The Rectangular Prism Surface Area Calculator calculates the total surface area of a box-shaped solid (a cuboid) from its length, width and height.
Enter the length, width and height below to calculate the surface area.
Rectangular Prism Surface Area Calculator
Surface area of a rectangular prism, cuboid or box — closed or open-top — from length, width and height.
It adds the areas of the six rectangular faces using the formula A = 2(lw + lh + wh). An open-top mode leaves out the lid, and the calculator also shows the lateral area of the four sides and the volume.
Formula
Closed rectangular prism:
A = 2(lw + lh + wh)
Open-top box (no lid):
A = lw + 2h(l + w)
Lateral area (the four sides only):
L = 2h(l + w)
Where:
- A = surface area
- l = length
- w = width
- h = height
How the Calculation Works
Step 1: Find the area of each pair of opposite faces: top and bottom (l × w), front and back (l × h), and the two ends (w × h).
Step 2: Add the three different face areas together: lw + lh + wh.
Step 3: Multiply by 2, because every face has an identical partner on the opposite side.
For an open-top box, the lid is removed, so only one l × w face is counted.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| l | Length (longest side of the base) | cm, m, in, ft |
| w | Width of the base | cm, m, in, ft |
| h | Height | cm, m, in, ft |
| A | Total surface area | cm², m², in², ft² |
| V | Volume (l × w × h) | cm³, m³, in³, ft³ |
It does not matter which side you call length, width or height — the surface area comes out the same.
Example Calculation
Closed box
Given: length = 8 cm, width = 5 cm, height = 4 cm
Formula: A = 2(lw + lh + wh)
Calculation: A = 2(8×5 + 8×4 + 5×4) = 2(40 + 32 + 20) = 2 × 92
Result: A = 184 cm²
Same box with no lid
Calculation: A = 8×5 + 2 × 4 × (8 + 5) = 40 + 104
Result: A = 144 cm²
The lateral area is 104 cm² and the volume is 8 × 5 × 4 = 160 cm³.
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
| 1 in² | 6.4516 cm² |
Shape Properties
A rectangular prism has 6 rectangular faces, 12 edges and 8 vertices. Opposite faces are identical, which is why the formula multiplies by 2. A cube is the special case where l = w = h, so A = 6a².
Net of a rectangular prism
If you unfold a box flat, you get its net: six rectangles in three matching pairs. The total area of the net equals the surface area of the box.
Dimensions Explained
Inside vs outside measurements
For wrapping, painting or cladding the outside, use outside dimensions. For lining the inside of a box or tank, use inside dimensions. With thick walls the two results can differ noticeably.
Mixed units
You can enter each side in a different unit (for example, length in ft and height in in). The calculator converts them before calculating.
Frequently Asked Questions
How do you find the surface area of a rectangular prism?
Multiply length × width, length × height and width × height, add the three results, then multiply by 2. For an 8 × 5 × 4 cm box the answer is 184 cm².
What is the formula for the surface area of a cuboid?
A = 2(lw + lh + wh). A cuboid and a rectangular prism are the same shape.
How do you find the surface area of a box without a lid?
Use A = lw + 2h(l + w), which counts the bottom and the four sides but not the top. Select the open-top mode in the calculator.
What is the lateral surface area of a rectangular prism?
It is the area of the four side faces only: L = 2h(l + w). It excludes the top and bottom.
What is the difference between surface area and volume of a rectangular prism?
Surface area (square units) is the area of the outside faces. Volume (cubic units) is the space inside: V = l × w × h.
How much wrapping paper do I need for a box?
Start with the box’s surface area, then add extra for overlaps and folded ends. The amount of overlap depends on how you wrap it, so the surface area is the minimum, not the exact amount to buy.