Rectangular Prism Calc
Calculate Surface Area & Volume with visual geometric nets.
Work Shown
A Rectangular Prism (often called a Cuboid or simply a “Box”) is a 3D shape where every pair of opposite faces is a rectangle. It is the most common geometric shape in modern life, from shipping containers to cereal boxes. This calculator computes all the essential metric properties of such a shape: Volume (Capacity), Total Surface Area (), Lateral Surface Area (), and the internal Diagonal length.
Features
1. Comprehensive Metrics: Instantly solves for , , and .
2. 3D Interactive Visuals: Toggle between a rotatable “3D Solid” view and an “Unfolded Net” view to visualize how the six faces connect.
3. Exclusions Mode: A practical feature for assignments or renovation projects. You can calculate the surface area of a room (prism) and subtract specific areas like windows or doors to get the *net* paintable area.
4. Unit Conversion: Enter dimensions in inches, feet, meters, or centimeters. The tool handles the conversions (e.g., inputting in inches but getting results in square feet).
5. Step-by-Step Work: Shows exactly how the “Front,” “Top,” and “Side” face areas are summed to reach the final answer.
Uses
- Packaging & Shipping: Determining the volume of a box to calculate shipping costs or material requirements for wrapping.
- Construction: Estimating concrete for a slab (Volume) or drywall for a room (Surface Area).
- Aquariums: Calculating the water capacity of a fish tank ( in cubic inches converted to gallons).
- HVAC & Storage: Determining the air volume of a room for heating load calculations.
Tips
- Lateral vs. Total: If you are painting a room, you usually want Lateral Area (walls only), not Total Surface Area (which includes the floor and ceiling).
- Diagonal Check: If you are trying to fit a long pole into a box, the Diagonal is the maximum length that will fit. It is often longer than the longest side.
- Open Top Boxes: If you need the surface area of an open-top box (like a swimming pool), assume standard Total Surface Area and then subtract the area of the Top face ().
FAQs
What is the difference between a Prism and a Cube?
A cube is a special type of rectangular prism where all three dimensions (, , ) are equal. All squares are rectangles, but not all rectangles are squares.
How do I find the diagonal?
Use the 3D Pythagorean theorem: . This represents the longest straight line you can draw inside the box.
Are the formulas different for a “Cuboid”?
No. “Cuboid” is just another name for a rectangular prism. The math is identical.
Final Words
The rectangular prism is the building block of the man-made world. Whether you are shipping a package, pouring concrete, or wrapping a gift, understanding its geometry is essential. This calculator transforms the three simple inputs of length, width, and height into a complete geometric profile, ensuring you have the exact numbers for your project.
