Sample Size Calculator

Determine the ideal sample size for your survey or research.

Last Updated: June 15, 2026

Survey Parameters

Confidence Level (%)

Margin of Error (%)

Typically 5% for surveys.

Population Size (Optional)

Only needed for small specific groups (< 20k).

Required Sample Size

385

Respondents

Sample Size vs Margin of Error

Notice how required sample size decreases drastically as you accept a higher margin of error.

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Sample Size Formula (Cochran's Formula)

Cochran's formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population.

n_{0} = \frac{Z ^{2} pq}{e ^{2}}

n_0The required sample size

ZThe Z-value found in a Z-table (e.g., 1.96 for 95% confidence)

pThe estimated proportion of the population (often 0.5 for maximum variability)

q1 - p

eThe desired margin of error (e.g., 0.05 for 5%)

Manual Step: Calculating Sample Size for an Unknown Population

Let's find the required sample size for a 95% confidence level (Z = 1.96) and a 5% margin of error (e = 0.05), assuming maximum variability (p = 0.5).

1. Identify Variables

Write down the known values.

Z=1.96, p=0.5, q=0.5, e=0.05

2. Multiply Proportions

Calculate the variance for the proportion.

p \times q = 0.5 \times 0.5 = 0.25

3. Square Z and Error

Square the Z-score and the margin of error.

Z^2 = 3.8416, e^2 = 0.0025

4. Calculate Top

Multiply the squared Z-score by the proportion variance.

3.8416 \times 0.25 = 0.9604

Result

Divide by the squared error. You need 385 people (always round up).

\frac{0.9604}{0.0025} \approx 384.16

The sample size and margin of error tables print this calculator's answer for populations from 50 to unlimited at 90%, 95% and 99% confidence, show the reverse calculation (the margin of error a sample you already have gives you), and work a population of 400 by hand.

Frequently Asked Questions

What is a good sample size for a survey?

For a 5% margin of error and 95% confidence level, a sample size of around 385 is often sufficient for large populations.

What does confidence level mean?

The confidence level (e.g., 95%) represents how sure you can be that the results from your sample reflect the real population. A 95% confidence level means if you ran the survey 100 times, 95 times the results would be within the margin of error.

How do I calculate sample size for a small population?

For smaller populations (under 10,000), you can use the Finite Population Correction (FPC) to reduce the required sample size. Our calculator handles this automatically if you provide a population size.

Common Standards

Market Research

95% Confidence, 5% Margin

Medical Study

99% Confidence, 1% Margin

Did you know?

For very large populations (over 100,000), the sample size requirement doesn't change much. That's why political polls can predict national results with just 1,000 respondents!

About the Sample Size

Determine the ideal sample size for your research survey. Adjust confidence levels and margin of error to get precise requirements.

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Calculator methods and editorial structure reviewed July 11, 2026. Results are estimates; verify regulated rates, eligibility rules, and professional decisions with the cited primary source.