Sample Size Calculator: Survey Margin of Error & Confidence

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Formula at a glance

Sample Size Calculator: Proportion — n = z²·p(1 − p) / E². Example: Survey: ±5% at 95% → Sample size needed: 385 — How the Sample Size Calculator works: Proportion — n = z²·p(1 − p) / E²

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📘 About the Sample Size Calculator

The sample size determines how precise a survey or study can be. More responses give a smaller margin of error, but the gain slows down: halving the margin of error needs four times the sample. For a large population, ±5% at 95% confidence needs 385 responses; ±3% needs 1,068.

Choose proportion (for percentages, yes/no questions) or mean, the confidence level and margin of error. Add the population size for a finite-population correction, and the expected response rate to see how many invitations to send.

🧮 Formula

Proportion

n = z²·p(1 − p) / E²

Mean

n = (z·σ / E)²

Finite population

n = n₀ / (1 + (n₀ − 1)/N)

✏️ Worked examples

Survey: ±5% at 95%

You enter
Estimating a	Proportion / percentage (surveys)
Confidence level	95%
Margin of error	5%
Expected proportion	50%
Standard deviation (for a mean)	15
Expected response rate	100%

You get
Sample size needed	385
Before rounding up	384.14588
Confidence · z	95% · 1.96

385 responses.

2,000 employees, 30% response

You enter
Estimating a	Proportion / percentage (surveys)
Confidence level	95%
Margin of error	5%
Expected proportion	50%
Standard deviation (for a mean)	15
Population size (optional)	2000
Expected response rate	30%

You get
Sample size needed	323
Before rounding up	322.38554
Confidence · z	95% · 1.96
Finite population correction	n = n₀ ÷ (1 + (n₀ − 1)/N) with n₀ = 384.146, N = 2,000
Invitations to send at 30% response	1,077

323 responses.

🧭 How to use this calculator

What you enter

Estimating a
Confidence level (%)
Margin of error (%)For a mean, in the data’s units.
Expected proportion (%)Use 50% if unsure.
Standard deviation (for a mean)
Population size (optional)
Expected response rate (%)

What you get

Sample size needed
Before rounding up
Confidence · z

❓ Frequently asked questions

Why is 385 the magic number?

With 95% confidence, ±5% margin and p = 50%, n = 1.96² × 0.25 / 0.05² ≈ 384.2, rounded up to 385.

Does the population size matter?

Only when the sample is a sizeable share of it. For populations above about 20,000 the sample size barely changes.

Why use p = 50%?

It gives the largest sample size, so you are safe whatever the true proportion turns out to be.

👥 Sample Size Calculator (Surveys & Studies)