Sample Size Calculator (Surveys)
How many respondents do I need for a given margin of error and confidence level?
Spec sheet
cochran_proportion · v1.0.0Cochran's formula with finite population correction
- 01
n₀ = z² · p(1 − p) / e² - 02
n = n₀ / (1 + (n₀ − 1)/N) - 03
invitations = n ÷ response rate
- Simple random sampling of a proportion; clustered or stratified designs need a design effect.
- Not a power analysis for comparing groups.
- Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wileytextbook
Worked example
computed by the same formula95 %, ±5 %, p = 50 %
- Confidence level
- 95 %
- Margin of error
- 5 %
- Expected proportion
- 50 %
- Expected response rate
- 100 %
- Completed responses needed
- 385
- People to invite
- 385
- Infinite-population size
- 385
- 1. z = 1.96
- 2. n₀ (unrounded) = 384.146
Questions
How is the sample size calculator calculated?
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Cochran's formula with finite population correction. n₀ = z² · p(1 − p) / e² · n = n₀ / (1 + (n₀ − 1)/N) · invitations = n ÷ response rate
Example: 95 %, ±5 %, p = 50 %?
›
Completed responses needed: 385; people to invite: 385.
What does this calculator not cover?
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Simple random sampling of a proportion; clustered or stratified designs need a design effect. Not a power analysis for comparing groups.
Where do the numbers come from?
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Sources: Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wiley. The formula is versioned (cochran_proportion v1.0.0) and covered by automated tests.
Is my data stored?
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No. The calculation runs in your browser and nothing is sent unless you choose to save a shareable link.
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