About the Surface Area Calculator
This surface area calculator finds the total outside area of the most common solid shapes: cube, rectangular prism (box), cylinder, sphere, hemisphere, cone and square pyramid. Along with the total it splits the answer into the lateral (side or curved) area and the area of the base or bases, and a chart shows how the two compare.
Surface area is what you need when covering or coating something — paint for a tank, wrapping paper for a box, sheet metal for a duct, insulation for a water heater or label stock for a can. Students can also use it to check textbook answers, since the formulas and working are shown.
Enter every dimension in the same unit and the result comes out in that unit squared; pick a real unit to also see the answer in square meters and square feet. Heights are perpendicular heights, not slant heights — the calculator works out slant heights for cones and pyramids itself.
With the default inputs, the total surface area is 52. Change any value above to recalculate instantly.
How to use the surface area calculator
- 1Choose the solid shape.
- 2Select your measuring unit.
- 3Enter the dimensions shown, using perpendicular height.
- 4Read the total, lateral and base areas.
- 5Add a margin (often 10%) if you are buying material to cover it.
Formula and method
Surface area is the sum of the areas of every face of a solid, as if you unfolded it into a flat net. A box has three pairs of rectangles; a cylinder unrolls into a rectangle 2πr wide and h tall plus two circles; a cone unrolls into a sector of area πrl plus its circular base.
Cones and pyramids need the slant height l, the distance up the sloping face. The calculator finds it from the perpendicular height with the Pythagorean theorem: l = √(r² + h²) for a cone and l = √((a/2)² + h²) for a square pyramid. A sphere has no flat faces, so all of its 4πr² counts as curved area.
- l, w, h
- Length, width and height
- a
- Edge of a cube or base side of a square pyramid
- r
- Radius
- l (cone/pyramid)
- Slant height, computed from r or a and h
Worked examples
Box 4 m × 3 m × 2 m
Faces: 2 × (4×3) = 24, 2 × (4×2) = 16 and 2 × (3×2) = 12, totalling 52 m². The four sides alone are 28 m², about 560 ft² overall.
Cylinder tank: radius 3 ft, height 10 ft
The curved side is 2π × 3 × 10 ≈ 188.50 ft² and the two ends add 2π × 9 ≈ 56.55 ft², giving about 245.04 ft² to paint.
Sphere with a 6 cm radius
4π × 6² = 144π ≈ 452.39 cm². A sphere has no flat base, so all of it is curved area.
Square pyramid: base 10, height 12
The slant height is √(5² + 12²) = 13. The four triangular faces cover 2 × 10 × 13 = 260, and the base adds 100, for 360 square units.
Frequently asked questions
What is surface area?+
Surface area is the total area of all the outside faces of a 3D object, measured in square units. Imagine unfolding the shape flat and adding up the area of every piece.
What is the difference between lateral and total surface area?+
Lateral surface area counts only the sides (or curved surface), leaving out the top and bottom bases. Total surface area includes the bases as well. An open-topped can or a pipe uses lateral area.
How do you find the surface area of a cylinder?+
Add the curved side, 2πrh, to the two circular ends, 2πr². For r = 3 and h = 10 that is 188.5 + 56.5 ≈ 245 square units.
Why do cones and pyramids need a slant height?+
Their sloping faces are tilted, so their area depends on the distance measured along the face, not straight up. The slant height is found from the vertical height with the Pythagorean theorem.
How is surface area different from volume?+
Surface area measures the outside skin in square units (for paint, wrapping, cladding); volume measures the space inside in cubic units (for capacity, fill material or liquid).