Volume of a Rectangular Prism Calculator

Enter a rectangular prism's length, width, and height to get its volume (V = lwh), surface area (SA = 2(lw + lh + wh)), and space diagonal (d = √(l² + w² + h²)).

Quick Facts

Volume formula
V = l × w × h
Multiply the three edge lengths; doubling any one dimension doubles the volume.
Surface area formula
SA = 2(lw + lh + wh)
Sum of the areas of all six rectangular faces.
Space diagonal formula
d = √(l² + w² + h²)
Follows from applying the Pythagorean theorem twice.

Your Results

Calculated
Volume
-
V = l × w × h, in cubic units
Surface Area
-
SA = 2(lw + lh + wh)
Space Diagonal
-
d = √(l² + w² + h²)
Base Area
-
Length × width

Ready

Enter length, width, and height, then press Calculate.

Formula and Method for the Volume of a Rectangular Prism

A rectangular prism (a box) has three pairs of identical rectangular faces defined by its length, width, and height. Because the shape is just a rectangle "extruded" upward, its volume is the base area times the height, which simplifies to multiplying all three edge lengths together: V = l × w × h. This calculator also derives the total surface area, the space diagonal (corner-to-corner through the box), and the base area from the same three dimensions.

How the calculation works

Enter the length, width, and height in the same unit and choose that unit. The calculator multiplies all three values to get the volume (in cubic units, such as ft³ or m³). It computes surface area by adding the areas of the three distinct faces (l×w, l×h, w×h) and doubling the sum, since each face has an identical opposite face: SA = 2(lw + lh + wh). It finds the space diagonal — the straight line from one corner of the box to the opposite corner — by applying the Pythagorean theorem twice: first to get the diagonal of the base (√(l² + w²)), then combining that with the height: d = √(l² + w² + h²).

Common mistakes

  • Confusing volume with surface area: a 10×6×4 ft box has a volume of 240 ft³ but a surface area of 2(60+40+24) = 248 ft², a different quantity measured in different units.
  • Mixing units: keep length, width, and height in one consistent unit — convert inches to feet, or centimeters to meters, before entering the values.
  • Diagonal vs. edge length: the space diagonal (√(l²+w²+h²)) is always longer than any single edge; do not substitute it for length, width, or height in the volume formula.

Real-world applications

  • Shipping and storage use volume to determine box capacity and how many units fit in a container or truck.
  • Packaging design uses surface area to estimate cardboard, wrapping, or label material needed.
  • Furniture and moving planning use the space diagonal to confirm an item can fit diagonally through a doorway or stairwell.
  • Concrete, soil, and tank sizing use volume directly to calculate material or fluid quantities.

Frequently Asked Questions

What is the formula for the volume of a rectangular prism?
Volume equals length times width times height: V = l × w × h. For example, a box that is 10 in long, 6 in wide, and 4 in tall has a volume of 10 × 6 × 4 = 240 in³.
How do I find the surface area of a rectangular prism?
Add up the areas of all six rectangular faces: SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height. This is twice the sum of the three distinct face areas, since each face has an identical opposite face.
How is the space diagonal of a rectangular prism calculated?
The space diagonal connecting opposite corners is d = √(l² + w² + h²), which follows from applying the Pythagorean theorem twice — once across the base and once up through the height.
Does it matter which dimension I call length, width, or height?
No. Volume, surface area, and the space diagonal are all symmetric in l, w, and h, so multiplying or adding them in any order gives the same result — label the dimensions however is most convenient for your measurements.

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