Surface Area Calculator
A surface area calculator adds all six faces of a rectangular box with 2 × (lw + lh + wh): an 8 × 5 × 3 ft box has 158 sq ft of surface.
Finding the surface area of a box
A surface area calculator adds up the area of every outside face of a rectangular box. Enter the length, width, and height in feet. The tool uses 2 × (length × width + length × height + width × height) and returns square feet.
Picture wrapping a gift. The paper needed to cover every side with no overlap is the surface area. A box has six faces, in three matching pairs.
The formula in plain words
- Top and bottom: length × width, two of them.
- Front and back: length × height, two of them.
- Left and right ends: width × height, two of them.
- Add the three face areas and double the total.
Doubling works because each face has a twin on the opposite side.
Worked example: a storage crate
A crate is 8 ft long, 5 ft wide, and 3 ft tall.
- Length × width: 8 × 5 = 40
- Length × height: 8 × 3 = 24
- Width × height: 5 × 3 = 15
- Sum: 40 + 24 + 15 = 79
- Surface area: 2 × 79 = 158 sq ft
Worked example: a whole room
A room is 12 ft long, 10 ft wide, and 8 ft tall.
- Length × width: 12 × 10 = 120
- Length × height: 12 × 8 = 96
- Width × height: 10 × 8 = 80
- Surface area: 2 × (120 + 96 + 80) = 592 sq ft
That 592 includes the floor and ceiling. If you are only painting the walls, you need 2 × (12 + 10) × 8 = 352 sq ft. The difference is the 240 sq ft of floor and ceiling.
Surface area for common box sizes
| Dimensions (ft) | Surface area |
|---|---|
| 2 × 2 × 4 | 40 sq ft |
| 8 × 5 × 3 | 158 sq ft |
| 10 × 10 × 10 | 600 sq ft |
| 12 × 10 × 8 | 592 sq ft |
A cube is the box with the least surface for its volume. A long, thin box has more skin for the same space inside.
How to measure
Use outside dimensions if you are covering the outside, such as painting a crate. Use inside dimensions if you are lining the inside, such as insulating a chest.
For a box with a missing face, such as an open-top planter, subtract the missing face. Take the full answer and remove length × width for the top.
For a shape that is not a box, break it into boxes and add their areas. Subtract the contact area where two pieces join, since that surface is hidden.
Surface area and volume
People often mix up surface area and volume. Surface area is a flat measure in square units and tells you how much covering you need. Volume is a space measure in cubic units and tells you how much the box holds. A box 8 ft by 5 ft by 3 ft has 158 sq ft of surface and 120 cubic feet of volume. Use the volume calculator for the second number.
Common mistakes
- Using the formula for walls only. If you need all six faces, include the top and bottom.
- Mixing inches and feet. Convert everything to feet first.
- Forgetting the hidden faces on stacked boxes.
- Using outside dimensions for an inside lining.
- Buying coating at exactly the area. Paint and sealant need extra for waste and second coats.
- Ignoring openings. Doors and windows in a room reduce the area to paint.
Related calculators
Get the space inside with the volume calculator or the cubic feet calculator. The square footage calculator handles flat areas such as floors.
Frequently asked questions
What is the surface area formula for a box?
Surface area = 2 × (length × width + length × height + width × height). For an 8 ft by 5 ft by 3 ft box, that is 2 × (40 + 24 + 15) = 158 sq ft.
Does this include the top and bottom?
Yes, all six faces are counted. If you only want the walls of a room, use the perimeter times the height instead: 2 × (length + width) × height.
What units does it use?
Enter all three dimensions in feet. The answer is in square feet. Convert inches to feet first by dividing by 12.
When would I need the surface area of a box?
To buy paint or sealant for a tank, crate, or cabinet, to estimate wrap or insulation for a duct or enclosure, or to figure out the coating on a metal box.
Does it work for a cube?
Yes. Enter the same number three times. A 10 ft cube has 2 × (100 + 100 + 100) = 600 sq ft.
Estimates only. Verify quantities with your supplier before purchasing.