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About this tool
Calculate total, lateral and base surface area of a cube, box, cylinder, cone, sphere, pyramid, prism or pipe, with formulas, steps, units and paint needed.
This Surface Area Calculator works out the total surface area of eleven solids and splits it into the lateral (side or curved) surface and the bases or faces. Choose a cube, cuboid, cylinder, cone, sphere, hemisphere, rectangular pyramid, triangular prism, capsule, conical frustum or tube, enter the dimensions, and use radius or diameter for round shapes. Slant heights for cones, pyramids and frustums are derived from the vertical height with the Pythagorean theorem, and a triangular prism uses Heron's formula for its ends. Results come in mm², cm², m², in², ft² or yd², with every step shown, plus a paint estimate based on coverage and coats. It all runs in your browser.
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Under Solid, pick a shape such as Cylinder, Cone, Pyramid, Triangular prism or Tube / pipe.
Choose Radius or Diameter for round solids, type each dimension (for example r = 3 and h = 10) and set the Length unit and Area unit, such as cm and m².
Read the Total surface area, the Lateral surface and each base or face, and check the Sketch and the Steps with slant heights.
In Paint or coating estimate, enter Coverage (m² per litre) such as 10 and the number of Coats to see litres and US gallons.
See the side or curved surface separately from the bases, plus the area of each face or end, so you can include only what you need.
Give the vertical height of a cone, pyramid or frustum; the slant height is calculated and listed, with the working in the steps.
Set coverage per litre and number of coats, optionally skip the base, and get litres and US gallons for the job.
Six area units with a conversion table, a labelled sketch of the solid and a copy button for the whole result.
| Solid | Lateral area | Total surface area |
|---|---|---|
| Cube | 4a² | 6a² |
| Cuboid / box | 2h(l + w) | 2(lw + lh + wh) |
| Cylinder | 2πrh | 2πr(r + h) |
| Cone | πrs, s = √(r² + h²) | πr(r + s) |
| Sphere | 4πr² | 4πr² |
| Hemisphere | 2πr² | 3πr² |
| Square pyramid | 2as, s = √(h² + (a/2)²) | a² + 2as |
| Triangular prism | (a + b + c)L | 2T + (a + b + c)L |
| Capsule | 2πra (cylinder part) | 2πr(2r + a) |
| Conical frustum | π(R + r)s, s = √((R − r)² + h²) | π(R + r)s + πR² + πr² |
| Tube / pipe | 2πRL outer, 2πrL inner | 2πL(R + r) + 2π(R² − r²) |
All lengths in one unit; areas are in that unit squared.
Lateral surface area covers only the sides of a solid, not its bases. For a cylinder it is the curved surface, 2πrh. Total surface area adds the bases: 2πrh + 2πr². Use lateral area for things like a label around a can, and total area for painting or wrapping the whole object.
Add the curved side to the two circular ends: SA = 2πrh + 2πr² = 2πr(r + h). A cylinder with a radius of 3 cm and a height of 10 cm has a total surface area of 78π ≈ 245.04 cm², of which 60π ≈ 188.50 cm² is the curved side.
First find the slant height s = √(r² + h²). The curved surface is πrs and the base is πr², so the total is πr(r + s). A cone with radius 3 and height 4 has a slant height of 5, a lateral area of 15π and a total of 24π ≈ 75.40 square units.
SA = 4πr², exactly four times the area of a circle with the same radius. A ball with a radius of 5 cm has a surface area of 100π ≈ 314.16 cm². A hemisphere has a curved area of 2πr² and, with its flat base, a total of 3πr².
A rectangular box has three pairs of identical faces, so SA = 2(lw + lh + wh). A box 4 × 3 × 2 has 2(12 + 8 + 6) = 52 square units. The four side walls alone, without the top and bottom, are 2h(l + w) = 28 square units.
Add the base to the triangular faces. For a square pyramid with side 6 and height 4, the slant height of each face is √(4² + 3²) = 5, so each face is ½ × 6 × 5 = 15. Four faces give 60, and with the 36 base the total is 96.
Add the two triangular ends to the three rectangular sides: SA = 2T + (a + b + c) × L, where T is the triangle's area and L the prism's length. For a 5-5-6 triangle (area 12) and a length of 10, that is 24 + 160 = 184 square units.
Divide the area by the paint's coverage and multiply by the number of coats. A 40 m² surface with paint covering 10 m² per litre needs 4 litres per coat, so 8 litres for two coats. Coverage is printed on the tin; rough, porous or bare surfaces usually need more.
Many processes happen at surfaces, so the surface-to-volume ratio matters. Small objects have more surface per unit of volume, which is why crushed ice melts faster than a block, fine powders dissolve quickly, and small animals lose heat faster than large ones.
Divide by 10,000, because one metre is 100 centimetres and area scales with the square of the length: 100 × 100 = 10,000. So 245 cm² is 0.0245 m². Going the other way, multiply square metres by 10,000 to get square centimetres.
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