If you are planning a survey, experiment, A/B test, or market research project, this online sample size calculator helps you estimate how many responses you need. Enter your assumptions below and get an instant recommendation for completed responses and total invites.
How this sample size calculator works
This calculator estimates the required sample size for a proportion. It is commonly used for survey planning (customer satisfaction, election polling, product feedback, and similar research). You provide your confidence level, margin of error, and an expected proportion, and the calculator returns the minimum recommended number of completed responses.
Core formula (infinite population)
- Z = z-score from your confidence level (for 95%, Z ≈ 1.96)
- p = expected proportion as a decimal (50% = 0.50)
- e = margin of error as a decimal (5% = 0.05)
Finite population correction (optional)
If your total population is not very large, the calculator applies a correction:
Where N is your population size. This often reduces the required sample when the audience is limited (for example, employees in one company or members of a small customer segment).
Input guide: choosing realistic assumptions
1) Confidence level
Most projects use 90%, 95%, or 99%. Higher confidence means a larger sample size.
- 90%: faster and cheaper, but less certainty
- 95%: common default for business and social research
- 99%: stricter certainty, often much larger sample
2) Margin of error
This is how precise you want your estimate to be. Smaller error bands require larger samples.
- ±5% is common in general surveys
- ±3% gives more precision, but may significantly increase cost
- ±1–2% is usually reserved for high-stakes studies with large budgets
3) Estimated proportion (response distribution)
If you are unsure, use 50%. That gives the most conservative (largest) sample size. If prior data suggests 20% or 80%, your required sample can be smaller.
4) Response rate
Completed responses are not the same as invitations sent. If you need 385 completed responses and expect a 50% response rate, you should invite roughly 770 people.
Example calculation
Suppose you want a 95% confidence level, ±5% margin of error, and unknown proportion (50%). For a large population, the recommended sample is about 385 completed responses. If your response rate is 40%, you should plan to invite about 963 people.
When you need more than this calculator
This tool is ideal for proportion-based surveys. For hypothesis testing, conversion experiments, and clinical-style studies, you may need statistical power analysis that includes effect size, power (typically 80% or 90%), and standard deviation assumptions.
- A/B testing often requires minimum detectable effect calculations
- Comparing means uses different formulas than proportions
- Clustered or stratified sampling may require design-effect adjustments
Best practices for better data quality
- Define your target population clearly before collecting data
- Use random sampling when possible to reduce bias
- Pilot test the survey to improve question clarity
- Track nonresponse and compare responders vs. nonresponders
- Document assumptions used in your sample size estimate
Quick FAQ
Is 50% always the right proportion to use?
Use 50% when uncertain. It is conservative and avoids underestimating the sample size.
Does a bigger population always need a much bigger sample?
No. Once populations are large, required sample size grows slowly. Precision settings usually matter more than total population size.
Can I trust results from a small sample if confidence is high?
Confidence level alone is not enough. You also need an acceptable margin of error and representative sampling.