Math & Statistics
Proportion Sample Size Calculator
Calculate the initial proportion sample requirement, finite-population adjusted completes, rounded target, invitations needed, and sampling fraction from expected proportion, target margin, critical value, population, response rate, and design effect.
Rounded-up completed sample target-
Expected proportion as decimal-
Target margin as decimal-
Initial sample size before finite correction-
Finite-population adjusted completes-
Invitations at entered response rate-
Completed target as population share-
Decision view
From precision target to fieldwork invitations
From precision target to fieldwork invitationsA staged planning path shows the initial requirement, finite-population correction, rounded completes, response-rate gross-up, and population coverage.
Exact scenario comparisonTarget margin of error (%) changes while all other entered assumptions remain constant.
| Target margin of error (%) | Rounded-up completed sample target | Expected proportion as decimal | Target margin as decimal | Initial sample size before finite correction | Finite-population adjusted completes | Invitations at entered response rate | Completed target as population share |
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How to use Proportion Sample Size Calculator
- Choose expected proportion, target margin, and critical value for the primary estimate.
- Enter population size only when the finite frame is well defined.
- Apply a documented design effect that reflects the planned sample design.
- Enter an achievable response rate and budget invitations separately from completed responses.
Calculator guide
Understanding Proportion Sample Size Calculator
Proportion sample-size planning moves through several distinct stages: a precision requirement, design-effect inflation, finite-population correction, whole-response rounding, and response-rate gross-up. This page keeps every stage visible.
Calculation method
How the calculation works
Solve the normal-approximation proportion formula, apply design effect and finite-population correction, then gross up completed responses for an entered response rate. In the Proportion Sample Size Calculator, the live scenario varies target margin of error (%) and tracks rounded-up completed sample target while the remaining results preserve the reconciliation path. Solve the normal-approximation proportion formula for an effectively infinite population, including design effect. Apply the finite-population denominator, round required completes upward, and divide by expected response rate to obtain invitations.
Detailed calculation process
Translate a precision target into fieldwork volume
The default plan targets a three-point margin for a 50% proportion in a population of 25,000 with design effect 1.2 and expected response rate 35%.
General formula: n0 = c^2 p(1-p)DEFF / e^2; nF = n0 / [1 + (n0-1)/N]; completes = ceil(nF); invitations = ceil(completes/r) The first formula solves for completed observations before finite correction. Population size can reduce that target, rounding protects the precision requirement, and response rate converts completes into invitation volume.
What each symbol means
Worked substitution with the default inputs
The defaults require 1,219 completed responses and 3,483 invitations, with completes equal to about 4.876% of the population.
Fieldwork path
Do not confuse completes with contacts
Each stage answers a different planning question and needs its own allowance.
Worked situations
Practical examples
- A conservative 50% planning share maximizes p(1-p).
- The finite correction reduces the default initial requirement from 1,280.533 to 1,218.185.
- At 35% response, 1,219 completes require 3,483 invitations after upward rounding.
Better inputs
Useful tips
- Round completed samples and invitations upward.
- Add operational reserves for unusable responses, subgroup targets, and attrition when relevant.
- Recalculate if design, response expectations, or primary analysis objectives change.
Before relying on the result
Limitations and common mistakes
- The result does not ensure subgroup precision, statistical power for comparisons, or sufficient rare outcomes.
- A single design effect may not capture stratification, clustering, unequal weights, and multiple estimands.
- Expected response rate does not address nonresponse bias, frame coverage, eligibility, unusable responses, or fieldwork constraints.
Reference
Key terms
- Initial requirement
- Completed sample before finite-population adjustment.
- Finite correction
- Reduction when sampling a material share of a defined population.
- Completed target
- Usable responses needed for the entered precision model.
- Invitation gross-up
- Completed target divided by expected response rate.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
Why round completed sample upward?
The calculated requirement is a minimum under the model; rounding downward could fall below it.
Why are invitations larger than completes?
Only the entered share of invitees is expected to produce a usable response.
Does a larger population always require a much larger sample?
Once population is large relative to n0, the initial precision formula dominates and population size has little additional effect.
Does this sample size guarantee representativeness?
No. Representativeness depends on frame, selection, response, weighting, measurement, and execution as well as count.