Plan surveys with precision by estimating how many responses you need for a proportion target based on confidence level error margin and expected rate with options for finite population correction design effects and response loss adjustments all wrapped in a stepwise calculator that guides you from inputs to actionable counts with explanations and examples
If fields are blank default values are used. Proportions above one are interpreted as percents for convenience.
| Quantity | Value |
|---|---|
Initial size ignoring FPC n0 | 384.15 |
After finite population correction n_fpc | 384.15 |
After design effect n_design | 384.15 |
| Completed responses required | 385 |
| Invitations required at given response rate | 482 |
All final counts are rounded up to the next whole number.
p. If unknown consider checking the conservative option which uses p = 0.5.E for the confidence interval on the proportion.The classical normal approximation for a two sided confidence interval on a single proportion leads to the well known requirement
n0 = (Z^2 × p × (1 - p)) / E^2
When sampling without replacement from a finite frame of size N apply the finite population correction
n_fpc = n0 / (1 + (n0 - 1)/N)
If your design uses clustering stratification or unequal weighting multiply by the design effect DEFF
n_design = n_fpc × DEFF
Finally round up to the next whole number for a practical requirement. If you expect a response rate r then invitations are approximately n_design / r treating r as a fraction.
For unknown p the conservative choice is p = 0.5 which maximizes p(1-p) and therefore yields the largest sample.
This calculator needs a few thoughtful inputs to give reliable guidance. Enter an expected proportion between zero and one as your best guess of success rate. Choose a confidence level to reflect how sure you wish to be. Set a target margin of error that you can accept. Add population size if sampling from a known frame. Include a design effect if clustering or stratification increases variance. Also add an anticipated response rate to plan invitations and reminders planning support.
Confidence level expresses how often your interval would capture the true proportion in repeated samples. Common choices are ninety five and ninety nine percent. Each level links to a Z score from the standard normal distribution. The margin of error is half the width of the desired interval. Smaller error needs more responses. The core relationship is simple yet powerful since sample size grows with the square of Z and shrinks with the square of the error for any study
When sampling from a relatively small finite population you can reduce the required sample using the finite population correction. First compute the initial size ignoring the frame then scale it by dividing by one plus the initial size minus one over the population size. Complex designs may inflate variance above a simple random plan. Capture that with a design effect greater than one. Multiply the corrected size by this factor to get a realistic requirement that suits your study context
Not everyone you contact will respond so plan invitations beyond the pure statistical requirement. Provide an expected response rate based on prior experience or pilot testing. The calculator will divide the needed responding sample by that rate to estimate invitations. If the study involves screening for eligibility consider additional oversampling to reach enough qualified participants. You can include a small buffer for breakage or missing data. These planning steps help turn theory into field ready execution with logistics and tracking
Use the results as a starting plan and review them with stakeholders. Check whether the underlying assumptions match your reality including expected proportion design features and population size. If your initial proportion is very uncertain try a sensitivity scan around several values to see the effect on requirements. When calculations produce a fractional count always round up. Keep records of the inputs your decisions and any changes so that your team can revisit choices after data collection for future learning
Use the conservative choice p = 0.5 which produces the largest required sample. If you later obtain a better estimate you can rerun the calculation to potentially reduce the requirement.
Pick an error that is meaningful for your decisions. For example if a three percentage point swing would change your action set E = 0.03. Tighter errors require larger samples.
The normal approximation is widely used and works well for moderate to large samples. For very small samples or extreme proportions consider an exact or adjusted method though planning usually stays similar.
Design effect accounts for variance inflation from complex sampling such as clustering weighting or stratification. A value above one increases the required sample relative to simple random sampling.
When the target population is not huge the correction reduces the required sample because sampling without replacement adds information efficiency compared with an infinite population assumption.
Always round up because fractions of respondents are not possible and rounding down would reduce coverage below the chosen confidence and error targets.
Yes. Provide an expected response rate and the tool converts required completes into invitations. You can also add buffers for eligibility screening or quality checks as needed.
This page focuses on confidence interval based sizing for a single proportion. For power based tests or two proportion comparisons use a dedicated power calculator tailored to your study design.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.