Rectangular Prism Diagonal
This calculator helps you find the length of the space diagonal of a rectangular prism (also known as a cuboid). Simply enter the length, width, and height, and we'll calculate the diagonal that connects opposite vertices through the interior of the prism.
Enter the length of the prism.
Enter the width of the prism.
Enter the height of the prism.
This calculator helps you find the length of the space diagonal of a rectangular prism (also known as a cuboid). Simply enter the length, width, and height, and we'll calculate the diagonal that connects opposite vertices through the interior of the prism.
d = √(l² + w² + h²)
Imagine you have a box that is 10 cm long, 5 cm wide, and 3 cm high. To find the space diagonal, you'd use the formula: d = √(10² + 5² + 3²) = √(100 + 25 + 9) = √134 ≈ 11.58 cm. This calculator does all the heavy lifting for you!
The space diagonal of a rectangular prism is the line segment that connects two opposite vertices (corners) of the prism, passing through its interior. It's the longest possible straight line you can draw inside the prism.
The formula for the space diagonal is an extension of the Pythagorean theorem. First, you find the diagonal of the base (d_base = √(l² + w²)). Then, you use this base diagonal and the height to find the space diagonal (d = √(d_base² + h²)), which simplifies to d = √(l² + w² + h²).
Yes! A cube is a special type of rectangular prism where all sides (length, width, and height) are equal. Simply enter the side length for all three inputs, and the calculator will give you the cube's space diagonal.
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