Surface Area Calculator
Compute the surface area of spheres, cones, cubes, cylinders, rectangular prisms, square pyramids and capsules.
Inputs
Total Surface Area
113.097336
Solid
sphere
Step by step
Formula
SA = 4πr²
Substitute
SA = 4 × π × 3²
Total Surface Area
= 113.09733553
How it works
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
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.