THE NUMBERS, EXPLAINED
How to use this calculator.
Place width is measured along the tabletop circumference, not as a straight chord. The usable percentage represents one combined arc. This gives geometric place capacity, not ergonomic or legal occupancy approval.
Start with your inputs
Enter table diameter (cm), required place-setting arc width (cm), usable circumference (%). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Table diameter (cm) | 180 |
| Required place-setting arc width (cm) | 60 |
| Usable circumference (%) | 100 |
A worked example
With the example inputs above, usable arc length (cm) is 565.486678. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Usable arc length (cm) | 565.486678 |
| Geometric places | 9 |
| Arc spacing per place (cm) | 62.831853 |
How this is calculated
Usable arc length (cm)
π × diameter × usable percentage ÷ 100.
Geometric places
Round down usable arc length ÷ required arc width.
Arc spacing per place (cm)
Divide usable arc by place count; if none fit, report that explicitly.
Symbols and units
- a
- Table diameter (cm)
- b
- Required place-setting arc width (cm)
- c
- Usable circumference (%)
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
Place width is measured along the tabletop circumference, not as a straight chord. The usable percentage represents one combined arc. This gives geometric place capacity, not ergonomic or legal occupancy approval.
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?
Usable arc length (cm); Geometric places; Arc spacing per place (cm). 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: Place width is measured along the tabletop circumference, not as a straight chord. The usable percentage represents one combined arc. This gives geometric place capacity, not ergonomic or legal occupancy approval.
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: geometric formulas and arithmetic ↗
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.
Read the quality report →