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VolumeCalcKit
Geometry

Rectangular Prism Volume Calculator

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

Instant results
Real-time calculation
Accurate & reliable
Standard SI formulas
Free to use
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Length (l)Height (h)Width (w)
Technical Dimension Schematic100% Vector
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 Standard 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)
Rectangular Prism Formulas & Geometry Derivations
Volume Formula:V = l × w × h
Total Surface Area:A = 2(lw + lh + wh)
3D Space Diagonal:d = √(l² + w² + h²)
Base Face Diagonal:d_base = √(l² + w²)
Worked Engineering Example: Shipping Crate Dimensions

Problem: A wooden industrial transport crate has outer dimensions Length = 2.4 m, Width = 1.2 m, and Height = 1.5 m.

• Volume V = 2.4 m × 1.2 m × 1.5 m = 4.3200 m³

• Liquid Equivalent: 4.32 m³ × 1,000 = 4,320 Liters (1,141.22 US Gallons)

• Total Surface Area = 2 × ((2.4×1.2) + (2.4×1.5) + (1.2×1.5)) = 2 × (2.88 + 3.60 + 1.80) = 16.560 m²

• Corner-to-Corner 3D Space Diagonal d = √(2.4² + 1.2² + 1.5²) = √(5.76 + 1.44 + 2.25) = √9.45 ≈ 3.074 meters

Common Use Cases
  • Internal vs. External Box Dimensions: Corrugated cardboard wall thickness (single-wall vs. double-wall) reduces internal usable volume by 0.5 to 1.5 cm per side. Always use interior dimensions when calculating package product fit.
  • Max Item Length (Diagonal Rule): The longest rigid item (e.g., a pipe, ski, or steel rod) that can fit inside a rectangular box is equal to the 3D space diagonal d = √(l² + w² + h²).
  • Stacking Optimization: In palletizing (48×40 inch GMA pallets), carton dimensions designed with integer submultiples (e.g., 16×12 or 24×20 inches) maximize truck cubic efficiency and minimize shipping air costs.

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

A rectangular prism (also called a rectangular cuboid, right box, or rectangular parallelopiped) is a 3-dimensional polyhedron bounded by six rectangular faces meeting at right (90°) angles. It is the most common shape encountered in manufacturing, architecture, shipping cartons, and room layout design.

  1. Measure the Length (l): Measure the longest horizontal dimension of the rectangular base.
  2. Measure the Width (w): Measure the shorter horizontal dimension perpendicular to the length.
  3. Measure the Height (h): Measure the vertical dimension perpendicular to the base.
  4. Ensure consistent units: Convert all three dimensions into the same unit (e.g. all in meters, all in centimeters, or all in inches) prior to multiplication.
  5. Multiply Length × Width × Height: Compute V = l × w × h to obtain cubic volume.

Frequently Asked Questions

How do you calculate the volume of a rectangular prism?
Multiply its three dimensions together: Volume = Length × Width × Height (V = l × w × h). Ensure all dimensions are measured in the same unit of measure before multiplying.
What is the difference between a rectangular prism and a cuboid?
There is no difference in geometry. 'Rectangular prism' and 'rectangular cuboid' are interchangeable mathematical terms describing a 3D solid with 6 rectangular faces joined at right angles.
How do you calculate the space diagonal of a rectangular box?
The 3D space diagonal from one bottom corner to the opposite top corner is calculated using the extended Pythagorean theorem: d = √(l² + w² + h²).
How do you calculate surface area of a rectangular prism?
Because a rectangular prism has 3 pairs of matching rectangular faces (top/bottom, front/back, left/right), the total surface area formula is A = 2 × (l×w + l×h + w×h).
How do you convert rectangular prism volume to liters or gallons?
If dimensions are in meters, 1 cubic meter equals 1,000 Liters (or 264.172 US Gallons). If dimensions are in inches, divide total cubic inches by 231 to obtain US Gallons, or divide by 61.0237 to get Liters.
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