Surface Area Calculator
Find the total surface area of a sphere, cylinder, cube, rectangular prism, cone or square pyramid. Pick the shape and enter its dimensions in one unit. For every shape except the sphere, the calculator also splits the total into the lateral area and the area of the base, or of the top and bottom. Results are in that unit squared.
How to use the Surface Area Calculator
- Enter your numbers in the Surface Area Calculator above.
- Press the Calculate Surface Area button to see the result.
- To try other numbers, change any value and press the button again.
Common surface area formulas
Sphere: 4πr² · · · Cylinder: 2πr² + 2πrh · · · Cube: 6s² · · · Rectangular prism: 2(lw + lh + wh) · · · Cone: πr² + πr√(r² + h²) · · · Square pyramid: s² + 2s√((s/2)² + h²)
Surface area is the total area of the outside faces of a 3D shape. For the cone and the square pyramid, h is the vertical height you enter, and the square root in each formula turns it into the slant height. The lateral area leaves out the base, or the top and bottom: 2πrh for a cylinder, πr times the slant height for a cone, 2s times the slant height for a square pyramid, 4s² for a cube and 2h(l + w) for a rectangular prism. The calculator rounds every result to 4 decimal places.
Worked example
A cylinder with radius 5 cm and height 12 cm: SA = 2π(25) + 2π(5)(12) = 50π + 120π = 170π ≈ 534.0708 cm². Of that, 376.9911 cm² is the lateral area and 157.0796 cm² the top and bottom. A sphere of the same radius: 4π(25) = 100π ≈ 314.1593 cm².
Frequently asked questions
What's the difference between lateral and total surface area?
Lateral surface area leaves out the base, or the top and bottom. Total surface area includes them. For a cylinder the lateral area is 2πrh and the total is 2πrh + 2πr². The calculator shows both for every shape except the sphere, which has no base.
Why does the sphere have minimal surface area?
For a given volume, a sphere has the smallest possible surface area. Surface tension pulls a bubble or a drop toward the shape with the least surface, which is why they come out round.
What unit is the result in?
The square of the unit you enter. Enter centimeters and the area is in square centimeters, enter feet and it is in square feet. Use the same unit for every dimension, because the calculator does not convert between units.