Proportion Sample Size Calculator

Example Data Table

Formula Used

The calculator also multiplies the base sample by the design effect when cluster or complex sampling is expected.

How to Use This Calculator

1. Choose a confidence level or enter a custom z-score.
2. Enter the desired margin of error as a percentage.
3. Enter the expected proportion. If unknown, use 50% for a conservative estimate.
4. Add population size only when you want finite population correction.
5. Set design effect above 1.00 for clustered or weighted sampling designs.
6. Enter the expected response rate so the final recommendation reflects nonresponse.
7. Press Submit to display the result above the form, directly below the page header.
8. Use the CSV and PDF buttons to export the calculated output.

Precision, Confidence, and Variability

Proportion studies depend on the balance between certainty and operational cost. At 95% confidence and 5% margin of error, a survey with p = 0.50 usually starts near 384.16 observations before rounding. That value appears often because the 50% assumption maximizes variance and produces the most conservative plan. When prior evidence suggests p = 0.20 or p = 0.80, the required sample falls because variability declines.

Effect of Margin of Error

Margin of error drives sample growth nonlinearly. Reducing error from 5% to 4% does not create a small change; it increases the base requirement materially because error sits in the denominator as a squared term. For example, a 95% design with p = 0.50 rises from about 385 cases at 5% error to roughly 601 at 4% error. Tightening to 3% moves the requirement close to 1,068.

Influence of Confidence Level

Higher confidence means a larger z-score and a larger sample. Using p = 0.50 and 5% error, 90% confidence produces about 271 observations, while 95% requires about 385 and 99% reaches about 664 before other adjustments. This pattern matters when management requests stronger certainty without expanding fieldwork resources.

Finite Population Correction

Finite population correction becomes relevant when the target universe is not very large. If the base sample is near 385 but the full population is only 1,200, the corrected sample drops noticeably. That reduction prevents oversampling while preserving statistical quality. For very large populations, the correction becomes negligible and can be ignored safely.

Design Effect and Response Planning

Complex designs increase variance, so design effect scales the initial sample upward. A base estimate of 385 becomes 462 when the design effect is 1.20. If expected response is 80%, the issued sample must then rise to about 578. This adjustment is essential for clustered surveys, panel studies, and operational settings with incomplete participation.

Operational Use in Survey Design

This calculator helps analysts compare scenarios quickly and document assumptions consistently. Teams can test alternative confidence levels, margins, and response rates before launch. That makes budget planning stronger, supports methodology notes, and helps decision-makers see why one survey may need 300 completes while another needs more than 1,000. across regions, products, service lines, and departments.

FAQs