Side areas, curved surfaces, and bases
Total area equals the side or curved area plus all bases. A cylinder and box include two bases; a cone includes one circular base; a sphere has no separate base.
To estimate paint quantity from area, coat count, and coverage, use the Paint Calculator .
The formula
For a box, length and width describe the base and height describes its vertical extent. Cone slant height is calculated from perpendicular height and radius using the Pythagorean theorem. Surface area conversions use square length factors.
Worked example
A closed box 3 m long, 2 m wide, and 4 m high has side area 40 m² and two bases totaling 12 m², giving 52 m². A cone with radius 3 m and height 4 m has slant height 5 m and total area 24π m², approximately 75.398224 m².
How to use this calculator
- Select a closed solid and one length unit.
- Enter the dimensions; a cone needs perpendicular height, not slant height.
- Read the labeled breakdown to decide which surfaces your task actually includes.
Which faces are included?
The total represents every outer surface of the ideal closed shape. For a cylindrical container with an open top, subtract one circular base from the total. For a box with an open top, subtract length times width once. This tool labels the base contribution so those adjustments can be made without confusing it with side area.
Slant height belongs to a cone’s side
Unrolling the curved surface of a right circular cone gives a circular sector. Its area depends on slant height, which follows the surface from apex to edge. The perpendicular height entered here is shorter. The tool derives slant height before calculating the curved area, and reports it only when the selected solid is a cone.
Geometric area and material coverage
A surface area is a starting measurement for wrapping, painting, or comparing shapes. It does not include overlaps, seams, interior surfaces, cutouts, coats, or wastage. A sphere’s curved area is also its total area because it has no planar bases. For paint quantities, use the paint calculator with the required coverage and coat count.
Assumptions & limitations
What this calculation assumes
- Boxes and cylinders are closed; cones are right circular cones with one base.
What to keep in mind
- No hollow thickness, oblique cones, irregular surfaces, or material allowance.
Common questions
Is surface area the same as volume?
No. Surface area uses square units and measures the boundary. Volume uses cubic units and measures enclosed space.
Why do cylinders have twice the circle area in the base result?
A closed cylinder has two equal circular ends. Each end contributes πr² to total area.