Rectangular Prism Volume Calculator: Formula, Surface Area and Step-by-Step Answer
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Enter the length, width and height of the box.
A rectangular prism that is 8.0000 by 5.0000 by 3.0000 cm has a volume of 120.0000 cm³, a surface area of 158.0000 cm² and a space diagonal of 9.8995 cm.
Show the steps
- Volume = length × width × height = 8.0000 × 5.0000 × 3.0000 = 120.0000 cm³.
- Surface area = 2(lw + lh + wh) = 2(40.0000 + 24.0000 + 15.0000) = 158.0000 cm².
- Space diagonal = √(l² + w² + h²) = 9.8995 cm.
Rectangular prism
V = l w h
Surface area = 2(lw + lh + wh)
Diagonal = √(l² + w² + h²)
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A rectangular prism, or cuboid, is a box with six rectangular faces. Its volume is length × width × height. Use it for boxes, rooms, tanks, bricks and shipping cartons.
Enter the three dimensions in one unit and get the volume, the surface area, the space diagonal and the base area.
How to use it
- Enter the length, width and height.
- Pick the unit.
- Read the volume, surface area, diagonal and steps.
Rectangular prism formulas
- Volume: V = l × w × h
- Surface area: 2(lw + lh + wh)
- Space diagonal: √(l² + w² + h²)
Example
A box 8 cm by 5 cm by 3 cm has volume 8 × 5 × 3 = 120 cm³ and surface area 2(40 + 24 + 15) = 158 cm².
Sources
Quick check: test yourself
A box is 5 cm by 8 cm by 2 cm. What is its volume?
Correct answer: 80 cm³. Volume = 5 × 8 × 2 = 80.
What is the surface area of a 5 × 8 × 2 box?
Correct answer: 132 cm². Add the areas of the six faces: 2(lw + lh + wh).
If every side of a cube doubles, the volume becomes
Correct answer: 8 times as large. 2 × 2 × 2 = 8.
Pick an answer for each question.
Common questions
How do I find the volume of a rectangular prism?
Multiply length by width by height.
What is the difference between volume and surface area?
Volume is the space inside, in cubic units. Surface area is the total area of the faces, in square units.
What is the space diagonal?
The longest straight line inside the box, from one corner to the opposite corner: √(l² + w² + h²).
Is a cube a rectangular prism?
Yes. A cube is a rectangular prism with equal length, width and height.
How do I get liters?
1,000 cm³ equals 1 liter.
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