Calculate the space diagonal of a rectangular prism (box) given its length, width, and height. Also computes face diagonals and surface area.
Space Diagonal: 5.39 Face Diagonals: l×w: 5.00 l×h: 4.47 w×h: 3.61 Surface Area: 52.00
Formula: d = √(l² + w² + h²). The space diagonal connects opposite corners of the rectangular prism through the interior.
What is a Rectangular Prism Diagonal?
A rectangular prism (also called a cuboid or rectangular box) is a three-dimensional shape with six rectangular faces . The space diagonal is the line segment connecting two opposite vertices of the prism through its interior .
d = √(l² + w² + h²)
Where:
- d — space diagonal
- l — length
- w — width
- h — height
The space diagonal is the longest distance inside a rectangular prism . Additionally, each face has its own diagonal:
- Base face diagonal: √(l² + w²)
- Side face diagonal: √(l² + h²)
- End face diagonal: √(w² + h²)
Applications include packaging design, construction, furniture fitting, and electronics — anywhere you need to know if an object fits inside a box or its maximum internal dimension.
How to Use This Calculator
- Enter length: Input the length of the rectangular prism.
- Enter width: Input the width of the rectangular prism.
- Enter height: Input the height of the rectangular prism.
- Calculate: Click the “Calculate Diagonal” button or press Enter.
- Reset: Use the “Reset” button to restore default values.
- Interpretation: Results show the space diagonal, each face diagonal, surface area, and volume. For example, a 4×3×2 box has a space diagonal of 5.39 units — the longest possible distance inside the box.