Surface Area Calculator
The total, side and base surface area of a box, cube, cylinder, sphere, cone, pyramid, capsule, hemisphere, frustum, tube or triangular prism.
Result
Total surface area: 52 ft²
A measurement, not a material estimate. Add a margin before buying paint or coating.
- Side area (lateral)
- 28 ft² (4,032 in², 2.6013 m²)
- Every face except the top and bottom
- Area of one base
- 12 ft² (1,728 in², 1.1148 m²)
- Volume
- 24 ft³ (41,472 in³, 179.5325 gal, 679.6043 L)
https://calcgallery.com/geometry/surface-area-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Surface Area Calculator
- Choose the solid.
- Enter its dimensions in any units. For a cone or pyramid, enter the vertical height; the page works out the slant.
- Read the total surface area, then the side area and the base area separately.
The formulas
| Solid | Total surface area | Side (lateral) | One base |
|---|---|---|---|
| Box | 2(lw + lh + wh) | 2h(l + w) | l × w |
| Cube | 6s² | 4s² | s² |
| Cylinder | 2πr² + 2πrh | 2πrh | πr² |
| Sphere | 4πr² | — | — |
| Cone | πr² + πrs | πrs | πr² |
| Rectangular pyramid | lw + l × s₁ + w × s₂ | l × s₁ + w × s₂ | l × w |
| Capsule | 2πrL + 4πr² | — | — |
| Hemisphere | 3πr² | 2πr² | πr² |
| Frustum of a cone | πR² + πr² + π(R + r)s | π(R + r)s | πR² |
| Tube | 2π(R² − r²) + 2πh(R + r) | 2πh(R + r) | π(R² − r²) |
| Triangular prism | 2A + (a + b + c)L | (a + b + c)L | A |
For the cone, s is the slant height √(r² + h²). For the pyramid, s₁ = √(h² + (w ÷ 2)²) is the slant height of the two faces along the length and s₂ = √(h² + (l ÷ 2)²) of the two along the width.
Total or lateral
The total surface area counts every face. The lateral area counts the sides only, leaving out the top and bottom. For a cylinder it is the curved wall, for a box the four walls, and for a cone or pyramid the sloping faces. The lateral area is usually what matters when painting a tank, cladding a column or wrapping a pipe, so the page gives it separately along with the area of one base. That way you can add back just the ends you need.
Slant height
The sloping faces of a cone and a pyramid are measured along the slope, not straight up. The page takes the vertical height, because that is usually what you can measure, and works out the slant itself. A cone of radius 3 and height 4 has a slant of exactly 5. That gives a side area of 15π, not the 12π you would get by using the height by mistake. A pyramid on a rectangular base has two slants, one for each pair of faces, and the page uses both.
The capsule
A capsule is a cylinder with a hemisphere on each end. Its side area is the cylinder’s curved wall. The two rounded ends add up to one whole sphere, 4πr². It has no flat base, so no base area is given.
The hemisphere, frustum, tube and triangular prism
A hemisphere is half a sphere with its flat disc. The curved part is half of 4πr², so 2πr², and the disc adds πr², for 3πr² in all. Leave the disc out for a dome that sits on something.
A frustum is a cone with its top cut off parallel to the base, the shape of a bucket, a lampshade or a tapered planter. Its side uses its own slant, s = √((R − r)² + h²), where R and r are the bottom and top radii and h the vertical height. It has two different ends, so the base shown is the bottom one, πR², and the top adds πr² to the total.
A tube, a hollow cylinder, has a wall on the outside and on the inside, and two ring-shaped ends. The side area counts both walls, 2πRh + 2πrh. For a pipe painted on the outside only, use 2πRh, which is the cylinder page’s side area for the outer radius.
A triangular prism is a triangle carried straight back through a length L. Enter its three sides and the page finds the triangle’s area A from them by Heron’s formula, so the end does not have to be a right triangle. The three rectangular faces together are the perimeter times L.
With your numbers
- Surface = 2 × (l × w + l × h + w × h), with 4 ft, 3 ft and 2 ft
- Surface = 52 ft²
Quick reference
A measurement, not a material estimate. Add a margin before buying paint or coating.
| Example | Total surface area |
|---|---|
| Box, 4 × 3 × 2 ft | 52 ft² |
| Cube, 3 m sides | 54 m² |
| Cylinder, radius 0.5 m, 2 m high | 7.854 m² |
| Sphere, radius 3 m | 113.0973 m² |
| Cone, radius 3 m, 4 m high | 75.3982 m² |
| Pyramid, 5 × 3 m base, 4 m high | 50.511 m² |
| Capsule, radius 2 m, 6 m straight | 125.6637 m² |
| Hemisphere, radius 3 m | 84.823 m² |
| Frustum, radii 3 and 1 m, 4 m high | 87.6144 m² |
| Tube, radii 0.5 and 0.4 m, 2 m long | 11.8752 m² |
| Triangular prism, 3-4-5 ft end, 10 ft long | 132 ft² |
Common questions about the Surface Area Calculator
- Do I want the total or the lateral area for painting?
- Usually the lateral area, the sides only. The walls of a round tank, a column or a silo are its lateral area. The bottom sits on the ground and the top may be a separate roof. Add one base if you are also coating the lid or the floor. Use the total only when every face is being covered.
- Why is a sphere’s area exactly four times its great circle?
- A sphere of radius r has a surface area of 4πr², and the circle through its middle, the great circle, has an area of πr². Archimedes showed that a sphere has the same surface area as the curved side of a cylinder that just fits round it. That cylinder is 2r tall and 2πr round, so its side is 2πr × 2r = 4πr².
- How do I handle an open-topped tank?
- Add the side area to one base area. That covers the walls and the floor, leaving the open top uncounted. For an open box, use the side area plus the area of one base, shown separately below the total.
- How do I turn a surface area into an amount of paint?
- Divide the area by the coverage printed on the tin, then multiply by the number of coats. The paint calculator does this for walls and allows for doors and windows. Rough or porous surfaces need more than the tin says.