Area Calculator
Quick Formulas
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Area Formulas and Calculations
What is Area?
Area is the measure of space inside a two-dimensional shape. It's expressed in square units (square feet, square meters, square inches, etc.). Understanding area is essential for construction, landscaping, flooring, painting, and many other applications.
Area Formulas by Shape
Rectangle / Square
Area = length × width
A rectangle has four right angles. A square is a special rectangle where all sides are equal.
Example: A room 12 ft × 10 ft = 120 square feet
Triangle
Area = ½ × base × height
The height must be perpendicular to the base. For any triangle, pick any side as the base and use the perpendicular distance to the opposite vertex as height.
Example: Base 8 cm, height 5 cm = ½ × 8 × 5 = 20 cm²
Circle
Area = π × r²
The radius (r) is the distance from the center to any point on the circle. π (pi) is approximately 3.14159.
Example: Radius 7 in = π × 7² = π × 49 ≈ 153.94 in²
Trapezoid
Area = ½ × (base₁ + base₂) × height
A trapezoid has two parallel sides (the bases). The height is the perpendicular distance between the two parallel sides.
Example: Bases 6 and 10, height 4 = ½ × (6+10) × 4 = 32 units²
Ellipse
Area = π × a × b
An ellipse is like a stretched circle. 'a' and 'b' are the semi-major and semi-minor axes (half the width and half the height).
Example: Semi-axes 5 and 3 = π × 5 × 3 ≈ 47.12 units²
Parallelogram
Area = base × height
A parallelogram has two pairs of parallel sides. The height is perpendicular to the base, not the slanted side length.
Example: Base 9, height 6 = 9 × 6 = 54 units²
Sector (Pie Slice)
Area = (θ/360) × π × r²
A sector is a "pie slice" of a circle. θ (theta) is the central angle in degrees.
Example: Radius 10, angle 90° = (90/360) × π × 100 ≈ 78.54 units²
Unit Conversions
| From | To | Multiply by |
|---|---|---|
| Square feet | Square meters | 0.0929 |
| Square meters | Square feet | 10.764 |
| Square inches | Square cm | 6.452 |
| Square yards | Square feet | 9 |
| Acres | Square feet | 43,560 |
Real-World Applications
Flooring & Carpet
Calculate room area to determine how much flooring material you need. Add 10% for waste and cuts.
Paint Coverage
Calculate wall area to determine paint needs. One gallon typically covers 350-400 square feet.
Landscaping
Calculate lawn area for fertilizer, seed, or sod. Irregular shapes can be broken into simpler shapes.
Real Estate
Property prices are often quoted per square foot. Area helps compare property values accurately.
Tips for Complex Shapes
For irregular shapes, divide them into simpler shapes (rectangles, triangles, etc.), calculate each area separately, then add them together. For shapes with cutouts, calculate the total area and subtract the cutout area.
Frequently Asked Questions
How do I calculate the area of a rectangle?
Multiply the length by the width. For example, a room that is 12 feet long and 10 feet wide has an area of 12 x 10 = 120 square feet. This formula works for any rectangle, including squares.
What is the formula for the area of a circle?
The area of a circle is A = pi x r squared, where r is the radius (the distance from the center to the edge). If you know the diameter, divide it by 2 to get the radius first.
How do I find the area of an irregular shape?
Break the irregular shape into simpler shapes like rectangles, triangles, and circles. Calculate the area of each simple shape separately, then add them together. For shapes with holes, subtract the hole area from the total.
Why is area measured in square units?
Area measures two-dimensional space, so it uses square units (square feet, square meters, etc.). Think of it as counting how many 1x1 unit squares would fit inside the shape.