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Geometry

Rectangular Prism Volume Calculator

Calculate the volume, surface area, and space diagonal of rectangular prisms, boxes, and cuboids.

Cuboid / Box GeometryLength (l)Height (h)Width (w)

V = l × w × h

Rectangular Prism Results
Decimals:
Volume in M3Live Output
24m3
Additional Computed Dimensions
Surface Area
52 m²
Space Diagonal (3D)
5.3852 m
Equivalent Standard Volume Units
Liters (L)
24,000 l
Cubic Centimeters (cm³)
24,000,000 cm3
Cubic Feet (ft³ / cu ft)
847.552 ft3
Cubic Inches (in³)
1,464,569.8583 in3
Cubic Yards (yd³)
31.3908 yd3
US Liquid Gallons (gal)
6,340.1293 us_gal
Imperial Gallons (UK gal)
5,279.262 imp_gal

Mathematical Formula & Step-by-Step Derivation

SI Normalized Math
General Formula:
V = Length × Width × Height
Live Calculation With Your Input Values:
11. Rectangular Prism Volume Formula
Formula: V = Length × Width × Height
Substituted: V = (2 m) × (3 m) × (4 m)
Step Result: V = 24 m3

Normalized in SI: (2 m) × (3 m) × (4 m) = 24 m³

22. Total Surface Area
Formula: A = 2(lw + lh + wh)
Substituted: A = 2 × [(2 × 3) + (2 × 4) + (3 × 4)]
Step Result: A = 52 m²
33. Space Diagonal (Corner to Corner)
Formula: d = √(l² + w² + h²)
Substituted: d = √(2² + 3² + 4²)
Step Result: d = 5.3852 m (5.3852 m)

How to Calculate the Volume of a Rectangular Prism (Cuboid)

A rectangular prism (also called a rectangular cuboid or box) is a polyhedron with 6 rectangular faces, 12 edges, and 8 vertices. Opposite faces are parallel and congruent.

  1. Measure the Length (l), Width (w), and Height (h) along the three perpendicular axes.
  2. Multiply the base area (l × w) by the height (h).
  3. To find total surface area, sum the areas of all 6 faces: A = 2(lw + lh + wh).
  4. To find the corner-to-corner 3D diagonal, apply the 3D Pythagorean theorem: d = √(l² + w² + h²).

Rectangular Prism Formulas

Volume: V = l × w × h
Surface Area: A = 2(l·w + l·h + w·h)
Space Diagonal: d = √(l² + w² + h²)

Example: Shipping Crate Dimensions

A wooden crate measures 2m long, 3m wide, and 4m tall:

• Volume V = 2m × 3m × 4m = 24.0000 m³ (24,000 Liters)

• Surface Area A = 2 × (6 + 8 + 12) = 52.0000 m²

• Diagonal d = √(4 + 9 + 16) = √29 ≈ 5.3852 meters

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