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Sample Size Calculator

Calculate required sample size for statistical studies and surveys. Free, fast, accurate — no signup, mobile-friendly, w

Study Type

Parameters

Typically 90%, 95%, or 99%

Percentage points (e.g., 5 for ±5%)

Use 50% if unknown (most conservative)

Common Scenarios

📏 Effect Size Guide

Cohen's d: Small=0.2, Medium=0.5, Large=0.8
f² (regression): Small=0.02, Medium=0.15, Large=0.35
f (ANOVA): Small=0.1, Medium=0.25, Large=0.4
r (correlation): Small=0.1, Medium=0.3, Large=0.5

Required Sample Size

Sample Size

385

participants needed

Z-Score

1.96

95% confidence

Margin of Error

4.99

percentage points

CI Lower Bound

45%

confidence interval

CI Upper Bound

55%

confidence interval

Sample Adequacy: Good

Sample size is good for most statistical analyses

📋 Recommendations

•Sample size provides good statistical power

Step-by-Step Calculation

1Given: Confidence level = 95%, Margin of error = 5%
2Expected proportion p = 50% = 0.500
3Z-score for 95% confidence = 1.960
4Formula: n = (Z² × p × (1-p)) / E²
5n = (1.960² × 0.500 × 0.500) / 0.050²
6n = 384.1 ≈ 385

How it works

A sample size calculator finds how many responses a survey needs for a target margin of error and confidence level. Bigger samples narrow the margin, but with diminishing returns — precision improves with the square root of the sample size.

Sample size for a proportion

n = z² · p · (1 − p) ÷ E²
z
z-score for the confidence level (1.96 for 95%)
p
estimated proportion (0.5 for the safest, largest n)
E
margin of error (e.g. 0.05)

Worked example

  • 95% confidence (z = 1.96)
  • p = 0.5, margin E = 5%
  1. n = 1.96² × 0.5 × 0.5 ÷ 0.05²
  2. = 0.9604 ÷ 0.0025

≈ 385 responses needed.

Good to know

  • Using p = 0.5 gives the most conservative (largest) sample when you don't know the true proportion.
  • For small populations, a finite-population correction lowers the required n.
  • Halving the margin of error roughly quadruples the sample size.

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Frequently Asked Questions

What sample size do I need for a survey?

It depends on your confidence level, margin of error, and expected proportion: n = z²p(1-p)/e². For 95% confidence and a ±5% margin of error, the classic answer is 385 respondents.

What is the margin of error?

It's the ± range around your estimate within which the true population value likely falls. Tightening it is expensive: halving the margin of error requires four times the sample size.

How does confidence level affect sample size?

Higher confidence widens the z-score and inflates the sample: 90% uses z = 1.645, 95% uses 1.96, and 99% uses 2.576. Moving from 95% to 99% confidence increases the required sample by roughly 73%.

Does the size of the population matter?

Surprisingly little once the population is large — surveying a city or a country needs nearly the same sample. When you sample more than about 5% of a small population, apply the finite population correction to shrink the requirement.

What proportion (p) should I assume if I don't know it?

Use p = 0.5, the most conservative choice, because it maximizes variance and therefore the required sample size. If prior research suggests a different proportion, using it can justifiably reduce your sample.