THE NUMBERS, EXPLAINED
How to use this calculator.
Uniform scaling changes volume by scale cubed and surface area by scale squared. Both volumes must use the same units and refer to closed meshes. This tool does not inspect a mesh file.
Start with your inputs
Enter current closed-mesh volume, target volume. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Current closed-mesh volume | 100 |
| Target volume | 800 |
A worked example
With the example inputs above, linear scale factor is 2. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Linear scale factor
((800) ÷ (100))^(1 ÷ 3) = 2
Scale (%)
((800) ÷ (100))^(1 ÷ 3) × 100 = 200
Surface-area factor
((800) ÷ (100))^(2 ÷ 3) = 4
| Result | Example answer |
|---|---|
| Linear scale factor | 2 |
| Scale (%) | 200 |
| Surface-area factor | 4 |
How this is calculated
Linear scale factor
(b ÷ a)^(1 ÷ 3)
Scale (%)
(b ÷ a)^(1 ÷ 3) × 100
Surface-area factor
(b ÷ a)^(2 ÷ 3)
Symbols and units
- a
- Current closed-mesh volume
- b
- Target volume
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
Uniform scaling changes volume by scale cubed and surface area by scale squared. Both volumes must use the same units and refer to closed meshes. This tool does not inspect a mesh file.
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?
Linear scale factor; Scale (%); Surface-area factor. 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: Uniform scaling changes volume by scale cubed and surface area by scale squared. Both volumes must use the same units and refer to closed meshes. This tool does not inspect a mesh file.
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.
Read the quality report →