Rectangular Prism Calculator – Guide & Formulas
Calculate the volume, diagonal length, and surface area of a rectangular prism (box) instantly with custom dimensions.
Find all parameters of a rectangular prism, cuboid, or standard cardboard box. Solves total capacity, surface area, and three-dimensional diagonal lengths.
Key Takeaway
Use the free Rectangular Prism Calculator to calculate the volume, diagonal length, and surface area of a rectangular prism (box) instantly with custom dimensions. Get instant results with step-by-step explanations.
How to Use the Rectangular Prism Calculator
- Enter the length, width, and height of the rectangular prism.
- Check the computed volume, total surface area, and space diagonal.
- Use this tool to design shipping packages, storage rooms, or aquarium capacities.
The Formula
Variable Definitions
- V: Volume of the rectangular prism
- A: Total outer surface area
- l, w, h: Length, width, and height dimensions
Shipping Box Capacity
A standard shipping box has dimensions of 12 inches long, 8 inches wide, and 10 inches high. Find its volume.
- Step 1: Set length = 12, width = 8, height = 10.
- Step 2: Multiply the three inputs: 12 * 8 * 10 = 960.
- Step 3: The box has a volume of 960 cubic inches.
- Step 4: Calculate surface area: 2 * (12*8 + 12*10 + 8*10) = 2 * (96 + 120 + 80) = 592 square inches.
Frequently Asked Questions
What is a space diagonal?
A space diagonal is the straight-line distance between two opposite corners of the prism, cutting through the center in three-dimensional space, solved with d = √(l² + w² + h²).
Is a cube a rectangular prism?
Yes. A cube is a special case of a rectangular prism where the length, width, and height are all perfectly equal.
How do you convert cuboid volume to liters?
If dimensions are in centimeters, divide the volume in cm³ (mL) by 1,000 to get the capacity in liters.