THE NUMBERS, EXPLAINED
How to use this calculator.
Stage retention assumptions are supplied, not estimated. Required initial enrollment is rounded upward; expected surviving participants remain fractional.
Start with your inputs
Enter target study completers (count), retention at successive recruitment stages (%). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Target study completers (count) | 80 |
| Retention at successive recruitment stages (%) | 80,50 |
A worked example
With the example inputs above, combined retention (%) is 40. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Combined retention (%) | 40 |
| Required initial enrollment (count) | 200 |
| Expected completers from rounded enrollment (count) | 80 |
How this is calculated
Combined retention (%)
Multiply successive stage retention fractions.
Required initial enrollment (count)
Divide target by combined retention and round up.
Expected completers from rounded enrollment (count)
Multiply rounded enrollment by combined retention.
Symbols and units
- a
- Target study completers (count)
- b
- Retention at successive recruitment stages (%)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Stage retention assumptions are supplied, not estimated. Required initial enrollment is rounded upward; expected surviving participants remain fractional.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Combined retention (%); Required initial enrollment (count); Expected completers from rounded enrollment (count). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Stage retention assumptions are supplied, not estimated. Required initial enrollment is rounded upward; expected surviving participants remain fractional.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
OpenStax Prealgebra 2e — arithmetic and proportions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
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