Calculator
Quick notes
- Surface area is the total outside area of the solid.
- Volume is the space inside the solid.
- Inputs must use the same length unit.
Example data table
| Solid | Dimensions | Surface area | Volume |
|---|---|---|---|
| Cube | a = 4 cm | 96 cm² | 64 cm³ |
| Rectangular prism | l = 8, w = 5, h = 10 cm | 340 cm² | 400 cm³ |
| Sphere | r = 6 cm | 452.39 cm² | 904.78 cm³ |
| Cylinder | r = 3, h = 10 cm | 245.04 cm² | 282.74 cm³ |
Formula used
- Cube:
SA = 6a²,V = a³ - Rectangular prism:
SA = 2(lw + lh + wh),V = lwh - Sphere:
SA = 4πr²,V = (4/3)πr³ - Cylinder:
SA = 2πr(r + h),V = πr²h - Cone:
SA = πr(r + √(r² + h²)),V = (1/3)πr²h - Right triangular prism:
SA = (a + b + √(a² + b²))L + ab,V = (1/2)abL
a, b legs; l, w, h prism dimensions; r radius; L prism length.How to use this calculator
- Select a solid from the dropdown.
- Choose a length unit and rounding preference.
- Enter the dimensions shown for your solid.
- Click Calculate to view surface area and volume.
- Use the download buttons to export the computed summary.
FAQs
1) What is the difference between surface area and volume?
Surface area measures the outside covering of a solid. Volume measures the space inside. Both use the same input lengths, but area is squared and volume is cubed.
2) Do I need to convert units before using it?
Use one consistent length unit for all inputs. If your measurements mix units, convert them first, then select the matching unit so the output labels stay correct.
3) Why does the cone require a square root?
Cone surface area uses slant height. Slant height comes from the right triangle formed by radius and vertical height, so it is computed with √(r² + h²).
4) Are results exact or rounded?
Internally, calculations use full precision. Displayed values are rounded using your selected decimals, which also controls exported CSV and PDF values.
5) Which sphere formula does this use?
It uses surface area 4πr² and volume (4/3)πr³. These assume a perfect sphere and a radius measured from the center to the surface.
6) Can I calculate a triangular prism that is not right angled?
This version assumes a right triangle base. For other triangles, you would need the triangle area and the full perimeter to compute lateral area accurately.
7) What should I do if I get an input error?
Check that every required field is filled and greater than zero. Also confirm you selected the correct solid so the visible inputs match your shape.
8) What is included in the downloads?
Exports include the solid name, unit, inputs used, formulas, surface area, and volume. This makes it easy to attach results to notes or assignments.