Rectangular Prism Calculator

Category: Geometry
- April 17, 2025
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Calculate the volume, surface area, diagonal length, and other properties of a rectangular prism (or cuboid). Enter the length, width, and height below.

Enter Dimensions

Enter the length, width, and height to calculate various properties of the rectangular prism.

Display Options

About Rectangular Prisms

A rectangular prism (also called a cuboid) is a three-dimensional shape with six rectangular faces. All angles in a rectangular prism are right angles (90°). It's a common shape found in everyday objects like boxes, rooms, and buildings.

Key Formulas
  • Volume: V = length × width × height
  • Surface Area: SA = 2(length × width + length × height + width × height)
  • Space Diagonal: d = √(length² + width² + height²)
  • Face Diagonals:
    • Front/Back face: d₁ = √(length² + height²)
    • Top/Bottom face: d₂ = √(length² + width²)
    • Left/Right face: d₃ = √(width² + height²)
Special Cases
  • Cube: A rectangular prism where length = width = height
  • Square Prism: A rectangular prism where length = width
Applications
  • Architecture: Planning rooms, buildings
  • Engineering: Designing containers, parts
  • Packaging: Optimizing box dimensions
  • Shipping: Calculating volume and costs
  • Construction: Determining material quantities

What Is the Rectangular Prism Calculator?

The Rectangular Prism Calculator is a practical online tool that helps you calculate key properties of a rectangular prism (also known as a cuboid). Whether you're working on a construction project, optimizing packaging dimensions, or simply learning geometry, this calculator provides quick and accurate results for volume, surface area, diagonal length, and more.

Volume: \( V = \text{length} \times \text{width} \times \text{height} \)

Surface Area: \( SA = 2 \times (\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height}) \)

Space Diagonal: \( d = \sqrt{\text{length}^2 + \text{width}^2 + \text{height}^2} \)

Why Use This Calculator?

This tool is useful for:

  • Students: Easily explore 3D shapes and reinforce concepts like volume and surface area.
  • Teachers: Provide interactive support for geometry lessons or comparisons with triangle area tools.
  • Professionals: Quickly calculate measurements for construction, design, and shipping.
  • DIY Projects: Ensure accurate cutting and space usage in home improvement tasks.

How to Use the Calculator

Follow these simple steps to get the results you need:

  • Select Calculation Type: Choose whether you want to find properties from known dimensions, or determine dimensions from a given volume or surface area.
  • Enter Known Values: Fill in the length, width, and height, or specify volume/surface area and known sides.
  • Adjust Settings (Optional): Set decimal precision and enable options like formulas, step-by-step instructions, and 3D visualization.
  • Click "Calculate": View the results, including volume, surface area, diagonal lengths, and more.

What Can It Calculate?

The calculator gives you detailed insights into a rectangular prism’s geometry, including:

  • Volume and Surface Area
  • Space Diagonal and Face Diagonals
  • Length, Width, and Height (if only partial values are known)

It can also reverse-engineer missing measurements based on a given volume or surface area, a feature commonly found in advanced tools like a volume calculator or surface area tool.

Real-World Applications

Common uses for this tool include:

  • Calculating the volume of shipping boxes
  • Estimating materials needed for construction or renovations
  • Planning room dimensions and layouts in architecture
  • Optimizing storage space in engineering or interior design

FAQs

  • Can I use this for cubes?
    Yes. If all sides are equal, the calculator treats it as a cube automatically.
  • Can I solve for a missing side?
    Absolutely. Just enter the known values and the calculator will figure out the rest, similar to a triangle side and angle finder.
  • What units can I use?
    The calculator supports various units like meters, feet, inches, and more. You can select your preferred unit from the dropdown menus.
  • What if I only know the volume or surface area?
    No problem. Enter the volume or surface area and any known side(s). The tool will solve the rest, like a geometry surface area calculator or Pythagorean theorem tool might.
  • Is this the same as a cube calculator?
    It can be! Just set all three dimensions to the same value, and you’ll get the same results a cube volume formula would provide.

How This Calculator Compares to Other Tools

While this tool specializes in 3D rectangular prisms, many users also benefit from using related tools like:

For geometry enthusiasts, using the rectangular prism calculator along with these tools offers a full-featured math toolkit—from basic triangle geometry helpers to full 3D space calculators.

Final Thoughts

The Rectangular Prism Calculator is a helpful solution for quickly calculating geometric properties without needing to memorize or manually apply formulas. Whether you're exploring geometry, planning a space, or estimating materials, this tool makes it easy to get the numbers you need with clarity and confidence.