Surface Area of a Rectangular Prism Calculator
Enter the length, width and height of a rectangular prism (box/cuboid) to instantly find its total surface area across all six faces, plus its volume and space diagonal.
units
units
units
Six rectangular faces: TSA = 2(lw + lh + wh)
- 1
Top/bottom face (l × w)
8 × 5 = 40 - 2
Front/back face (l × h)
8 × 3 = 24 - 3
Side face (w × h)
5 × 3 = 15 - 4
Total surface area
2 × (40 + 24 + 15) = 158Multiply the sum of the three distinct face areas by 2, since faces come in opposite pairs.
How does this calculator work?
A rectangular prism has six rectangular faces. Total surface area = 2(lw + lh + wh), which adds all three pairs of opposite faces. Volume = l·w·h. Space diagonal = √(l²+w²+h²). Enter length, width and height in the same unit to get area in square units and volume in cubic units.
Formula
How this is calculated
A rectangular prism (also called a cuboid or box) has six rectangular faces arranged in three opposite pairs. The top and bottom each have area l × w, the front and back each have area l × h, and the two sides each have area w × h. Because faces come in identical pairs, the total surface area is simply twice the sum of those three face types: TSA = 2(lw + lh + wh).
The volume of the prism is the product of all three dimensions: V = l × w × h. This represents the number of unit cubes that fill the interior. The space diagonal (the longest internal diagonal connecting opposite corners) is found by extending the Pythagorean theorem to three dimensions: d = √(l² + w² + h²).
All inputs must be positive and share the same unit. A cube is the special case where l = w = h, which simplifies the surface area to 6l² and the volume to l³.
Frequently asked questions
A rectangular prism (or cuboid) is a three-dimensional shape with six rectangular faces, all internal angles of 90°, and opposite faces equal and parallel. Everyday examples include bricks, boxes, rooms and books.
A cube is a special rectangular prism where all three dimensions are equal (l = w = h). For a cube, TSA = 6l² and V = l³. This calculator handles the general case, but you can set all three inputs equal to solve a cube.
The space diagonal is the longest straight line through the interior of a rectangular prism, connecting two opposite vertices (corners). Its length is d = √(l² + w² + h²) by the three-dimensional extension of the Pythagorean theorem.
Also known as
TG we-Calculate Editorial Team. (2026). Surface Area of a Rectangular Prism Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/surface-area-rectangular-prism-calculator
TG we-Calculate Editorial Team. "Surface Area of a Rectangular Prism Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/surface-area-rectangular-prism-calculator.
TG we-Calculate Editorial Team, "Surface Area of a Rectangular Prism Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/surface-area-rectangular-prism-calculator
@misc{wecalculate_surface_area_rectangular_prism_calculator, title = {Surface Area of a Rectangular Prism Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/surface-area-rectangular-prism-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?