Sample Size Calculator

Estimate the required sample size for a survey from confidence level, margin of error, expected proportion, and optional population size.

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Confidence level

Margin of error (%) Expected proportion (%) Population size (optional)

385

Required sample size

95%

Confidence level

±5%

Margin of error

Sample size (infinite pop.)	385
Expected proportion	50%
Critical z-value	1.96
Population size	Infinite

Survey Research

Sample size — how many people do you need to survey?

A sample size calculator tells you how many respondents a survey needs to produce results that are statistically reliable at a given confidence level and margin of error. Getting this number right before running a poll, A/B test, or research study prevents both under-powered studies (which miss real effects) and wasteful over-sampling (which costs time and money).

About this calculator

Reviewed 2026-03-15

Methodology

Sample sizes are calculated using the standard formula n₀ = Z² × p × (1 − p) / E², where Z is the two-tailed critical value for the chosen confidence level. Finite population correction n = n₀ / (1 + (n₀ − 1) / N) is applied when a population size is provided. Results are rounded up to the nearest integer using the ceiling function. Critical z-values are: 80% → 1.2816, 85% → 1.4395, 90% → 1.6449, 95% → 1.9600, 99% → 2.5758.

Limitations

This calculator assumes simple random sampling. Cluster, stratified, or systematic sampling designs require different formulas and typically different sample sizes.
Sample size calculations assume the population is homogeneous in the characteristic being measured. Highly variable populations may need larger samples than the formula suggests.
Non-response bias and question wording can undermine survey validity regardless of sample size. Collecting the required number of responses does not guarantee representative results.
For proportions very close to 0% or 100%, the normal approximation breaks down and exact binomial methods may be more appropriate.

Disclaimer

This calculator provides a statistical guideline for survey planning. It is not a substitute for professional research design advice, and actual required sample sizes may vary based on sampling methodology and study objectives.

Sources

See our calculation methodology and editorial standards for how this estimate is produced.

Confidence level and margin of error

Confidence level (typically 95%) expresses how often the true population value would fall within your reported margin of error if you repeated the survey many times. A 95% confidence level means 95 out of 100 independent samples would produce an interval containing the true value.

Margin of error (often ±5%) is the maximum expected difference between the survey result and the true population value. Cutting the margin of error in half requires roughly four times as many respondents because the relationship is quadratic — halving E quadruples n.

Sample size formula

The standard formula for an infinite (or very large) population uses the critical z-value for the chosen confidence level, the margin of error, and the expected proportion p. Setting p = 0.5 gives the most conservative (largest) required sample, which is why 50% is the default when the true proportion is unknown.

n₀ = Z² × p × (1 − p) / E²

Z is the critical value for the confidence level, p is the expected proportion, E is the margin of error (as a decimal).

n = n₀ / (1 + (n₀ − 1) / N)

Finite population correction: N is the total population size. Applied when surveying a significant fraction of the population.

Critical z-values for common confidence levels

Each confidence level maps to a fixed z critical value from the standard normal distribution: 80% → 1.282, 85% → 1.440, 90% → 1.645, 95% → 1.960, 99% → 2.576. The 95% level is by far the most common in published research and business surveys.

Moving from 95% to 99% confidence increases the required sample size by about 73% (for p = 0.5, E = 5%) because the z-value grows from 1.96 to 2.58 — a 31% increase that gets squared in the formula.

Finite population correction

When your population is small enough that your sample would represent a substantial fraction of it, the standard formula overestimates the required sample size. The finite population correction reduces n proportionally — for a population of 1,000 and an infinite-population requirement of 385, the corrected sample size is about 278.

Leave the population size blank if your population is large (over 100,000) — the correction becomes negligible (less than 0.4%) and the infinite-population formula is sufficient.

Why use 50% as the expected proportion?

The variance term p × (1 − p) in the formula is maximised when p = 0.5, giving the largest and most conservative sample size estimate. If you have prior knowledge suggesting the true proportion is close to 10% or 90%, using that value instead will reduce the required sample size significantly.

For example, at 95% confidence and ±5% margin of error, p = 0.5 requires 385 respondents, but p = 0.1 (or 0.9) requires only 139 — a 64% reduction. Use the conservative 50% when you have no prior estimate.

Frequently asked questions

What happens if I get fewer responses than the required sample size?

Your margin of error will be wider than intended. If you aimed for ±5% at 95% confidence but only reached half the required sample, your actual margin of error is approximately ±7%. The survey results are still valid, but the uncertainty around them is larger than planned.

Does sample size depend on total population size?

For large populations (over 100,000) the required sample size is nearly independent of total population — 385 people can represent a city of 1 million almost as well as a city of 10 million, at the same confidence and margin of error. Population size only matters materially when you are sampling a significant fraction of a small, finite group.

What confidence level should I use?

95% is the standard for most academic research, business surveys, and published polls. Use 99% when the stakes are high (medical, legal, safety contexts) and 90% when resources are limited and some additional uncertainty is acceptable. 80% is rarely used outside of preliminary or exploratory work.

Is a larger sample always better?

Larger samples reduce margin of error, but with sharply diminishing returns. Going from 100 to 400 respondents cuts the margin of error roughly in half. Going from 400 to 1,600 halves it again. Beyond a certain point, the cost of additional responses outweighs the modest improvement in precision. Survey design quality, response bias, and sampling method often matter more than a few extra respondents.

Sample Size Calculator

Sample size — how many people do you need to survey?

Confidence level and margin of error

Sample size formula

Critical z-values for common confidence levels

Finite population correction

Why use 50% as the expected proportion?

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