Area Calculator
Calculate area instantly with our math tool. Shows detailed work, formulas used, and multiple solution methods. See charts, tables, and visual results.
Formula
Rectangle: A = l × w | Circle: A = πr² | Triangle: A = ½bh
Area measures the space enclosed by a 2D shape. Each shape has its own formula: Rectangle = length × width, Circle = π × radius², Triangle = ½ × base × height, Trapezoid = ½(a+b) × h, Ellipse = π × a × b.
Worked Examples
Example 1: Room Flooring (Rectangle)
Problem: A room is 12 feet by 15 feet. How much flooring is needed?
Solution: A = l × w = 12 × 15 = 180 sq ft\nP = 2(12 + 15) = 54 ft (for baseboards)\nDiagonal = √(144 + 225) = √369 ≈ 19.21 ft
Result: Area: 180 sq ft | Perimeter: 54 ft
Example 2: Circular Garden
Problem: A circular garden has a radius of 6 meters. Find the area and circumference.
Solution: A = πr² = π × 36 ≈ 113.10 m²\nC = 2πr = 2 × π × 6 ≈ 37.70 m\nDiameter = 12 m
Result: Area: 113.10 m² | Circumference: 37.70 m
Frequently Asked Questions
What is the formula for the area of a circle?
The area of a circle is A = πr², where r is the radius. The circumference is C = 2πr or C = πd (where d is the diameter). For example, a circle with radius 7 has area = π × 49 ≈ 153.94 square units and circumference = 2π × 7 ≈ 43.98 units.
How do I find the area of a triangle?
The most common formula is A = ½ × base × height. You can also use Heron's formula when you know all three sides: A = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 is the semi-perimeter. For a right triangle, the two legs serve as base and height.
What is the difference between area and perimeter?
Area measures the space inside a 2D shape (in square units like cm², m², ft²), while perimeter measures the total distance around the outside edge (in linear units like cm, m, ft). For example, a 4×3 rectangle has area = 12 square units but perimeter = 14 units. Two shapes can have the same perimeter but different areas, and vice versa.
How do I calculate the area of an ellipse?
The area of an ellipse is A = π × a × b, where a and b are the semi-major and semi-minor axes. Unlike a circle (where a = b = r), an ellipse has two different radii. The circumference of an ellipse has no simple exact formula; Ramanujan's approximation C ≈ π(a+b)(1 + 3h/(10+√(4-3h))) where h = ((a-b)/(a+b))² gives excellent results.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
What formula does Area Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.