Area Calculator - Free Area Calculator for Rectangle, Circle, Triangle, Trapezoid, Parallelogram, and Ellipse with Formulas and Unit Conversions
Area Calculator
Material Calculator (Optional)
Ready to Calculate Area?
Select a shape, enter dimensions, and click "Calculate Area" to get instant results
Supports rectangle, circle, triangle, trapezoid, parallelogram, ellipse, regular polygons, and irregular shapes with material calculator
Understanding Area and Area Calculations
What is Area?
Area is the measurement of the space inside a two-dimensional shape. It's expressed in square units (square feet, square meters, square inches, etc.) and represents how much surface a shape covers.
Understanding area is essential for many real-world applications: calculating flooring needs, determining paint coverage, planning garden layouts, measuring property size, and solving geometry problems.
Area Formulas for Common Shapes
Rectangle
Formula: Area = Length × Width
Example: A rectangle 10 ft × 8 ft = 80 sq ft
Circle
Formula: Area = π × r² (where r = radius)
Example: A circle with radius 5 ft = π × 25 = 78.54 sq ft
Triangle
Formula: Area = (Base × Height) ÷ 2
Example: A triangle with base 10 ft and height 8 ft = (10 × 8) ÷ 2 = 40 sq ft
Trapezoid
Formula: Area = ((Base₁ + Base₂) × Height) ÷ 2
Example: Bases 10 ft and 8 ft, height 6 ft = ((10 + 8) × 6) ÷ 2 = 54 sq ft
Parallelogram
Formula: Area = Base × Height
Example: Base 10 ft, height 8 ft = 80 sq ft
Ellipse
Formula: Area = π × a × b (where a and b are semi-axes)
Example: Semi-major axis 5 ft, semi-minor axis 3 ft = π × 5 × 3 = 47.12 sq ft
Area Unit Conversions
| Unit | Square Feet | Square Meters |
|---|---|---|
| 1 Square Foot | 1.00 | 0.0929 |
| 1 Square Meter | 10.764 | 1.00 |
| 1 Square Yard | 9.00 | 0.836 |
| 1 Acre | 43,560 | 4,047 |
| 1 Hectare | 107,639 | 10,000 |
Calculating Area of Irregular Shapes
For irregular or complex shapes, break them down into basic shapes (rectangles, triangles, circles) and calculate each separately:
- Divide the irregular shape into basic geometric shapes
- Calculate the area of each basic shape
- Add all areas together for total area
- For shapes with cutouts, subtract cutout areas from total
Example: An L-shaped room can be divided into two rectangles. Calculate each rectangle's area separately, then add them together to get the total area.
Frequently Asked Questions
How do I calculate the area of a rectangle?
To calculate rectangle area: Area = Length × Width. Example: A rectangle 10 feet long × 8 feet wide = 80 square feet. Simply multiply the length by the width. This formula works for any rectangle, regardless of size. For squares (special rectangles), length equals width, so area = side².
How do I calculate the area of a circle?
Circle area formula: Area = π × r², where r is the radius (half the diameter). Example: A circle with radius 5 feet has area = π × 5² = 3.14159 × 25 = 78.54 square feet. If you know diameter instead: divide by 2 to get radius, then use the formula. π (pi) ≈ 3.14159.
How do I calculate the area of a triangle?
Triangle area formula: Area = (Base × Height) ÷ 2. Example: A triangle with base 10 feet and height 8 feet has area = (10 × 8) ÷ 2 = 80 ÷ 2 = 40 square feet. The height is the perpendicular distance from the base to the opposite vertex. This formula works for all triangles.
How do I calculate the area of a trapezoid?
Trapezoid area formula: Area = ((Base₁ + Base₂) × Height) ÷ 2. Example: A trapezoid with bases 10 feet and 8 feet, and height 6 feet has area = ((10 + 8) × 6) ÷ 2 = (18 × 6) ÷ 2 = 108 ÷ 2 = 54 square feet. The two bases are the parallel sides, and height is the perpendicular distance between them.
How do I calculate the area of an irregular shape?
For irregular shapes: 1) Break the shape into basic shapes (rectangles, triangles, circles), 2) Calculate area of each basic shape separately, 3) Add all areas together for total area. For shapes with cutouts: Calculate full shape area, subtract cutout areas. Example: L-shaped room = Rectangle 1 + Rectangle 2. This method works for any complex shape.
What is the difference between area and perimeter?
Area measures the space inside a shape (square units like sq ft, sq m). Perimeter measures the distance around a shape (linear units like feet, meters). Example: A 10×8 ft rectangle has area = 80 sq ft (space inside) and perimeter = 36 ft (distance around). Area is 2D (length × width), perimeter is 1D (sum of all sides).
How do I convert between different area units?
Common area unit conversions: 1 square foot = 0.0929 square meters, 1 square meter = 10.764 square feet, 1 square yard = 9 square feet, 1 acre = 43,560 square feet, 1 hectare = 10,000 square meters = 2.47 acres. To convert: Multiply by conversion factor. Example: 100 sq ft × 0.0929 = 9.29 sq m. Our calculator automatically converts between units.
Can I calculate area for 3D shapes?
This calculator calculates 2D area (flat surfaces). For 3D shapes, you need surface area or volume: Surface area = sum of all face areas, Volume = area of base × height. Example: A box (rectangular prism) has 6 faces - calculate area of each face and add together for total surface area. For volume: length × width × height.