📦 Rectangular Box Calculator
Calculate volume, length, width, or height for boxes, boards, and rectangular prisms
Enter Box Dimensions
l=length, w=width, h=height
📊 Results
Length (l)
20 cm
Width (w)
15 cm
Height (h)
10 cm
Volume
3,000 cm³
Surface Area
1,300 cm²
Space Diagonal
26.9 cm
Base Area
300 cm²
Perimeter
70 cm
📝 Step-by-Step Solution
Given: l = 20 cm, w = 15 cm, h = 10 cm
Volume: V = l × w × h = 20 × 15 × 10 = 3,000 cm³
Surface Area: SA = 2(lw + lh + wh) = 2(300 + 200 + 150) = 1,300 cm²
Space Diagonal: d = √(l² + w² + h²) = √(400 + 225 + 100) = 26.93 cm
Base perimeter: P = 2(l + w) = 2(20 + 15) = 70 cm
📐 Rectangular Box Formulas
Volume: V = l × w × h
Surface Area: SA = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
Base Area: A = l × w
Perimeter (base): P = 2(l + w)
Understanding Rectangular Boxes
📦 Rectangular Prism
Also called cuboid. Six rectangular faces, 12 edges, 8 vertices. All angles are 90°. Most common 3D shape.
📏 Three Dimensions
Length, width, height. Multiply all three for volume. Order doesn't matter (commutative).
📐 Surface Area
Sum of all 6 faces. Three pairs of identical rectangles: 2(lw) + 2(lh) + 2(wh).
↗️ Space Diagonal
Corner to opposite corner. 3D Pythagorean theorem: d = √(l² + w² + h²).
Frequently Asked Questions
What is the volume formula for a rectangular box?
V = length × width × height. Multiply all three dimensions
together. Unit is cubic (cm³, m³, ft³, etc.).
How do I find length from volume?
l = V / (w × h). Divide volume by the product of width and height.
Works for any missing dimension.
What is the difference between cuboid and rectangular prism?
Same shape, different names. Both mean a 3D box with rectangular
faces. Cube is special case where all sides equal.
How do I calculate surface area?
SA = 2(lw + lh + wh). Add areas of all six faces. Three pairs of
identical rectangles.
What is the space diagonal?
Longest line inside the box. Corner to opposite corner through
center. d = √(l² + w² + h²).
How do I convert cubic inches to liters?
Divide by 61.024. 1 liter = 61.024 in³. Or: 1 in³ = 0.0164 L.
What if my box is a cube?
l = w = h = s. Volume = s³. Surface area = 6s². Use our cube
calculator for specialized features.
How do I find box dimensions from volume?
Need two dimensions. One dimension = V ÷ (other two). Can't find
all three from volume alone.
What is base area used for?
Floor/footprint of the box. A = l × w. Useful for stacking
calculations and floor space.
How accurate is this calculator?
Mathematically exact. Uses V = lwh with full precision. Round
results as needed for practical use.
Can I use different units for each dimension?
Convert first. All dimensions must be same unit before
multiplying. Our calculator assumes consistent units.
How do I calculate shipping box volume?
Inside dimensions. Measure internal l, w, h. Multiply for actual
capacity. Shipping uses outside dimensions.
What is dimensional weight?
Volume-based shipping weight. DIM weight = (L × W × H) ÷ factor
(usually 139 or 166). Compare to actual weight.
How does doubling dimensions affect volume?
Volume multiplies by 8. Doubling all three dimensions: 2×2×2 = 8×
original volume.
What is board foot measurement?
Lumber volume unit. 1 board foot = 144 in³ = 1 ft × 1 ft × 1 in.
Used for pricing wood.
How do I calculate cardboard needed for a box?
Use surface area. SA = 2(lw + lh + wh). Add extra for flaps, tabs,
and overlap.
What is the face diagonal?
Diagonal of one face. Bottom: √(l² + w²). Side: √(w² + h²). Front:
√(l² + h²).