Academic managers online nowFree quote in 3 minutes. Assignments from $19.Submit assignment →

Free, no account, nothing storedThe arithmetic runs in your browser. Nothing you type is sent to us.All 100 calculators →

Statistics & Data Science · pattern A, Numeric fields

How many responses you actually need.

Enter your confidence level, margin of error and expected proportion for the required sample size, with the finite-population correction applied where your population is small.

Inputs

Critical z value1.645 for 90%, 1.96 for 95%, 2.576 for 99%.Margin of error%The precision you need, plus or minus.Expected proportion0.5 is the conservative choice.Population sizeFor the finite-population correction.Expected response rate%To estimate how many to invite.

The formula used

n = z²p(1 − p) ÷ e²

Use p = 0.5 when you have no prior estimate: it maximises the required size, so the result is a safe upper bound.

Sample size needed

385

Unadjusted n: 385
Adjusted for a finite population: 373
Invitations needed at your response rate: 1,244
n for a 3% margin: 1,068
n for a 1% margin: 9,604
Share of the population sampled: 3.11 %

Precision costs quadratically.

Halving the margin of error multiplies the sample size by four, which is why national polls settle around 1,000 respondents for a three-point margin and why a one-point margin is rarely attempted. Population size matters far less than students expect: above roughly 20,000 the required sample barely moves, so a national survey and a city survey need similar numbers.

Questions about sample size

Why does population size barely matter?: Because the finite-population correction only bites when the sample is a large fraction of the whole. Sampling 400 from 20,000 and from 20 million gives almost the same precision.
What if I cannot reach the target?: Report the margin of error you actually achieved and discuss non-response. A smaller honest sample with stated limits is worth more than a claimed precision you did not reach.
Does this work for a mean rather than a proportion?: No — for a mean the formula is n = (zs ÷ e)², which needs an estimate of the standard deviation rather than a proportion.

More in Statistics & Data Science

15 tools in this topic, all free and all running in your browser.

All Statistics & Data Science tools

A calculator handles the arithmetic. It cannot teach you the method.

If the number is not the part you are stuck on, that is what the service is for — a specialist who explains the working, not just the answer.

Submit an assignment See what it costs

Statistical output here is for coursework and learning. Reported p-values and intervals assume the conditions stated on the page; nothing here checks whether those conditions hold for your data.