Area Calculator

Area is the two-dimensional quantity expressing the size of a bounded planar surface. This free Area Calculator computes the exact square area for all

Mathematics

Geometric Shape

Dimension 1 (Length / Radius / Base)

Dimension 2 (Width / Height / Second Base)

Formula & Methodology

Rectangle: Area = Length × Width Circle: Area = π × Radius² Triangle: Area = ½ × Base × Height Trapezoid: Area = ½ × (Base₁ + Base₂) × Height

To calculate area, identify the geometric boundary shape and apply its standardized formula: - Rectangle: Multiply length by width. - Circle: Square the radius and multiply by π (approx 3.14159). - Triangle: Multiply the base by perpendicular height and divide by 2. - Trapezoid: Average the two parallel bases and multiply by the perpendicular height.

Total Area (Rectangle)

Overview

Area is the two-dimensional quantity expressing the size of a bounded planar surface. This free Area Calculator computes the exact square area for all primary geometric polygons and curves, including rectangles, circles, triangles, and trapezoids.

Calculating area is fundamental in flooring and carpeting installations, real estate lot sizing, painting walls, agriculture land yield planning, and mechanical drafting. This tool provides instant conversions and perimeter cross-checks.

Worked Examples

Example 1: Area of a 10m × 5m Room

Shape: Rectangle, Length = 10, Width = 5

Multiply dimensions: 10 × 5 = 50.
Perimeter check: 2 × (10 + 5) = 30m.

Final Answer: 50.00 sq units

Example 2: Area of a Circular Patio (Radius = 7 ft)

Shape: Circle, Radius = 7

Square radius: 7² = 49.
Multiply by π: 49 × 3.14159 = 153.94 sq ft.

Final Answer: 153.94 sq units

Example 3: Triangular Gable Wall (Base 12 ft, Height 6 ft)

Shape: Triangle, Base = 12, Height = 6

Multiply base and height: 12 × 6 = 72.
Divide by 2: 72 ÷ 2 = 36 sq ft.

Final Answer: 36.00 sq units

Shape	Dimensions	Formula	Area Result
Rectangle	L = 10, W = 5	10 × 5	50.00
Circle	Radius = 5	π × 5²	78.54
Triangle	Base = 10, Height = 6	0.5 × 10 × 6	30.00
Square	Side = 8	8 × 8	64.00
Circle	Radius = 10	π × 10²	314.16

Shape

Dimensions

Formula

Area Result

Rectangle

L = 10, W = 5

10 × 5

50.00

Circle

Radius = 5

π × 5²

78.54

Triangle

Base = 10, Height = 6

0.5 × 10 × 6

30.00

Square

Side = 8

8 × 8

64.00

Circle

Radius = 10

π × 10²

314.16

Frequently Asked Questions

In what units is area expressed?

Area is always expressed in square units (e.g., square feet ft², square meters m², square inches in², or acres).

How do you convert square feet to square yards?

Divide square feet by 9 (since 1 yard = 3 feet, and 1 sq yd = 3 × 3 = 9 sq ft). For example, 90 sq ft = 10 sq yds.

Can area ever be negative?

No. Area measures physical spatial extent and is always strictly positive (or zero for a point/line).

Does the calculator accept decimal values?

Yes. You can enter any positive decimal measurement with full floating-point accuracy.

How do you calculate the area of an irregular shape?

Deconstruct the irregular shape into smaller standard polygons (rectangles and triangles), calculate the area of each component, and sum them together.