📦 Rectangular Box Calculator 2026
Calculate surface area, volume, diagonal, and face areas
Enter Box Dimensions
l = length, w = width, h = height
d = space diagonal
d = space diagonal
📊 Results
Length
10 cm
Width
6 cm
Height
4 cm
Surface Area
248 cm²
Volume
240 cm³
Space Diagonal
12.33 cm
Face Diag (l×w)
11.66 cm
Face Diag (l×h)
10.77 cm
Face Diag (w×h)
7.21 cm
📝 Step-by-Step Solution
Given: l = 10 cm, w = 6 cm, h = 4 cm
Surface Area = 2(lw + lh + wh) = 2(60 + 40 + 24) = 248 cm²
Volume = l × w × h = 10 × 6 × 4 = 240 cm³
Space Diagonal = √(l² + w² + h²) = √(100+36+16) = 12.33 cm
📐 Rectangular Box Formulas
Surface Area: A = 2(lw + lh + wh)
Volume: V = l × w × h
Space Diagonal: d = √(l² + w² + h²)
Face Diagonal: dface = √(a² + b²)
Find Dimension: l = V / (w × h)
Understanding Rectangular Prisms
📦 Shape
6 rectangular faces, 12 edges, 8 vertices. All angles 90°. Also called rectangular parallelepiped or cuboid. Cube is special case where l=w=h.
📐 Surface Area
A = 2(lw + lh + wh). Sum of all 6 face areas. Three pairs of identical opposite faces.
📦 Volume
V = l × w × h. Length × Width × Height. Space inside the box. Cubic units.
↗️ Diagonals
Space diagonal: √(l²+w²+h²). Longest line inside box. Face diagonals: √(a²+b²) for each face pair.
Frequently Asked Questions
What is the surface area formula for a rectangular box?
A = 2(lw + lh + wh). Sum of all six faces. Two faces each of l×w,
l×h, and w×h.
What is the volume formula for a rectangular box?
V = l × w × h. Length times width times height. Also called
capacity. Measured in cubic units.
How do I find the space diagonal of a box?
d = √(l² + w² + h²). 3D Pythagorean theorem. Goes from one corner
through interior to opposite corner.
How do I find a face diagonal?
d = √(a² + b²). Standard 2D Pythagorean theorem. There are three
different face diagonals on a rectangular box.
What is the difference between rectangular box and cube?
Cube: all sides equal (l=w=h). Rectangular box: can have different
lengths. Cube is special case of rectangular prism.
How do I find a missing dimension from volume?
Rearrange V = lwh. l = V/(wh), w = V/(lh), h = V/(lw). Divide
volume by product of known dimensions.
What is the perimeter of a rectangular box?
Total edge length = 4(l + w + h). There are 4 edges of each
dimension. Useful for framing or edge binding.
How do I calculate cardboard for a box?
Use surface area. A = 2(lw + lh + wh). Add extra for flaps,
overlaps, and waste. Consider net layout.
What is a rectangular prism?
Same as rectangular box. 3D shape with 6 rectangular faces. Also
called cuboid or rectangular parallelepiped.
How does doubling dimensions affect volume?
Volume increases 8×. (2l)(2w)(2h) = 8lwh. Surface area increases
4×. Same scaling law as cube.
What is the lateral surface area?
Alat = 2h(l + w). Four side faces only, excluding top
and bottom. Used for wrapping sides only.
How do I find dimensions to maximize volume?
For fixed surface area, cube maximizes volume. l = w = h gives
most volume. For fixed perimeter/edge, same answer.
What are real-world examples?
Shipping boxes, rooms, aquariums, refrigerators, books, bricks, cereal
boxes. Most common 3D shape in everyday life.
How do I convert between volume units?
1 m³ = 1000 L = 1,000,000 cm³. 1 ft³ = 7.48 gallons = 28.3 L. Keep
input dimensions in same unit.
What is the ratio of surface area to volume?
Decreases as size increases. Larger boxes are more efficient (less
surface per volume). Important for packaging, biology, heat transfer.
How do I find weight of hollow box?
Calculate material volume × density. Material volume = outer
volume - inner volume. Or surface area × thickness.
How accurate is this calculator?
Uses exact mathematical formulas. Results are precise for given
inputs. Assumes perfect right angles.