Area & Volume Calculator
Calculate area and volume of circles, rectangles, and cubes
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Area and Volume in Geometry
Area is the amount of space occupied by a two-dimensional shape, while volume is the amount of space occupied by a three-dimensional shape. Understanding how to calculate area and volume is fundamental in mathematics, engineering, and many practical applications.
Area Formulas
Circle
A = πr²
Where r is the radius
Rectangle
A = l × w
Where l is length and w is width
Triangle
A = ½ × b × h
Where b is base and h is height
Trapezoid
A = ½ × (b₁ + b₂) × h
Where b₁ and b₂ are the bases
Volume Formulas
Sphere
V = (4/3)πr³
Where r is the radius
Cylinder
V = πr²h
Where r is radius and h is height
Cube
V = a³
Where a is side length
Cone
V = (1/3)πr²h
Where r is radius and h is height
Practical Examples
Example: Calculate room area
If a rectangular room is 5 meters long and 4 meters wide, the area = 5 × 4 = 20 square meters.
Example: Calculate water tank volume
If a cylindrical tank has a radius of 2 meters and height of 3 meters, the volume = π × 2² × 3 ≈ 37.7 cubic meters.