Area & Volume Calculator

Calculate the area and volume of various geometric shapes with our easy-to-use calculator. Get instant results and formulas for all common shapes and solids.

Area & Volume Calculator

Select Shape

$Square$

Area = side × side

Side Length

$Rectangle$

Area = length × width

Length

Width

$Circle$

Area = π × radius²

Radius

$Triangle$

Area = (1/2) × base × height

Base

Height

$Trapezoid$

Area = (1/2) × (a + c) × h

where a and c are parallel sides and h is height

First Parallel Side (a)

Second Parallel Side (c)

Height (h)

$Parallelogram$

Area = base × height

Base

Height

Select Shape

$Cube$

Volume = side × side × side

Side Length

$Rectangular Prism$

Volume = length × width × height

Length

Width

Height

$Sphere$

Volume = (4/3) × π × radius³

Radius

$Cylinder$

Volume = π × radius² × height

Radius

Height

$Cone$

Volume = (1/3) × π × radius² × height

Radius

Height

$Pyramid$

Volume = (1/3) × base area × height

Base Length

Base Width

Height

Common Formulas

Area Formulas:

Square: A = s²
Rectangle: A = l × w
Circle: A = πr²
Triangle: A = ½bh

Volume Formulas:

Cube: V = s³
Rectangular Prism: V = l × w × h
Sphere: V = ⁴⁄₃πr³
Cylinder: V = πr²h

Understanding Area and Volume

Area and volume are fundamental geometric measurements that help us understand the size and capacity of objects in the physical world.

What is Area?

Area measures the amount of space inside the boundary of a two-dimensional shape. It is expressed in square units, such as square meters (m²) or square feet (ft²). Area is essential in various applications, from determining the amount of paint needed for a wall to calculating land prices.

What is Volume?

Volume measures the amount of space occupied by a three-dimensional object. It is expressed in cubic units, such as cubic meters (m³) or cubic feet (ft³). Volume is crucial for calculating the capacity of containers, determining material requirements for construction, and many other practical applications.

Frequently Asked Questions

Why do we square the radius in the circle area formula?

The formula for the area of a circle (A = πr²) involves squaring the radius because a circle can be thought of as consisting of infinitely many concentric rings. Each ring's area is proportional to both its circumference (2πr) and its width (dr). When integrated from 0 to the full radius, this gives us πr². Another way to understand it is that area is a two-dimensional measurement, so we need two length measurements multiplied together, and in a circle, the radius is used twice.

How do I convert between different units of area?

To convert between units of area, you need to remember that area units are squared. For example, to convert from square meters (m²) to square centimeters (cm²), you would multiply by 10,000 because 1 m = 100 cm, and 100² = 10,000. Some common conversions: 1 m² = 10.764 ft², 1 acre = 43,560 ft², 1 km² = 100 hectares = 0.3861 mi². Our calculator automatically handles unit conversions when you select different units.

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Area & Volume Calculator