Solverly

Sample Size Calculator (Proportion)

Know how many responses you need before you launch a survey, A/B test, or quality check. This tool shows the minimum sample size required to estimate a proportion (like a conversion or defect rate) at a chosen confidence level and margin of error—so you plan fieldwork with clear precision targets rather than guessing.

The Sample Size Calculator lets you set confidence, margin of error, and an expected rate (plus optional population size for finite correction) to compute the number of observations you should collect. The goal is to balance accuracy with cost—ensuring results are reliable enough to inform decisions without overspending on data collection. Enter your assumptions below to get a right-sized plan in seconds.

Find the minimum sample size for a proportion — with confidence level, margin of error, and finite population correction.

Enter study parameters

Common: 90, 95, 99.

Absolute margin around the true proportion.

Use 50 if unsure (most conservative).

Adds finite population correction.

Summary

z-value
1.960
p × (1−p)
0.25
n₀ (infinite)
384.15
n₀ (ceil)
385
n (finite)
—
n (finite, ceil)
—

We round sample sizes up to whole units for planning. The z-value matches a two-tailed confidence level.

We estimate the **minimum sample size** to measure a population proportion within a target **margin of error** at a chosen **confidence level**. When the expected proportion is unknown, using **50%** yields a conservative (larger) sample size. We also include an optional **finite population correction**.

Results interpretation

  • n₀ (infinite): Required sample size assuming a very large population.
  • n (finite): Corrected for a known population size; always round up.
  • z-value: Two-tailed standard normal value for the given confidence level.
  • p × (1−p): Proportion variance; largest at p = 0.5.

How it works

We translate your confidence and margin inputs into a precise n using standard survey sampling formulas.

Formulas, steps, assumptions, limitations

Core formula: n₀ = z² · p · (1 − p) / e², where e is the absolute margin (e.g., 0.05), and z corresponds to the two-tailed confidence level.

Finite population correction: n = (N · n₀) / (N + n₀ − 1), round up.

Conservatism: If p is unknown, p = 0.5 maximizes variance and returns the largest required n.

Assumptions: Simple random sampling; independence; large-sample normal approximation for proportions.

Limitations: Stratification, clustering, design effects, and nonresponse are not modeled here.

Use cases & examples

Customer survey

Target 95% confidence and ±5% around an unknown adoption rate → p̂ = 50%.

Quality checks

For a factory line of 12,000 units, add finite correction to reduce n appropriately.

Public polling

If a prior poll shows ~30%, set p̂ = 30% to reflect current expectations.

FAQ: Sample size for proportions

What inputs do we need?
Confidence %, margin of error %, expected proportion p̂ %, and optionally a population size.
What’s the formula?
n₀ = z²·p·(1−p)/e² with a two-tailed z for the confidence level.
How do we apply finite correction?
n = (N·n₀)/(N + n₀ − 1), then round up.
What should we choose for p̂?
Use 50% if unknown for a conservative (largest) sample size.
Is the margin of error absolute?
Yes—e.g., ±5% means e = 0.05 around the true proportion.
Can we use this on small populations?
Yes; the finite population correction reduces n noticeably for small N.

How to compute sample size for a proportion

Enter a confidence level, a margin, an expected p̂, and optionally a population size. We return n and the z-value used.

  1. Enter confidence level (e.g., 95%).
  2. Enter margin of error (e.g., 5%).
  3. Enter p̂ (e.g., 50% if unknown).
  4. Optionally provide population size for finite correction.
  5. Review n₀ and n (finite), then round up for planning.
Tools
  • Calculator (optional)
  • Our Copy link button to share inputs
Tips
  • Reducing the margin or increasing confidence will increase n.
  • Use p̂ from prior data when available to avoid over- or under-sizing.

Designing proportion studies with the right sample size

We plan proportion studies by balancing **precision** (margin of error), **confidence**, and **feasibility**. The formula n₀ = z²·p·(1−p)/e² captures that tradeoff concisely. When the population is finite, we apply a correction so we don’t oversample beyond what’s needed.

Why confidence and margin move together

Higher confidence demands larger z, which inflates n for the same margin. Tightening the margin also grows n quadratically because e sits in the denominator squared. We use this relationship to scope realistic targets.

Choosing p̂ responsibly

Prior data, pilots, or domain knowledge can justify a p̂ other than 50%. If we truly have no clue, 50% is a safe default since it maximizes variance. For rare outcomes, using a smaller p̂ can shrink n substantially.

When the population is not “infinite”

For small or closed populations, the finite correction returns a smaller but still defensible n. We round up to whole units and consider practical issues like nonresponse or screening failures.

Beyond the basics

Complex designs (strata, clusters, unequal probabilities) change variance. In those cases, we introduce a design effect (DEFF) that multiplies n₀. Our simple calculator assumes simple random samples.