Math
Area Calculator
Calculate the area of any shape instantly — rectangle, square, circle, triangle, parallelogram, trapezoid, or ellipse. Enter your measurements and get the area with the formula shown.
A = length × width
Area Formulas for All Shapes
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = l × w | 4 × 3 = 12 |
| Square | A = s² | 4² = 16 |
| Circle | A = π × r² | π × 5² = 78.54 |
| Triangle | A = ½ × b × h | ½ × 8 × 6 = 24 |
| Parallelogram | A = b × h | 10 × 4 = 40 |
| Trapezoid | A = ½ × (a + b) × h | ½ × (6+10) × 4 = 32 |
| Ellipse | A = π × a × b | π × 6 × 4 = 75.40 |
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Frequently Asked Questions
How do you calculate the area of a rectangle?
Area of a rectangle = Length × Width. Example: a rectangle that is 8 meters long and 5 meters wide has an area of 8 × 5 = 40 square meters (40 m²). This formula also applies to squares (where length = width), giving Area = side².
How do you calculate the area of a circle?
Area of a circle = π × radius² (approximately 3.14159 × r²). Example: a circle with radius 7 cm has area = 3.14159 × 7² = 3.14159 × 49 = 153.94 cm². Remember: radius is half the diameter. If you know the diameter, divide by 2 first.
How do you calculate the area of a triangle?
Area of a triangle = ½ × base × height. The height must be perpendicular (at a right angle) to the base — not the slant side. Example: a triangle with base 10 m and perpendicular height 6 m has area = ½ × 10 × 6 = 30 m². For triangles where you know all three sides but not the height, use Heron's formula: A = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2.
What is the area formula for a trapezoid?
Area of a trapezoid = ½ × (a + b) × height, where a and b are the two parallel sides and height is the perpendicular distance between them. Example: a trapezoid with parallel sides of 6 m and 10 m, and a height of 4 m: Area = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 m².
How do you find the area of an irregular shape?
For irregular shapes, common methods include: breaking it into simpler shapes (rectangles, triangles) and adding their areas; the grid/counting method (overlay a grid and count squares); integration for curved shapes; or using the Shoelace formula for polygons with known vertex coordinates. This calculator handles standard geometric shapes — for land area, a GIS tool or surveyor measurement is most accurate.
What are the most common area units and how do they convert?
Common area units: 1 m² = 10,000 cm² = 10.764 ft². 1 km² = 1,000,000 m² = 100 hectares = 247.1 acres. 1 acre = 4,047 m² = 43,560 ft². 1 hectare = 10,000 m² = 2.471 acres. 1 ft² = 144 in² = 0.0929 m². For land measurement, acres are common in the US, while hectares are used in most other countries.
What is the difference between area and perimeter?
Area measures the 2D space inside a shape (in square units like m² or ft²). Perimeter measures the total length of the boundary around a shape (in linear units like m or ft). Example for a 4×6 rectangle: Area = 4 × 6 = 24 m² (the space inside). Perimeter = 2×(4+6) = 20 m (the distance around the edge). Area is relevant for flooring, painting walls, and land. Perimeter is relevant for fencing, framing, and borders.