How to use it
- Pick a solid shape.
- Choose the unit of your measurements.
- Enter the dimensions.
- Read the surface area in square units, square feet and square meters.
Surface area formulas
Surface area is the total area of all the faces or curved surfaces of a solid.
| Shape | Surface area |
|---|---|
| Cube | SA = 6a² |
| Rectangular box | SA = 2(lw + wh + lh) |
| Cylinder | SA = 2πr² + 2πrh |
| Sphere | SA = 4πr² |
| Cone | SA = πr² + πr√(r² + h²) |
| Square pyramid | SA = a² + 2a√((a/2)² + h²) |
| Frustum | SA = π(R² + r² + (R + r)√((R − r)² + h²)) |
| Triangular prism | SA = 2(√3/4)a² + 3ah |
The calculator shows the formula for the shape you pick, the result in your unit and in square feet and square meters, and the volume too. It runs in your browser.
Worked examples
- Cube with 3 in edges: 6 × 9 = 54 sq in.
- Box 4 × 3 × 2 ft: 2(12 + 6 + 8) = 52 sq ft.
- Cylinder with radius 3 in and height 10 in: 2π × 9 + 2π × 30 = 78π ≈ 245.04 sq in.
- Sphere with radius 5 in: 4π × 25 ≈ 314.16 sq in.
- Cone with radius 3 in and height 4 in: the slant height is 5 in, so SA = 9π + 15π = 24π ≈ 75.40 sq in.
Lateral area vs. total surface area
Total surface area includes every face: for a cylinder, both circular ends and the curved side. Lateral area is just the sides.
- Cylinder lateral area: 2πrh (the label on a can)
- Cone lateral area: πr × slant height
- Box lateral area: 2h(l + w) (the four walls of a room)
For a can with a 1.5 in radius and 4.5 in height, the label is about 2π × 1.5 × 4.5 ≈ 42.4 sq in.
Painting and wrapping
Surface area tells you how much material covers an object: paint, wrapping paper, fabric, insulation or sheet metal.
Example: painting a wooden storage chest 4 ft × 2 ft × 2 ft. Total area = 2(8 + 4 + 8) = 40 sq ft. If you skip the bottom, subtract 4 × 2 = 8 sq ft, leaving 32 sq ft. At about 350 sq ft per gallon (check your paint label), one quart covers two coats easily.
Add some extra for overlaps when wrapping, and use the square footage calculator for the walls of a room.
Common mistakes
- Using diameter instead of radius. Halve the measurement across the circle first.
- Confusing height with slant height on cones and pyramids. The formula needs the vertical height; the calculator computes the slant height for you.
- Counting faces you will not cover. Subtract the bottom or any open side when estimating materials.
- Mixing units. Square inches and square feet differ by a factor of 144.
For volume in gallons or cubic feet, see the volume calculator.
Surface area to volume ratio
As an object gets bigger, its volume grows faster than its surface area. Doubling the edge of a cube multiplies its surface area by 4 but its volume by 8. That is why crushed ice melts faster than a block of the same weight, why small animals lose heat faster than large ones, and why chips of wood catch fire more easily than logs. The calculator shows both numbers, so you can compare the ratio for your own shapes.
Frequently asked questions
What is the surface area of a cylinder?
SA = 2πr² + 2πrh, the two circular ends plus the curved side.
How do I find the surface area of a box?
Add the areas of the six faces: 2(lw + wh + lh).
What is the surface area of a sphere?
4πr². A sphere with a 5-inch radius has about 314.16 square inches.
What is the difference between surface area and volume?
Surface area measures the outside covering in square units; volume measures the space inside in cubic units.
Does the calculator give lateral area?
It gives total surface area. For the sides only, subtract the bases: for a cylinder, 2πr².
Last updated: November 12, 2026