Sample Size Calculator
Reviewed by CalcMulti Editorial Team·Last updated: ·← Statistics Hub
Choosing the right sample size is critical in research. Too small and your results are unreliable; too large and you waste time and money. This calculator gives you the minimum sample size needed to achieve a desired confidence level and margin of error.
Used for surveys, polls, clinical trials, A/B tests, and any study where you need to estimate a population proportion with known precision.
Formula
n = Z² × p(1−p) / E² (with finite correction: n_adj = n / (1 + (n−1)/N))
- n
- required sample size
- Z
- z-score for desired confidence level (1.96 for 95%)
- p
- estimated proportion (use 0.5 for maximum sample size)
- E
- margin of error (e.g. 0.05 for ±5%)
- N
- population size (for finite population correction)
Typical: 5% (most surveys)
Use 50% if unknown (maximum sample size)
Quick Reference — Common Sample Sizes
Assuming p = 50%, large population:
| Confidence | ±1% MOE | ±3% MOE | ±5% MOE | ±10% MOE |
|---|---|---|---|---|
| 90% | 6,765 | 752 | 271 | 68 |
| 95% | 9,604 | 1,068 | 385 | 97 |
| 99% | 16,587 | 1,844 | 664 | 166 |
Common Mistakes in Sample Size Planning
Confusing sample size with response rate
Sample size = number of completed responses needed. If your response rate is 30%, you need to contact 3× your required sample size to collect enough responses.
Using p = 0.5 when you have a prior estimate
p = 0.5 is the conservative default but gives the largest sample size. If you expect ~20% approval rate, use p = 0.2 and reduce your sample size by 36%.
Forgetting the finite correction for small populations
For populations under 10,000, applying the finite correction can substantially reduce the required sample size — sometimes by 50% or more.
Choosing Your Margin of Error — What Level of Precision Do You Need?
| Use Case | Target MOE | Required n (95% CL) | When appropriate |
|---|---|---|---|
| National political poll | ±3% | 1,068 | High stakes, broadcast-quality results |
| Product satisfaction survey | ±5% | 385 | Standard market research |
| Internal team survey | ±7% | 196 | Directional insights, lower budget |
| Early-stage A/B hypothesis | ±10% | 97 | Exploratory — refine before scaling |
| Academic research (published) | ±3–5% | 385–1,068 | Depends on journal standards |
Assumes p = 50% (conservative maximum). For expected proportions far from 50%, actual required n will be lower.
Case Study: Sizing a User Preference Survey for an App Redesign
A UX researcher at a SaaS company needed to survey users about a major app redesign. Based on internal prototype testing, the team expected around 60% of users to prefer the new design over the old. They wanted 95% confidence with a ±5% margin of error.
Using p = 0.60: n = 1.96² × 0.60 × 0.40 / 0.05² = 369. The active user base was 2,400, so the finite population correction applied: n_adj = 369 / (1 + 368 / 2,400) = 315. Sending 315 surveys was sufficient — not the entire user population.
After collecting 315 responses, 63.2% preferred the new design — within the ±5% expected range. Because the result was well above the 50% decision threshold (with a CI of [58.2%, 68.2%]), the product team approved the redesign for launch without needing a larger sample. Pre-calculating the sample size prevented both over-surveying and inconclusive results.
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Disclaimer
Sample size calculations are estimates based on statistical formulas. Real-world studies may require adjustments for non-response rates, stratification, clustering, and other design factors. Consult a statistician for complex study designs.