Rectangular Prism Volume Calculator
Calculate the volume, surface area, and space diagonal of a rectangular prism (box): V = l × w × h
Enter Length, Width, and Height
Surface Area: 108.00 square units
Space Diagonal: 7.81 units
Calculations:
Volume: V = l × w × h = 6 × 4 × 3 = 72.00 cubic units
Surface Area: SA = 2(lw + lh + wh) = 2(24 + 18 + 12) = 2(54) = 108.00 square units
Space Diagonal: d = √(l² + w² + h²) = √(36 + 16 + 9) = √61 = 7.81 units
Rectangular Prism Formulas
Volume: V = l × w × h
Surface Area: SA = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
where: - l = length - w = width - h = height
How to Calculate Box Volume
- Measure the length: The longest horizontal dimension
- Measure the width: The shorter horizontal dimension
- Measure the height: The vertical dimension
- Multiply all three: Volume = length × width × height
Understanding Rectangular Prisms
A rectangular prism (cuboid) has six rectangular faces, twelve edges, and eight vertices. All angles are right angles. A cube is a special case where l = w = h. The space diagonal connects opposite corners and passes through the interior of the prism.
Real-World Applications
Rectangular prism calculations are used in: - Shipping and packaging: Calculating box volumes for shipping costs - Construction: Concrete volume for foundations and walls - Storage: Determining capacity of rooms and containers - Aquariums: Calculating water volume for fish tanks - Moving: Estimating truck space needed - Manufacturing: Material requirements for boxes
Common Questions
What is the formula for rectangular prism volume?
The rectangular prism (box) volume formula is V = length × width × height. Simply multiply the three dimensions together to find the volume.
How do you find the surface area of a rectangular prism?
The surface area formula is SA = 2(lw + lh + wh), where l is length, w is width, and h is height. This adds up the areas of all six faces.
What is a rectangular prism?
A rectangular prism (also called a cuboid or box) is a 3D shape with six rectangular faces. All angles are 90 degrees. A cube is a special rectangular prism where all sides are equal.