Sample Size Calculator with Design and Response Adjustments
Estimate required completed responses for a proportion or mean, then inflate for design effect and expected response rate and apply finite-population correction.
Study precision and population assumptions
Required sample size
sample size calculator: method, formulas and interpretation
The sample size calculator uses a dedicated calculation path for this exact problem rather than a generic input-and-output shell. Inputs are normalized before the formula is applied, and the result panel exposes the assumptions needed to audit the answer.
Proportion and mean formulas
The sample size calculator uses an expected proportion for binary outcomes or an expected standard deviation for a mean. When no reliable proportion is known, 0.5 produces the largest variance and therefore a conservative simple-random-sample requirement for the selected margin of error.
Design effect, population and response rate
The sample size calculator multiplies by the entered design effect before rounding completed responses upward. Finite-population correction is applied only when a population size is entered. The invitation count then divides by the expected response rate. These adjustments are planning assumptions; complex surveys should use design-specific methods and account for subgroup precision.
Worked use and validation
The sample size calculator rejects missing, non-finite or physically impossible values with a specific message. Load the worked example to inspect the complete calculation and compare it with a manual result before relying on a planning estimate.
How to read the output
The sample size calculator separates the primary result from supporting quantities, unit conversions and limitations. Display rounding does not replace the unrounded values used inside later steps. Use consistent inputs and preserve the stated model when comparing scenarios.
Rounding and recruitment reserve
The sample size calculator always rounds the required completed sample upward because a fractional participant cannot satisfy the precision target. It then inflates that completed count for the expected response rate. The invitation number is not a guarantee; eligibility failures, incomplete records and subgroup targets can require an additional recruitment reserve.
Why use 0.5 for an unknown proportion?
It maximizes p(1−p) and produces the largest simple-random-sample requirement.
Does the result guarantee representativeness?
No. Sampling quality depends on coverage, selection, response and measurement, not only count.
What is design effect?
It inflates simple-random-sample variance to reflect clustering, weighting or another design feature.