Sample Size Calculator
Enter how many people are in the group you want to learn about, how sure you want to be and how much error you can live with. You get the number of completed responses to aim for.
- Finite population correction
- Response rate built in
- 80% to 99% confidence
Uses Cochran's formula with a finite population correction. Assumes a simple random sample.
Most surveys need fewer responses than people expect. Once a population passes a few thousand, the sample barely grows. A town of 20,000 and a country of 60 million both need about 385 responses for ±5% at 95% confidence. What changes the number most is the margin of error you choose.
Sample sizes at a glance
These figures assume 50% proportion, the cautious default. Find your population row and read across to the margin of error you need.
| Population | ±10% | ±5% | ±3% | ±1% |
|---|---|---|---|---|
| 100 | 50 | 80 | 92 | 99 |
| 500 | 81 | 218 | 341 | 476 |
| 1,000 | 88 | 278 | 517 | 906 |
| 5,000 | 95 | 357 | 880 | 3289 |
| 10,000 | 95 | 370 | 965 | 4900 |
| 50,000 | 96 | 382 | 1045 | 8057 |
| 100,000 | 96 | 383 | 1056 | 8763 |
| 1,000,000 | 97 | 385 | 1066 | 9513 |
| Unlimited | 97 | 385 | 1068 | 9604 |
Notice how little the numbers change past 10,000 people. That is the finite population correction fading out, and it is why national polls of about 1,000 people can be accurate to about ±3%.
How the margin of error drives the sample
This is the setting with the biggest effect. Move the slider to change the margin of error and compare three population sizes.
The relationship is an inverse square. Going from ±5% to ±2.5% takes you from 385 to about 1,537 responses. Decide what precision you really need before you commit the budget.
How to work out a sample size
Four decisions, then one formula. Step through the choices in the order a researcher makes them.
Define the population
Count everyone your result should describe, such as all customers from last year or all staff in one company.
The formula is n = z² × p(1 − p) ÷ e², then adjusted for a small population with n ÷ (1 + (n − 1) ÷ N). The calculator does both.
Picking a confidence level
Higher confidence costs more responses. Compare the three most used levels for a large population at ±5%.
One in ten samples could fall outside your margin. Fine for early product feedback or internal polls.
The standard for published surveys, market research and most academic studies.
Only one sample in a hundred should miss. You need about 70% more responses than at 95%.
Academic work usually uses 95%. Quick internal polls sometimes accept 90%. Medical and safety research often goes to 99% because the cost of a wrong answer is high.
Before you send the survey
A large sample cannot fix a biased one. Run through these points first.
Tick each item as you go.
Sample size controls random error only. If the people who answer differ from the people who do not, a bigger sample just gives you a more confident wrong answer.
What each input changes
Five numbers decide the result. Each tile explains one result.
Matters for groups under about 20,000. Above that the sample hardly grows.
How often the true value falls inside your margin across repeat surveys.
The plus or minus on your result. Halving it needs four times the sample.
Answers near 50% vary most, so 50 gives the safest sample.
Turns completed responses into the number of invitations to send.
If you only change one thing, change the margin of error. Population size barely matters once it is large, and the proportion matters only when you have good prior data.
Frequently Asked Questions
No question matches that search.
What sample size do I need for a population of 1,000?
At 95% confidence and ±5% margin of error you need 278 completed responses. At ±3% it rises to 517.
Why is 385 such a common sample size?
It is the answer for a large population at 95% confidence, ±5% margin and 50% proportion: 1.96² × 0.25 ÷ 0.05² = 384.16, rounded up.
Does a bigger population need a bigger sample?
Only up to a point. A population of 1,000 needs 278 responses, 100,000 needs 383 and 10 million needs 385, all at ±5%.
What proportion should I enter?
Use a figure from an earlier study if you have one. If not, enter 50%. It produces the largest sample, so you will not fall short.
Is the sample size the number of people I invite?
No. It is the number of completed responses. Divide it by your expected response rate to get invitations.
What is a good margin of error?
±5% is common for general surveys. Use ±3% when you need to spot small changes between groups or over time.
Can I use this for A/B tests?
Not directly. A/B tests compare two rates and need a power calculation. Use the effect size calculator to size the expected difference first.
What is the finite population correction?
A small adjustment for when your sample is a large share of the population. It lowers the sample needed for small groups.
Get the number, then get it right
Set the margin of error you can act on, keep 95% confidence unless you have a reason to change it, and plan invitations around a realistic response rate. Then spend your effort on reaching a fair mix of people, because that matters as much as the count.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.