Surface Area Calculator: Rectangular Prism / Box
Calculate the total surface area of a rectangular prism (box) from length, width, and height.
Rectangular Prism Calculator
Calculate surface area and volume of a rectangular prism
Quick Tips
- • Use the same units for all dimensions
- • Surface area units are squared
- • Volume units are cubed
What is Surface Area of a Box?
The surface area of a rectangular prism (box) is the total area of all six faces (top, bottom, front, back, left, right).
If you’re wrapping a box with paper or painting it, surface area tells you how much material you need.
Surface Area Formula
A rectangular prism has 3 unique face pairs:
- Two faces of area l × w
- Two faces of area l × h
- Two faces of area w × h
Total Surface Area: SA = 2(lw + lh + wh)
Face-by-Face Breakdown
| Face | Area | How many faces | Contribution |
|---|---|---|---|
| Top & Bottom | l × w | 2 | 2lw |
| Front & Back | l × h | 2 | 2lh |
| Left & Right | w × h | 2 | 2wh |
How to Calculate Surface Area (Step-by-Step)
- 1Compute lw (length × width).
- 2Compute lh (length × height).
- 3Compute wh (width × height).
- 4Add them: lw + lh + wh.
- 5Multiply by 2: SA = 2(lw + lh + wh).
- 6Keep units squared (cm², m², in², etc.).
Worked Example
| Given (l, w, h) | lw | lh | wh | Surface Area |
|---|---|---|---|---|
| 10, 5, 2 | 50 | 20 | 10 | SA = 2(50 + 20 + 10) = 160 |
Units tip: If length/width/height are in cm, your surface area will be in cm². Surface area is always a squared unit.
Diagram: Rectangular Prism Dimensions
Common Mistakes
- Forgetting to multiply by 2 (there are pairs of identical faces).
- Mixing units (e.g., l in cm but w in inches). Convert to one unit first.
- Confusing surface area with volume (volume is lwh, surface area is 2(lw + lh + wh)).
- Writing the answer in linear units instead of squared units.
Special Cases
- Cube: If l = w = h = a, then SA = 6a².
- Open-top box: If there is no top face, subtract one lw face from total surface area.
Surface Area FAQs
What is the surface area of a cube?
If all sides are equal (l = w = h = a), surface area becomes SA = 6a².
Is surface area the same as volume?
No. Surface area measures the outside covering (2D), while volume measures space inside (3D). Volume of a box is V = lwh.
What if my box has no lid (open-top box)?
Compute total surface area normally, then subtract the area of the missing top face (l × w).
What units will the answer be in?
Surface area uses squared units. If l, w, h are in meters, the result is in m².
Do I need to use decimals or exact values?
Either works. Decimals are fine. Just keep consistent units.