THE NUMBERS, EXPLAINED
How to use this calculator.
Treats filament as a constant-diameter solid cylinder. Density is in g/cm³ and diameter in mm; these units cancel to metres in the length formula. Gross mass must include the same empty spool.
Start with your inputs
Enter gross spool mass (g), empty spool mass (g), material density (g/cm³), filament diameter (mm). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Gross spool mass (g) | 700 |
| Empty spool mass (g) | 200 |
| Material density (g/cm³) | 1.25 |
| Filament diameter (mm) | 2 |
A worked example
With the example inputs above, remaining filament (g) is 500. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Remaining filament (g)
(700)-(200) = 500
Estimated length (m)
((700)-(200)) ÷ (1.25) ÷ (π × ((2) ÷ 2)^2) = 127.323954
| Result | Example answer |
|---|---|
| Remaining filament (g) | 500 |
| Estimated length (m) | 127.323954 |
How this is calculated
Remaining filament (g)
a-b
Estimated length (m)
(a-b) ÷ c ÷ (π × (d ÷ 2)^2)
Symbols and units
- a
- Gross spool mass (g)
- b
- Empty spool mass (g)
- c
- Material density (g/cm³)
- d
- Filament diameter (mm)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
π is the circle constant, approximately 3.141592653589793.
Assumptions and limits
Treats filament as a constant-diameter solid cylinder. Density is in g/cm³ and diameter in mm; these units cancel to metres in the length formula. Gross mass must include the same empty spool.
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?
Remaining filament (g); Estimated length (m). 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: Treats filament as a constant-diameter solid cylinder. Density is in g/cm³ and diameter in mm; these units cancel to metres in the length formula. Gross mass must include the same empty spool.
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: algebra and proportional reasoning ↗
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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