Rectangular Prism Volume Calculator

Calculate the volume of a box (rectangular prism) easily. Enter length, width, and height – get instant results with unit conversion and 3D visualization.

Formula: Volume = length × width × height (V = l · w · h)

5×3×2
10×4×3
Cube 2.5
12×8×6 (box)
Unit cube
Volume Calculation Results
1. Given dimensions
l = 5 cm w = 3 cm h = 2 cm
2. Apply formula
V = l · w · h = 5 × 3 × 2
3. Volume
30 cm³
= 0.00003 m³ (alternative units)
4. Visualization

Schematic representation (not to scale, proportions preserved).

Understanding Rectangular Prism Volume

A rectangular prism (also called a rectangular solid, a box, or a cuboid) is a three-dimensional shape with six rectangular faces. Its volume measures the space it occupies.

Volume formula:

V = l × w × h

where l = length, w = width, h = height. All dimensions must be in the same unit.

Step-by-step example

1
Measure or identify the three dimensions. Example: a box has length 8 cm, width 5 cm, height 3 cm.
2
Multiply length × width to get the area of the base. 8 cm × 5 cm = 40 cm².
3
Multiply the base area by the height. 40 cm² × 3 cm = 120 cm³.

Why this formula works

The volume of any prism is the area of its base times its height. For a rectangular prism, the base is a rectangle (area = l × w), so V = (l × w) × h.

Real‑life applications

  • Packing and shipping: Calculate how many items fit in a box, or the volume of a container.
  • Construction: Determine concrete needed for a rectangular footing, or the volume of a room.
  • Aquariums & pools: Find water capacity.
  • Moving: Estimate the space required for furniture.

Common unit conversions (volume)

  • 1 m³ = 1,000,000 cm³
  • 1 ft³ = 1,728 in³
  • 1 liter = 1,000 cm³ (useful for liquid volumes)
  • 1 gallon (US) ≈ 231 in³

Frequently Asked Questions

All three dimensions must be in the same unit before multiplying. Use the unit selector above to choose your unit; the calculator assumes all inputs are in that unit.

Not directly. Surface area and volume are different properties. You would need additional information (like the ratios of sides) to find volume from surface area alone.

A cube is a special rectangular prism where all sides are equal. Its volume is V = s³, where s is the side length. The calculator works for cubes too – just enter the same value for length, width, and height.

The calculator displays the volume in cubic units (cm³, m³, etc.). Below the main result, you’ll see an approximate conversion to an alternative unit (e.g., liters for cm³, cubic feet for inches). Use the conversion factors mentioned above for precise conversions.