exceeds 5% — roughly when your population is under 10,000.

Results are for informational purposes only.