Free Survey Sample Size Calculator

Understanding sample sizes

The bigger your sample, the closer your survey result is likely to be to the true value in the population.
What’s less obvious is how big that sample needs to be for a chosen level of accuracy. That’s exactly what the calculator above answers.

If you’re planning to buy consumer panels, knowing the right sample size prevents overspending (too many responses) and misleading conclusions (too few). A sample that’s too small for the population can swing your results just by chance—always plan for an appropriate margin of error and confidence level.

What the inputs mean

• Population size (N) — How many people are in the group you care about. Leave blank if very large or unknown.
• Confidence level (z) — How sure you want to be that the true value lies within the margin of error (90%, 95%, 99% are common).
  Typical z-scores: 1.645 (90%), 1.96 (95%), 2.576 (99%).
• Margin of error (e) — The ±% you’re willing to tolerate around the estimate (e.g., ±5%).
• Expected proportion (p) — Your best guess of the percentage you’ll observe (use 50% if unsure; it gives the largest required sample and is a safe default).

The math the calculator uses

For a proportion estimate:

• Infinite population (approximation):
  n₀ = (z² · p · (1 − p)) / e²

• Finite population correction (when N is known):
  n = (N · n₀) / (n₀ + N − 1)

Here p and e are proportions (0–1). The calculator rounds up to the next whole response.

Why does p=50% give the largest n? Because p(1−p) is maximized at 0.25 (50/50 split), which is the most “uncertain” case.

Worked example

• Population N = 10,000
• Confidence 95% (z = 1.96)
• Margin of error e = 5%
• Proportion p = 50%

1) Infinite-pop sample: n₀ ≈ 384.16
2) Finite correction: n ≈ (10,000 × 384.16) / (384.16 + 9,999) ≈ 370
Require: 370 completes

If you expect a 25% response rate, invite ≈ 370 / 0.25 = 1,480 people.

Buying respondents? Quick rules of thumb

• 95% ±5% with large N → ≈ 385 completes
• 95% ±3% with large N → ≈ 1,067 completes
• 90% ±5% with large N → ≈ 271 completes
  Finite populations reduce these slightly (the calculator applies FPC automatically).

Why the curve isn’t “linear”

Lowering the margin of error from 5% to 2.5% does not double the required sample—it quadruples it (because e² is in the denominator). That’s why very tight precision requires large, sometimes impractical, samples.

When to adjust the sample size

• Expected response rate (rr): plan invites = n / rr.
• Design effect (DEFF): if using clustered/complex sampling, use adjusted n = n × DEFF (e.g., DEFF 1.3–1.5 is common for clustered lists).
• Subgroup analysis: ensure each subgroup you want to analyze meets its own sample requirement.

Calculating sample size manually (showing the work)

1. Choose z for your confidence level.
2. Set e (your tolerated ±%).
3. Pick p (use 50% if unsure).
4. Compute n₀.
5. If population is known, apply the finite population correction to get n.
6. Round up and adjust for response rate/design effect if needed.

After crunching the numbers—or simply using the calculator—you’ll get the number of responses needed to reach your chosen accuracy. Tweak the inputs to see how changes in precision, confidence, or assumed proportion affect your sample.

Final notes

• A too-small sample can mislead; a too-large one wastes budget.
• There’s always a margin of error—report it alongside the result.
• Use consistent definitions and the same time window for population and responses.
• If in doubt, use p = 50% and 95% ±5% as a pragmatic starting point, then refine.

Armed with these principles—and the calculator—you can plan surveys that deliver reliable, defensible results without overspending.