Sample Size Calculator

Use finite-population correction only when the population is actually finite and known

The initial sample-size formula treats the population as very large relative to the sample. If you are sampling without replacement from a known finite population, entering N applies the standard finite-population correction and can reduce the required n.

The result is still a formula-based planning target. Clustered designs, unequal selection probabilities, expected nonresponse, weighting and practical recruitment constraints can require a larger sample than this simple-random-sample calculation.

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How many people must complete a 95% confidence survey?

Suppose a school wants to estimate a yes/no proportion with a ±5 percentage-point margin of error using a simple random sample. We know neither the expected proportion nor the sample result. Set confidence to 95%, use the conservative planning value p = 0.50, and enter a 5% margin.

1. Start without a population correction. The normal-approximation calculation is 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16. Round up to 385 completed responses, not 384.
2. If the population is only 1,000 people and sampling is without replacement, the finite-population adjustment is 384.16 ÷ (1 + 383.16 ÷ 1,000) ≈ 277.74. Round up to 278 completed responses.
3. Plan for people who do not respond separately. If 80% of invited people are expected to complete the survey, 278 ÷ 0.80 = 347.5, so roughly 348 invitations would be a planning starting point. This response assumption is not part of this calculator and is not a guarantee.

When this answer is not reliable

The formula assumes a probability sample and the specified confidence/margin model. It cannot correct selection bias, volunteer-only surveys, cluster sampling, misreported answers, or a very low response rate. Sampling 278 volunteers does not become a representative random sample simply because the number matches. If your course applies design effects or another precision method, use that method instead.

Try Margin of Error Calculator to inspect the reverse relationship between sample size and precision. Results are planning estimates, not guarantees about a real survey.

Formula

n₀ = z*² × p × (1 − p) ÷ e²; optional finite-population n = n₀ ÷ [1 + (n₀ − 1) ÷ N], rounded up

Separate completed surveys from invitations you must send

1. Suppose a survey estimates a proportion with 95% confidence, a ±5-percentage-point margin of error and an unknown population proportion. Enter 50% as the planning proportion. The large-population calculation rounds up to 385 completed responses.
2. If the entire eligible population contains 1,200 people and the finite-population correction applies, the calculator reduces that target to 292 completed responses. It does not automatically calculate recruitment volume.
3. If you independently assume a 60% response rate, divide 292 by 0.60 and round up: you would plan roughly 487 invitations to aim for 292 responses. The actual number could differ.

What the result tells you

The sample-size result estimates how many usable responses are needed under the stated statistical assumptions. Invitations are a separate operational estimate, not an output of the calculator.

Before you use the result

The formula assumes an appropriate probability-sampling design. An assumed response rate is not a guarantee, and sending more invitations does not resolve nonresponse bias. Cluster sampling, weighting, design effects and the finite-population eligibility definition may require a different method.

Useful for

• Statistics coursework
• Survey sample-size planning
• Finite-population sample planning
• Margin-of-error scenarios

Supporting guides

• Sample Size for a Proportion Guide