THE NUMBERS, EXPLAINED
How to use this calculator.
Continuous-capacity approximation with constant daily arrivals and handling time. Whole-message capacity is rounded downward before the projection.
Start with your inputs
Enter new messages each day (count/day), handling time (minutes/message), daily review budget (minutes/day), starting inbox backlog (count), days to project (count). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| New messages each day (count/day) | 40 |
| Handling time (minutes/message) | 2 |
| Daily review budget (minutes/day) | 60 |
| Starting inbox backlog (count) | 100 |
| Days to project (count) | 5 |
A worked example
With the example inputs above, daily message capacity (count/day) is 30. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Daily message capacity (count/day) | 30 |
| Backlog after projection (count) | 150 |
| Daily capacity surplus (count/day) | -10 |
How this is calculated
Daily message capacity (count/day)
Round available minutes divided by handling minutes downward.
Backlog after projection (count)
Add daily arrivals minus capacity for every day, floored at zero.
Daily capacity surplus (count/day)
Subtract arrivals from processing capacity; negative means backlog grows.
Symbols and units
- a
- New messages each day (count/day)
- b
- Handling time (minutes/message)
- c
- Daily review budget (minutes/day)
- d
- Starting inbox backlog (count)
- e
- Days to project (count)
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
Continuous-capacity approximation with constant daily arrivals and handling time. Whole-message capacity is rounded downward before the projection.
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?
Daily message capacity (count/day); Backlog after projection (count); Daily capacity surplus (count/day). 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: Continuous-capacity approximation with constant daily arrivals and handling time. Whole-message capacity is rounded downward before the projection.
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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