Rectangular Prism Calculator (Volume, Surface Area & Diagonal)
Rectangular Prism Calculator (Volume, Surface Area & Diagonal)
A rectangular prism (also called a cuboid or a box) is any 3D shape with six rectangular faces meeting at right angles - shipping boxes, rooms, and bricks are all rectangular prisms. Enter the length, width, and height (in whatever unit you like), and this calculator finds the volume, total surface area, and the space diagonal, along with a diagram and the full step-by-step working.
- V = l × w × h, so a box measuring 6 × 4 × 3 has a volume of 6 × 4 × 3 = 72 cubic units.
- SA = 2(lw + lh + wh), the sum of all 6 rectangular faces (each pair of opposite faces is identical) - the same 6×4×3 box has a surface area of 2(24 + 18 + 12) = 108 square units.
- The space diagonal is d = √(l² + w² + h²) - useful for checking whether an object will fit diagonally in a box, e.g. shipping a long item into a smaller-looking package. The 6×4×3 box has a diagonal of √(36+16+9) = √61 ≈ 7.81 units.
How do I find the volume of a rectangular prism?
Multiply length by width by height: V = l × w × h. A 6 × 4 × 3 box has a volume of 6 × 4 × 3 = 72.
How do I find the surface area of a box?
Add up the areas of all 6 faces: SA = 2(lw + lh + wh). For a 6 × 4 × 3 box: SA = 2(24 + 18 + 12) = 108.
Rectangular Prism Calculator (Volume, Surface Area & Diagonal)
A rectangular prism (also called a cuboid or a box) is any 3D shape with six rectangular faces meeting at right angles - shipping boxes, rooms, and bricks are all rectangular prisms. Enter the length, width, and height (in whatever unit you like), and this calculator finds the volume, total surface area, and the space diagonal, along with a diagram and the full step-by-step working.
- V = l × w × h, so a box measuring 6 × 4 × 3 has a volume of 6 × 4 × 3 = 72 cubic units.
- SA = 2(lw + lh + wh), the sum of all 6 rectangular faces (each pair of opposite faces is identical) - the same 6×4×3 box has a surface area of 2(24 + 18 + 12) = 108 square units.
- The space diagonal is d = √(l² + w² + h²) - useful for checking whether an object will fit diagonally in a box, e.g. shipping a long item into a smaller-looking package. The 6×4×3 box has a diagonal of √(36+16+9) = √61 ≈ 7.81 units.
How do I find the volume of a rectangular prism?
Multiply length by width by height: V = l × w × h. A 6 × 4 × 3 box has a volume of 6 × 4 × 3 = 72.
How do I find the surface area of a box?
Add up the areas of all 6 faces: SA = 2(lw + lh + wh). For a 6 × 4 × 3 box: SA = 2(24 + 18 + 12) = 108.