Appearance

Sample Size Calculator

By Calxy · Updated · Calculation methodology

Find how many survey answers you need from your confidence level, margin of error, population size and response rate.

Printed from Calxy · https://www.calxy.net/math/sample-size-calculator

Check your inputs—Complete valid inputs to calculate a current result.
percentage points

How close you want the survey answer to be to the truth, for example ±5 points.

%

Your best guess of the answer. Not sure? Keep 50%: it gives the safest (largest) sample.

How many people are in the whole group. Use 0 if it is very large or unknown.

%

The share of invited people you expect to answer.

Completed responses needed

385

  • People to invite at the entered response rate385
  • Normal critical value1.9600

Simple random sampling and a normal-approximation planning model. Nonresponse bias, clustering and design effects are not accounted for. A 50% expected proportion gives the largest required sample.

How this was calculated

  1. Turn the 95% confidence level into a z-score (a number from the bell curve that says how sure you want to be). Higher confidence means a bigger z.z for 95% confidenceAnswer: z = 1.959963985
  2. Write the percentages as decimals, then work out how many answers you need for a very large group. p is your guess of the answer and E is the margin of error.n₀ = z² × p × (1 − p) ÷ E²Put in your numbers: n₀ = 1.959963985² × 0.5 × 0.5 ÷ 0.05²Answer: n₀ = 384.1458821
  3. No population size was entered, so the group is treated as very large and no correction is needed.n = n₀Answer: n = 384.1458821
  4. You cannot ask part of a person, so always round up to the next whole number.Round upPut in your numbers: 384.1458821 → 385Answer: 385 completed responses
  5. Not everyone answers. If 100% of the people you invite reply, divide by that share to see how many people to invite, then round up.Invitations = responses ÷ response ratePut in your numbers: 385 ÷ 1Answer: 385 people to invite

Sample size in simple words

A survey asks a sample (some of the people) instead of everyone. The sample size is how many answers you need so the result is close enough to what everyone would say.

Three choices set the size. The margin of error is how close you need to be, such as within 5 percentage points. The confidence level is how sure you want to be, such as 95%. The expected proportion is your best guess of the answer; 50% is the safest guess because it needs the most answers.

Example: at 95% confidence (z = 1.96), a 5-point margin and a 50% guess, n = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16. You cannot ask part of a person, so round up to 385 answers.

If the whole group is small, you need fewer. For a school of 1,000 students the same survey needs 278 answers. If only half the people you ask will reply, invite twice as many.

Formula and method

For expected proportion p and margin e, n₀ = z²p(1 − p)/e². A finite population N adjusts this to n₀/[1 + (n₀ − 1)/N]; round up.

Worked example

At 95% confidence, 50% expected proportion and a 5 percentage-point margin, an unspecified population needs 385 completed responses. A population of 1,000 needs 278.

Frequently asked questions

Does this guarantee a representative survey?

No. The calculation assumes simple random sampling. Selection bias, nonresponse bias and clustering can make the stated margin inappropriate.

References

Last updated . Results are estimates for informational purposes only.