Formula used
Surface area measures the exposed outer covering. Volume measures the enclosed three-dimensional space. Each formula depends on the selected shape dimensions.
| Shape | Surface area formula | Volume formula |
|---|---|---|
| Cube | 6s² | s³ |
| Rectangular prism | 2(lw + lh + wh) | lwh |
| Sphere | 4πr² | 4πr³/3 |
| Cylinder | 2πrh + 2πr² | πr²h |
| Cone | πr(r + l) | πr²h/3 |
| Torus | 4π²Rr | 2π²Rr² |
How to use this calculator
- Select the required three-dimensional shape.
- Choose direct or missing-dimension calculation mode.
- Enter every known measurement with its unit.
- Select output units and precision settings.
- Add coating, waste, fill, or density details.
- Enable comparison mode when another shape matters.
- Press Calculate and review every displayed result.
Example data
| Shape | Inputs | Surface area | Volume |
|---|---|---|---|
| Cube | s = 3 m | 54 m² | 27 m³ |
| Sphere | r = 2 m | 50.265 m² | 33.510 m³ |
| Cylinder | r = 1 m, h = 4 m | 31.416 m² | 12.566 m³ |
| Cone | r = 2 m, h = 5 m | 46.402 m² | 20.944 m³ |
Frequently asked questions
What is surface area?
Surface area measures all exposed outer faces. It uses squared measurement units. Closed shapes include every exterior boundary.
What is volume?
Volume measures enclosed three-dimensional space. It uses cubic measurement units. Capacity units can also represent volume.
What is lateral surface area?
Lateral area excludes selected bases. Curved shapes use curved surface area. This helps estimate wall materials.
Can inputs use mixed units?
Yes, every dimension has its own unit. Values convert into meters internally. Results then use chosen output units.
How are missing dimensions solved?
The calculator uses numerical bisection. Known dimensions remain fixed during solving. The selected target controls the result.
Does the ellipsoid result use an approximation?
Yes, ellipsoid surface area uses Knud Thomsen’s approximation. Volume remains exact mathematically. The approximation is accurate for ordinary shapes.
How does comparison scaling work?
Uniform scaling preserves shape proportions. Areas scale with the square factor. Volumes scale with the cube factor.
Can it estimate paint requirements?
Yes, enter coverage, coats, and waste. Price creates a cost estimate. Real products may require extra material.
Why might practical results differ?
Real objects may contain irregular details. Measurements can include tolerance and rounding. Always verify critical engineering requirements independently.