Sample Size Calculator — Surveys, Polls & Research Studies

Before you run a survey or study, the most important question is: how many people do I actually need to ask? Too few and your results are unreliable. Too many and you've wasted time and budget. The CalcHub Sample Size Calculator finds that minimum number based on your confidence level, acceptable margin of error, and how large your target population is.

The Three Inputs

1. Confidence Level — How certain do you want to be that your results reflect the true population? 95% is the standard for most research. 2. Margin of Error (E) — How much deviation from the true value is acceptable? ±5% is common for opinion polls; ±2% or less for medical or scientific research. 3. Population Size (N) — The total number of people you're trying to understand. For very large populations (cities, countries), this barely affects the result.

The Formula

For proportions (most common survey use case):

n = (z² × p × (1−p)) / E²

Then adjust for finite population:

n_adjusted = n / (1 + (n−1)/N)

Where:

• z = critical value (1.96 for 95% confidence)


• p = estimated proportion (use 0.5 if unknown — gives maximum sample size)


• E = margin of error as a decimal

Sample Size Reference Table

95% Confidence Level, p = 0.5:

Margin of Error	Population 1,000	Population 10,000	Large Population
±10%	88	96	97
±5%	278	370	385
±3%	517	964	1,068
±2%	706	1,936	2,401
±1%	906	4,900	9,604

Key insight: for large populations (10,000+), the sample size barely grows. A survey of the US (330 million people) at 95% confidence, ±3% needs the same ~1,068 people as surveying a city of 50,000. This surprises most people.

How to Use It

1. Choose your confidence level (90%, 95%, or 99%).
2. Set your margin of error. Enter 5 for ±5%.
3. Enter your population size. If you don't know it exactly, enter a large number like 1,000,000 — beyond a certain size it doesn't change the result.
4. Optionally adjust the proportion estimate if you expect results far from 50/50.

The Role of p = 0.5

If you expect roughly 50% of respondents to say "yes" (and 50% "no"), that's the most uncertain outcome — and gives the largest required sample size. If you expect 90% to say yes (like surveying existing customers about a popular feature), your required sample is smaller.

Expected Proportion	Required Sample (95%, ±5%)
0.50	385
0.70	323
0.90	139

When in doubt, use 0.5 — it's conservative and guarantees adequate power.

Why the Math Gives a Surprisingly Small Number

Statisticians often get disbelief when they say 1,000 people can represent a country. The answer is in the formula — sample size depends primarily on the desired margin of error and confidence, not the population size. The population size matters only when your sample represents a large fraction of it.

The math holds, but it assumes your sample is truly random. Convenience samples (whoever walks by, whoever clicks a link) can completely invalidate the statistical guarantees regardless of sample size.

For Studies Measuring Continuous Outcomes

When measuring means rather than proportions:

n = (z × σ / E)²

You need an estimate of the population standard deviation (σ), which often comes from previous research or a pilot study. Higher variability in the measured outcome requires a larger sample.

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What happens if I can't reach my calculated sample size?

A smaller sample gives you wider confidence intervals than planned. If you surveyed 200 people when you needed 385 for ±5%, your actual margin of error is around ±7%. That may or may not be acceptable depending on how you're using the results.

Should I include non-respondents in my sample size calculation?

Calculate the final sample size you need, then divide by your expected response rate to determine how many people you need to contact. If you need 385 completed responses and expect 40% to respond, contact at least 963 people.

Does sample size matter less for higher confidence?

Actually, higher confidence requires a larger sample, not smaller. To get 99% confidence at the same margin of error as 95%, you need more people — the 99% z (2.576) is larger than the 95% z (1.96), and since it's squared in the formula, the effect is significant.

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Related calculators: Confidence Interval Calculator · Z-Score Calculator · Standard Deviation Calculator