How to Calculate the Area of any 2D Shape

Calculate the exact square footage of any room or shape instantly using our Area Calculator, or learn the fundamental geometry formulas below.

Area is the amount of 2D space inside the boundary of a flat object. Whether you are buying paint for a bedroom, laying sod in a backyard, or doing middle school math homework, knowing how to calculate area is an essential life skill.

Because shapes vary drastically, mathematicians have developed specific formulas for each geometric polygon.

Squares and Rectangles

The most common and easiest shapes to calculate. Because their corners are perfect 90-degree right angles, you only need two measurements.

Formula: Area = Length × Width (or Base × Height)

Example: You want to carpet a bedroom that is 12 feet long and 10 feet wide. Area = 12 ft × 10 ft = 120 square feet.

Triangles

A triangle is mathematically exactly half of a rectangle. If you draw a diagonal line across a rectangle, you get two identical triangles.

Formula: Area = ½ × Base × Height

Example: A triangular sail on a boat has a base of 6 meters and a height of 8 meters. Area = 0.5 × 6 × 8 = 24 square meters.

(Note: The 'Height' must be the perpendicular distance from the base to the opposite point, not the length of the slanted side).

Circles

Circles are unique because they don't have straight sides. To calculate the area of a circle, we must use the mathematical constant Pi (π), which is approximately 3.14159.

Formula: Area = π × r² Where r is the radius (the distance from the exact center of the circle to the outer edge).

Example: You are building a circular patio with a radius of 5 feet.

1. Square the radius: 5 × 5 = 25
2. Multiply by Pi: 3.14159 × 25 = 78.54 Area = 78.54 square feet.

Irregular Shapes (The Deconstruction Method)

Very rarely is a room or a backyard a perfect square or a perfect circle. Real-world spaces are usually irregular polygons. To find the area of an irregular shape, you must use the "Deconstruction Method."

1. Break it down: Draw imaginary lines to break the complex shape into standard, simple shapes (like breaking an L-shaped room into two separate rectangles).
2. Calculate individually: Find the area of each of the smaller shapes using the standard formulas.
3. Add them together: The total area is the sum of the individual areas.

FAQ

What is the difference between Area and Perimeter? Area measures the flat space inside a shape (measured in square units). Perimeter measures the length of the outside boundary or fence around the shape (measured in linear units).

How do I calculate the area of a room if the measurements are in inches and feet? You must convert all measurements to a single unit before multiplying. A room that is 10 feet 6 inches by 12 feet must be calculated as 10.5 ft × 12.0 ft to get an accurate square footage reading.

---

Don't buy too much paint or flooring! Calculate precise square footage for any complex shape using the CalcUnit Area Calculator.