Rectangular Prism Surface Area Calculator
The surface area of a rectangular prism is SA = 2(lw + lh + wh), and this rectangular prism surface area calculator adds up all six faces the moment you type the length, width, and height. You'll see the total surface area, the lateral (side) area, and the base at once, in square inches, feet, centimeters, and meters. It handles a closed box or an open one with no lid, and it shows the formula and steps with every result.
- All six faces
- Lateral side area
- Closed or open box
- Box or cuboid
- Multiple units
Last updated June 15, 2026 Method: SA = 2(lw + lh + wh) Reviewed by the Calcowa math team
Enter a positive length, width, and height to see the surface area.
Show all units
SA = 2(4×3 + 4×2 + 3×2) = 52 in²
What is the surface area of a rectangular prism?
The surface area of a rectangular prism is the total area of its six outer faces, found with SA = 2(lw + lh + wh). For a box 4 by 3 by 2 inches, that's 2(12 + 8 + 6) = 52 square inches.
The faces come in three matching pairs: top and bottom, front and back, left and right. You work out the three different face areas, add them, and double the total, since you've got a matching pair on every side. It's the same idea as the area of a rectangular prism, just spread over six faces instead of one.
How do you calculate the surface area of a rectangular prism?
To find the surface area, work out the three face areas, add them, and double the total. Here's the full sequence:
- 1
Measure the three sidesMeasure the length, width, and height, all in the same unit.
- 2
Find the three face areasWork out l × w, l × h, and w × h, one for each pair of faces.
- 3
Add them upAdd the three areas together to cover one of each face.
- 4
Double the totalMultiply by 2, since every face has a matching one on the opposite side.
- 5
Convert the unitsConvert to square feet or square meters if that's what you need.
Lateral surface area of a rectangular prism
The lateral surface area is the four side walls on their own, without the top and bottom: LSA = 2(l + w) × h. Picture the band of paper that's wrapped around a box, or the paint on the sides of a tank. The calculator shows this lateral value next to the total, so you'll grab it when the lid and base don't need covering.
Surface area of an open box
An open box, like a tray, a drawer, or a fish tank, has no lid, so it's five faces instead of six: SA = lw + 2lh + 2wh, which is the full surface minus the top rectangle. Set the box type to Open top and the calculator drops the lid for you. That's the area to use for an open container or a box you only line on the inside.
Surface area and volume of a rectangular prism
A box has two measures that get mixed up. The surface area, 2(lw + lh + wh), is the outer skin you'd paint or wrap. The volume, l × w × h, is the space that's inside it. They're measured differently too: surface area comes out in square units, while volume is in cubic units. For the space inside, switch to the rectangular prism volume calculator.
A surface area example, step by step
Say you've got a closed box that's 30 cm long, 20 cm wide, and 15 cm tall. The three face areas are 30 × 20 = 600, 30 × 15 = 450, and 20 × 15 = 300. Add them for 1,350, then double.
SA = 2(600 + 450 + 300) = 2,700 cm²
lateral area 1,500 cm² + top and bottom 1,200 cm²
Type 30, 20, and 15 in centimeters above, and you'll get the matching square meters and square inches at once.
Units and accuracy
Calcowa shows the rectangular prism surface area in square millimeters, centimeters, meters, inches, feet, and yards all at once. Enter your three sides in any supported unit, and you'll get exact conversions, so the result suits wrapping, painting, cladding, and school work alike.
| Unit | Best for | Good to know |
|---|---|---|
| Square inches (in²) | Boxes, parcels, small panels | Default when you enter inches |
| Square feet (ft²) | Rooms, crates, wrapping | 1 ft² = 144 in² |
| Square centimeters (cm²) | Lab and school work | 1 in² = 6.4516 cm² |
| Square meters (m²) | Large tanks and walls | 1 m² = 10.7639 ft² |
| Square yards (yd²) | Flooring, cladding, big jobs | 1 yd² = 9 ft² |
Frequently asked questions
Is the area of a rectangular prism the same as its surface area?
Yes. When people say the area of a rectangular prism, they mean its surface area, the total of all six faces. A flat rectangle has a single area, but a box is 3D, so you add up the six faces with 2(lw + lh + wh).
The surface area of a rectangular prism is SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height. It adds the areas of all six faces. For a box 4 by 3 by 2 inches, that's 2(12 + 8 + 6) = 52 square inches.
Yes. The area of a rectangular prism means its surface area, the total of all six outer faces. A flat rectangle has one area, but a 3D box has six faces, so you add them all with 2(lw + lh + wh).
The lateral surface area is the four side walls without the top and bottom: 2(l + w) × h. It's what you'd paint on the sides of a box, or the label that wraps around it, leaving the lid and base off.
An open box has no lid, so you drop one top face and count five: SA = lw + 2lh + 2wh, which is the full surface minus the top rectangle. Set the box type to Open top and the calculator does that for you.
A rectangular prism has 6 faces, in three matching pairs. Opposite faces are equal, so the surface area doubles each of the three different face areas: 2 times lw, plus 2 times lh, plus 2 times wh.
Use the full surface area, SA = 2(lw + lh + wh), and add a little extra for overlap. The result panel shows the answer in square inches, feet, and meters, so you can match it to your wrapping or material.
Multiply the three sides: V = length × width × height. This calculator shows the volume next to the surface area, and our rectangular prism volume tool covers it in full.
Related calculators
Need the volume too, or a different solid? These geometry tools pair well with rectangular prism surface area.
The space inside the same box.
Cylinder surface areaTotal and curved area of a cylinder.
Cube surface areaA box with all sides equal.
Need a box surface area fast?
Try the calculator above, or browse every shape in the geometry hub.