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Rectangular Prism (Box) Calculator

Compute volume, surface area, and space diagonal of a rectangular prism (box) from length, width, and height.

Rectangular prism (box) formulas

VolumeV = l × w × h
Surface areaSA = 2(lw + lh + wh)
Space diagonald = √l2 + w2 + h2

Where l = length, w = width, h = height

Worked examples

  1. A box is 4 × 3 × 2 ft. Find its volume, surface area and diagonal.

    1. V = 4 × 3 × 2 = 24
    2. SA = 2(12 + 8 + 6) = 52
    3. d = √16 + 9 + 4 = √29

    Answer: V = 24 ft³, SA = 52 ft², d ≈ 5.39 ft

  2. How many gallons does a 30 × 12 × 16 inch aquarium hold?

    1. V = 30 × 12 × 16 = 5,760 in³
    2. 1 US gallon = 231 in³, so 5,760 ÷ 231

    Answer: ≈ 24.94 gallons

Tips & common mistakes

  • The space diagonal tells you the longest pole or rod that fits inside a box.