Area Calculator
Calculate area and perimeter for common 2D shapes, regular polygons, or an irregular shape defined by coordinates.
Shape Selection
Dimensions
Results
Additional Measurements
Formula Used:
A = s² = 1² = 1.000000 m²
Related Calculators
What is Area Calculator?
Understanding Area Calculations
Basic Area Formulas
Square
A = s²
Where s is the side length
Rectangle
A = l × w
Where l is length, w is width
Triangle
A = ½ × b × h
Where b is base, h is height
Circle
A = πr²
Where r is the radius
Trapezoid
A = ½(a + b) × h
Where a, b are parallel sides, h is height
Rhombus
A = ½ × d₁ × d₂
Where d₁, d₂ are the diagonals
Regular Polygons
Regular polygons have equal sides and angles. Common formulas:
- Pentagon: A = ¼√(25 + 10√5) × s²
- Hexagon: A = (3√3/2) × s²
- Octagon: A = 2(1 + √2) × s²
- General n-gon: A = ½ × n × apothem × side
Irregular Polygons
For irregular polygons defined by coordinates, we use the Shoelace formula (also known as the surveyor's formula):
A = ½|∑(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)|This formula works for any simple polygon when vertices are listed in order (clockwise or counterclockwise).
Practical Applications
Construction & Real Estate
Calculate flooring materials, paint coverage, landscaping areas, and property sizes.
Agriculture & Gardening
Determine seed quantities, fertilizer amounts, and irrigation requirements for different field shapes.
Manufacturing & Design
Calculate material usage, optimize cutting patterns, and design efficient layouts.
Unit Conversions
This calculator supports multiple area units with automatic conversions:
- 1 m² = 10,000 cm² = 10.764 ft²
- 1 acre = 4,047 m² = 43,560 ft²
- 1 hectare = 10,000 m² = 2.47 acres
- 1 km² = 1,000,000 m² = 100 hectares
Worked Area Examples
Rectangle: A 12 ft by 8 ft rectangle has area 12 × 8 = 96 ft² and perimeter 2(12 + 8) = 40 ft.
Triangle: A triangle with base 10 m and height 6 m has area ½ × 10 × 6 = 30 m².
Circle: A circle with radius 4 cm has area π × 4² ≈ 50.265 cm².