Rectangular Prism Volume Calculator
Calculate the volume, surface area, and space diagonal of a rectangular prism (cuboid). Enter the length, width, and height to get instant results with formulas and a visual breakdown. Perfect for students, teachers, engineers, and DIY projects.
What Is a Rectangular Prism?
A rectangular prism (also called a cuboid or rectangular box) is a three-dimensional shape with six rectangular faces, twelve edges, and eight vertices. All angles are right angles, and opposite faces are congruent. Common examples include bricks, books, shipping boxes, and rooms.
This calculator computes three key properties of a rectangular prism:
- Volume: The amount of space inside the prism. V = L × W × H
- Surface Area: The total area of all six faces. SA = 2(LW + LH + WH)
- Space Diagonal: The distance from one corner to the opposite corner. d = √(L² + W² + H²)
How Does the Rectangular Prism Volume Calculator Work?
The calculator uses standard geometric formulas:
Volume: V = L × W × H
Surface Area: SA = 2(LW + LH + WH)
Space Diagonal: d = √(L² + W² + H²)
Where L = Length, W = Width, H = Height
Simply enter the length, width, and height of your rectangular prism, and the calculator will instantly compute all three properties. You can switch between metric and imperial units and choose how to display the volume.
Why Use This Rectangular Prism Calculator?
- Three Properties: Calculates volume, surface area, and space diagonal.
- Unit Flexibility: Switch between metric (meters, centimeters) and imperial (feet, inches).
- Visual Representation: A 3D diagram shows the prism with labeled dimensions.
- Formula Display: See the formulas used and the step-by-step calculation.
- Free & Private: No registration, no data storage.
Real-World Applications
- Construction: Calculating concrete volume for rectangular foundations.
- Packaging: Determining box dimensions for shipping and storage.
- Interior Design: Estimating floor area and wall surface for painting.
- Aquariums: Calculating water volume for fish tanks.
- Education: Learning geometry and solving math problems.
❓ Rectangular Prism Calculator FAQ
What is a rectangular prism?
A rectangular prism (or cuboid) is a three-dimensional shape with six rectangular faces, twelve edges, and eight vertices. All angles are right angles, and opposite faces are congruent.
How do I calculate the volume of a rectangular prism?
Multiply the length by the width by the height. Formula: V = L × W × H. For example, a prism with length 5 m, width 3 m, and height 2 m has a volume of 30 m³.
How do I calculate the surface area of a rectangular prism?
Surface area = 2(LW + LH + WH). For example, with L=5, W=3, H=2: SA = 2(15 + 10 + 6) = 62 m².
What is the space diagonal of a rectangular prism?
The space diagonal is the distance from one corner to the opposite corner, going through the interior. Formula: d = √(L² + W² + H²).
What is the difference between volume and surface area?
Volume measures the space inside the prism (cubic units). Surface area measures the total area of all faces (square units).
How do I convert between cubic meters and liters?
1 cubic meter = 1,000 liters. The calculator can display the volume in liters automatically.
How do I convert cubic feet to gallons?
1 cubic foot = 7.48052 gallons (US). The calculator includes a gallons output option.
What is the difference between a rectangular prism and a cube?
A cube is a special type of rectangular prism where all three dimensions (length, width, height) are equal.
How do I calculate the volume of a rectangular prism in liters?
First calculate the volume in cubic meters (V = L × W × H), then multiply by 1000. The calculator does this for you.
What is the formula for the diagonal of a rectangular prism?
The space diagonal formula is d = √(L² + W² + H²). The face diagonal formulas are: dLW = √(L² + W²), dLH = √(L² + H²), dWH = √(W² + H²).
How do I find the height of a rectangular prism if I know the volume?
Rearrange the volume formula: H = V ÷ (L × W). For example, if V = 30 m³, L = 5 m, W = 3 m, then H = 30 ÷ 15 = 2 m.
What units can I use for rectangular prism measurements?
You can use meters, centimeters, feet, inches, and more. This calculator supports metric and imperial systems.
How many faces does a rectangular prism have?
A rectangular prism has 6 faces, 12 edges, and 8 vertices. All faces are rectangles, and opposite faces are congruent and parallel.
What is the difference between a rectangular prism and a rectangular pyramid?
A rectangular prism has rectangular faces and a constant cross-section. A rectangular pyramid has a rectangular base and triangular faces that meet at a single point (apex).
Can I use this calculator for a shipping box?
Yes. This calculator is perfect for determining the volume and surface area of shipping boxes, storage containers, and packages.
What is the surface area of a rectangular prism with dimensions 10×6×4?
SA = 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24) = 2(124) = 248 square units.
What is the volume of a rectangular prism with dimensions 8×5×3?
V = 8 × 5 × 3 = 120 cubic units.