THE NUMBERS, EXPLAINED
How to use this calculator.
Use a measured balloon density and relative size weights. Allocates the rounded total by largest fractional remainder; ties favour the earlier size. Weights need not sum to 100. Spare percentage is an additional quantity, not an expected failure probability.
Start with your inputs
Enter garland length (m), measured balloons per metre, size mix weights in your chosen order, spare percentage (%). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Garland length (m) | 5 |
| Measured balloons per metre | 20 |
| Size mix weights in your chosen order | 3,2 |
| Spare percentage (%) | 10 |
A worked example
With the example inputs above, balloon total including spares is 110. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Balloon total including spares | 110 |
| Counts by size in input order | 66, 44 |
How this is calculated
Balloon total including spares
Round up length × balloons per metre × (1 + spare percentage/100).
Counts by size in input order
Allocate total in proportion to weights, round down each, then give remaining balloons to the largest fractional remainders. Ties use input order.
Symbols and units
- a
- Garland length (m)
- b
- Measured balloons per metre
- c
- Size mix weights in your chosen order
- d
- Spare percentage (%)
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
Use a measured balloon density and relative size weights. Allocates the rounded total by largest fractional remainder; ties favour the earlier size. Weights need not sum to 100. Spare percentage is an additional quantity, not an expected failure probability.
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?
Balloon total including spares; Counts by size in input order. 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: Use a measured balloon density and relative size weights. Allocates the rounded total by largest fractional remainder; ties favour the earlier size. Weights need not sum to 100. Spare percentage is an additional quantity, not an expected failure probability.
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.
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