Surface Area Calculator
Compute the surface area of common three-dimensional solids.
About Surface Area Calculator
Surface area is the total area covering the outside of a 3-D solid. Sphere: 4πr². Cone: base circle (πr²) plus lateral surface (πrl) where l is the slant height. Cube: 6 faces each a². Cylinder: two circles (2πr²) plus curved side (2πrh). Rectangular prism: 2(lw + lh + wh). Square pyramid: square base (a²) plus 4 triangular faces. Capsule: hemisphere ends (4πr²) plus cylindrical side (2πrh).
Formulas
Sphere
SA = 4πr²
Cone
SA = πr² + πrl, l = √(r²+h²)
Cube
SA = 6a²
Cylinder
SA = 2πr² + 2πrh
Box
SA = 2(lw + lh + wh)
Square Pyramid
SA = a² + 2al, l = slant height
Capsule
SA = 2πrh + 4πr²
Worked example
With the default values below, Surface Area Calculator returns Total Surface Area of 113.097336. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Solidone of Sphere, Cone, Cube, Cylinder, Rectangular Prism (Box), Square Pyramid, Capsule
- Sphere
- Radius (r)minimum 0
- 3
- Height (h)minimum 0
- 6
- Side length (a)minimum 0
- 4
- Length (l)minimum 0
- 5
- Width (w)minimum 0
- 4
- Base side length (a)minimum 0
- 4
Results
- Total Surface Area
- 113.097336
- Solid
- sphere
Step by step
- 1Formula
- 2Substitute
- 3Total Surface Area= 113.09733553
Assumptions and limits
- The result is derived only from the 7 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the difference between lateral and total surface area?
Lateral (or curved) surface area covers only the sides, not the top or bottom. Total surface area includes all faces. For a cylinder, the lateral area is the curved sheet 2πrh, while the total includes the two circular ends.
How do you find the slant height of a cone?
The slant height l is the distance from the apex to the rim along the surface. It forms the hypotenuse of a right triangle with the radius r and vertical height h: l = √(r² + h²).
What units does surface area use?
Square units — the same length unit as your input, squared. If radius is in centimetres, surface area is in cm². Converting: 1 m² = 10 000 cm².