What is a Rectangular Prism?
A right rectangular prism is a box-shaped object — a 3-dimensional solid with six rectangular faces. It is also called a cuboid, box, or rectangular hexahedron. All angles are right angles (90°), and opposite faces are congruent and parallel rectangles.
Rectangular prisms can also be oblique — leaning to one side — in which case the lateral faces become parallelograms. Our calculator handles the right rectangular prism (all faces are rectangles).
How Do I Find the Volume of a Rectangular Prism?
We calculate the volume of a rectangular prism with the formula:
V = l × w × h
where l is the length, w is the width, and h is the height.
Example: For a cardboard box with l = 18 in, w = 12 in, h = 15 in:
- V = 18 × 12 × 15 = 3,240 in³
- That is also ≈ 1.875 ft³ or about 53.1 liters.
How Do I Find the Surface Area of a Rectangular Prism?
The surface area is the total area of all six rectangular faces — three pairs of opposite rectangles:
SA = 2(lw + lh + wh)
Using the same box (l = 18 in, w = 12 in, h = 15 in):
- Top/Bottom: 2 × (18 × 12) = 2 × 216 = 432 in²
- Front/Back: 2 × (18 × 15) = 2 × 270 = 540 in²
- Left/Right: 2 × (12 × 15) = 2 × 180 = 360 in²
- Total SA = 432 + 540 + 360 = 1,332 in²
This is also the amount of paper you would need to wrap that box perfectly.
How Do I Calculate the Diagonal of a Rectangular Prism?
The space diagonal (the longest diagonal) runs through the interior of the prism connecting two opposite vertices:
d = √(l² + w² + h²)
For the same box: d = √(18² + 12² + 15²) = √(324 + 144 + 225) = √693 ≈ 26.32 in
Measurement Systems Supported
Our rectangular prism calculator supports two measurement systems:
- US / Imperial: Input in inches (in). Results shown in in³ / ft³ / L (volume), in² / ft² (surface area), in / ft (diagonal).
- Metric: Input in centimeters (cm). Results shown in cm³ / m³ / L (volume), cm² / m² (surface area), cm / m (diagonal).
How to Calculate Volumes of Other Solids?
The rectangular prism is just one of many 3D shapes. Here are formulas for other common solids:
- Cube: V = a³ (all sides equal)
- Cylinder: V = π × r² × h
- Sphere: V = (4/3) × π × r³
- Cone: V = (1/3) × π × r² × h
- Triangular Prism: V = (1/2) × b × h × l
- Pyramid: V = (1/3) × Base Area × h
FAQs
- What is the difference between a cube and a rectangular prism?
- A cube is a special case of a rectangular prism where all three dimensions (length, width, height) are equal. A rectangular prism can have three different dimensions.
- How many faces, edges, and vertices does a rectangular prism have?
- A rectangular prism has 6 faces, 12 edges, and 8 vertices.
- Is a shoebox a rectangular prism?
- Yes! A shoebox is a perfect real-world example of a rectangular prism. So is a brick, a room, a fish tank, and most cardboard boxes.
- How do I find the volume of a fish tank?
- Measure the length, width, and depth (height) of the tank in the same unit, then multiply them together. For example, a tank 24 in × 12 in × 16 in holds 4,608 in³ = 2.667 ft³ ≈ 75.5 L.
- How much paper do I need to wrap a gift box?
- Calculate the surface area of the box using SA = 2(lw + lh + wh). Add about 10–15% extra for overlaps and folding.
- Can the calculator handle feet or meters directly?
- Enter values in inches (US/Imperial) or centimeters (Metric). To use feet, convert to inches first (1 ft = 12 in). To use meters, convert to centimeters (1 m = 100 cm).