Surface Area Calculator
Find how much material it takes to cover or wrap a 3D shape.
How to use the Surface Area Calculator
- Choose the shape.
- Enter the edge / base side.
- Enter the length.
- Enter the width.
- Enter the radius.
- Enter the height.
- Press Calculate. The result updates automatically as you type.
About the Surface Area Calculator
Surface area is the total area of all the faces or curved surfaces that enclose a solid. It is what you need when estimating paint for a tank, sheet metal for a duct, wrapping paper for a box, or insulation for a pipe. Unlike volume, it is measured in square units.
The lateral area excludes the top and bottom, which matters for an open-topped can, the label on a jar or the sides of a room you plan to paint. For cones and pyramids, be careful to distinguish the vertical height (center of the base to the tip) from the slant height (along the face); the calculator converts one to the other for you.
Formula
- Cube: 6s² | Box: 2(lw + lh + wh)
- Cylinder: 2πr² + 2πrh | Sphere: 4πr² | Closed hemisphere: 3πr²
- Cone: πr² + πrℓ, where slant height ℓ = √(r² + h²)
- Square pyramid: s² + 2sℓ, where ℓ = √((s/2)² + h²)
Example calculation
Using the default values:
- Shape = Cylinder
- Radius = 3
- Height = 5
the calculator returns:
- Total surface area: 150.796447 square units
- Lateral (side) area: 94.24778
- Base area: 28.274334
Frequently asked questions
How do I find the surface area of a cylinder?
Add the two circular ends (2πr²) to the curved side (2πrh). With r = 3 and h = 5: 18π + 30π = 48π ≈ 150.8 square units.
What is the difference between lateral and total surface area?
Lateral area covers only the sides. Total surface area also includes the base or bases.
Why is a sphere's surface area 4πr²?
It is exactly four times the area of a circle with the same radius, a result first proven by Archimedes.
Last updated: · Category: Math calculators