How many responses do you actually need?
Enter your population size, confidence level, and acceptable margin of error. We'll tell you the minimum sample, plus how many people to invite to get there.
Your population
The group you want to estimate
Precision
How confident, how close
That's the minimum number of completed responses you need at 95% confidence with ±5% margin.
You need to reach
Invite at 25% response
If pop. were infinite
Sample ratio
How it works
Precision has a price. Here's the receipt
Every survey trades off sample size for precision. Double your confidence, you roughly double the sample. Halve the margin of error, you quadruple it. This calculator tells you exactly where your budget buys you useful precision and where it just buys diminishing returns.
Population size matters less than most people think. Above ~10,000 people, the sample you need barely grows. The finite-population correction only kicks in hard for small, defined groups (your customer list, your team, a specific user segment).
Methodology
The classic Cochran formula
Formula
n = (z² · p · (1 − p)) / E² ÷ (1 + ((z² · p · (1 − p)) / E² − 1) / N)
- n
- Minimum completed responses required.
- z
- Z-score for your chosen confidence level (1.96 for 95%).
- p
- Estimated proportion. Use 0.5 if unknown, the most conservative choice.
- E
- Margin of error, as a decimal (0.05 for ±5%).
- N
- Population size, used for the finite-population correction.
Sampling tips
What most people get wrong
- 1
For general-population surveys, 400 responses is the minimum that produces margins below ±5%. Below that, you are guessing.
- 2
Know your confidence level before running the math. 95% is default; move to 99% only when decisions are genuinely irreversible.
- 3
Population correction matters when the pool is small. 400 of 1,000 people is stronger than 400 of 1,000,000.
- 4
If you have no prior estimate of the proportion, use 0.5. It gives the most conservative (largest) sample size.
- 5
Response rate affects how many you need to invite, not the sample-size math itself. Ask 5× your target for cold email surveys.
Run the math once. Run the form forever.
Try WittyForm freeMore calculators