📦 Rectangular Prism Calculator
Calculate volume, surface area, and other properties of a rectangular prism
How to Use This Calculator
Enter Three Dimensions
Input the length, width, and height of the rectangular prism. These are the three edge lengths of the box. Make sure all values are positive numbers.
Click Calculate
Press the "Calculate" button to compute volume, surface area, lateral area, and space diagonal of the rectangular prism.
Review All Results
View all calculated properties: volume (space inside), surface area (total outside area), lateral area (side faces only), and space diagonal (corner to opposite corner).
Formulas
Volume: V = l × w × h
Length × width × height
Surface Area: A = 2(lw + lh + wh)
Sum of areas of all six faces
Lateral Area: L = 2h(l + w)
Area of four side faces (excluding top and bottom)
Space Diagonal: d = √(l² + w² + h²)
Distance from one corner to the opposite corner
Where:
- l = length of the rectangular prism
- w = width of the rectangular prism
- h = height of the rectangular prism
- V = volume
- A = total surface area
- L = lateral surface area
- d = space diagonal
Example 1: Rectangular box with l = 5, w = 4, h = 3 units
Volume = 5 × 4 × 3 = 60 units³
Surface Area = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2 × 47 = 94 units²
Lateral Area = 2 × 3 × (5 + 4) = 6 × 9 = 54 units²
Diagonal = √(5² + 4² + 3²) = √(25 + 16 + 9) = √50 ≈ 7.07 units
Example 2: Box with l = 8, w = 6, h = 10 units
Volume = 8 × 6 × 10 = 480 units³
Surface Area = 2(48 + 80 + 60) = 2 × 188 = 376 units²
Lateral Area = 2 × 10 × (8 + 6) = 20 × 14 = 280 units²
Diagonal = √(64 + 36 + 100) = √200 ≈ 14.14 units
About Rectangular Prism Calculator
A rectangular prism (also called a rectangular box or cuboid) is a 3D shape with six rectangular faces. It has three pairs of parallel, congruent faces. This calculator computes volume, surface area, lateral area, and space diagonal from the three dimensions (length, width, height).
When to Use This Calculator
- Packaging: Calculate volume and surface area for boxes, containers, or packaging materials
- Architecture: Determine volumes and areas for rectangular rooms, buildings, or structures
- Construction: Estimate materials needed (paint, tiles, concrete) for rectangular spaces
- Shipping: Calculate box dimensions and volumes for shipping calculations
- Mathematics Education: Teach students about 3D geometry and rectangular prisms
- Storage: Determine storage capacity and surface area for rectangular storage units
Why Use Our Calculator?
- ✅ Multiple Properties: Calculates volume, surface area, lateral area, and diagonal
- ✅ Instant Results: Get all measurements immediately
- ✅ Complete Calculations: Shows step-by-step formulas for all properties
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Educational: Helps understand rectangular prism geometry
- ✅ Completely Free: No registration required
Understanding Rectangular Prisms
A rectangular prism has:
- 6 Rectangular Faces: Three pairs of parallel, congruent rectangles
- 12 Edges: Four edges of each length (l, w, h)
- 8 Vertices: Corners where three edges meet
- Volume: Amount of space inside = l × w × h
- Surface Area: Total area of all six faces = 2(lw + lh + wh)
- Lateral Area: Area of four side faces (excluding top and bottom)
- Space Diagonal: Longest distance between opposite corners = √(l² + w² + h²)
Real-World Applications
Packaging: A shipping box measures 30 cm × 20 cm × 15 cm. Volume = 9,000 cm³, Surface Area = 2(600 + 450 + 300) = 2,700 cm². This determines shipping costs and packaging material needed.
Construction: A rectangular room is 5 m × 4 m × 3 m. Volume = 60 m³ (airspace), Surface Area = 2(20 + 15 + 12) = 94 m² (wall and ceiling area for paint). Lateral Area = 2 × 3 × (5 + 4) = 54 m² (just walls).
Storage: A storage container 2 m × 1.5 m × 1 m has volume = 3 m³ (storage capacity) and surface area = 2(3 + 2 + 1.5) = 13 m² (material needed for construction).
Frequently Asked Questions
What is the difference between a cube and a rectangular prism?
A cube is a special type of rectangular prism where all three dimensions are equal (l = w = h). A rectangular prism can have different values for length, width, and height. All cubes are rectangular prisms, but not all rectangular prisms are cubes.
What's the difference between surface area and lateral area?
Surface area includes all six faces (top, bottom, and four sides). Lateral area includes only the four side faces, excluding the top and bottom bases. Lateral area is useful when you only need to cover the sides (like wrapping paper around a box without the lids).
How do I find the space diagonal?
The space diagonal is the longest line inside the prism, from one corner to the opposite corner. It's calculated using the 3D Pythagorean theorem: d = √(l² + w² + h²). This is different from face diagonals, which are on the faces.
Can I use this for a square prism?
Yes! A square prism is a rectangular prism where the base is a square (length = width). Just enter the same value for length and width. The formulas still work perfectly.
What units should I use?
Use any consistent units (meters, centimeters, inches, feet, etc.). Volume will be in cubic units (m³, cm³, etc.), and areas will be in square units (m², cm², etc.). Make sure all three dimensions use the same unit.
How do I find volume if I only know surface area?
You need at least two dimensions to calculate volume. If you only have surface area and one dimension, you can solve a system of equations. However, it's easier to measure or know at least two dimensions directly.