calculate sample size calculator

Sample Size Calculator (Survey Proportions)

Estimate how many responses you need for a statistically meaningful survey result.

Confidence Level

Margin of Error (%) Typical range: 3% to 7%.

Estimated Proportion, p (%) Use 50% if unsure (most conservative sample size).

Population Size (optional) Adds finite population correction when provided.

Design Effect (DEFF) Use 1 for simple random sampling; use higher values for complex sampling.

Expected Non-Response Rate (%) Adjusts how many people you should invite/contact.

Why sample size matters

If your sample is too small, your estimate can swing wildly and mislead decisions. If your sample is too large, you may waste time and budget. A good sample size strikes the balance between statistical confidence and practical constraints.

Whether you are running customer surveys, market research, employee feedback, or product testing, choosing an appropriate sample size helps you produce results you can trust.

What this calculator does

This calculator computes sample size for a proportion (yes/no, support/oppose, clicked/did not click, etc.) using standard survey statistics. It includes:

Confidence level (e.g., 95%)
Margin of error (e.g., ±5%)
Estimated population proportion (p)
Optional finite population correction
Design effect adjustment
Non-response inflation for contact targets

Core formula used

Step 1: Initial sample size (large population)

n0 = (Z² × p × (1 − p)) / e²

Z = z-score from confidence level
p = expected proportion (as a decimal)
e = margin of error (as a decimal)

Step 2: Finite population correction (optional)

n = n0 / (1 + (n0 − 1) / N)

If your total population N is known and not huge, this often reduces the required sample.

Step 3: Practical adjustments

Design effect: multiply by DEFF when sampling is clustered or weighted.
Non-response: divide by response rate to estimate how many people to invite.

How to choose each input

Confidence level

95% is a common default. Use 99% for higher certainty, but expect larger sample sizes.

Margin of error

Smaller margins require much larger samples. Going from 5% to 3% can nearly triple sample size.

Estimated proportion (p)

If you have no prior estimate, use 50%. This yields the largest required sample and is a conservative choice.

Population size

For very large populations, correction is negligible. For small populations, include N to avoid oversampling.

Example

Suppose you want 95% confidence, ±5% error, and no prior estimate (p = 50%). The base sample is roughly 385 completes for a large population. If you expect 20% non-response, invite around 482 people.

Common mistakes to avoid

Using a tiny sample and over-interpreting precise-looking percentages.
Ignoring non-response and ending up below target completes.
Using p too optimistically without evidence.
Forgetting design effect in complex survey designs.

When this calculator is not enough

This page is ideal for single-proportion survey planning. For A/B testing, mean comparisons, regression models, survival analysis, or multi-arm experiments, use specialized power analysis methods that account for effect size, variance, and statistical power directly.

Final takeaway

A sample size calculator is one of the most useful tools in practical statistics. Set clear assumptions, choose realistic response rates, and document your inputs. That gives you transparent, defensible results and better decisions.