Area Calculator
Calculate area instantly with our math tool. Shows detailed work, formulas used, and multiple solution methods. See charts, tables, and visual results.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Area Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: Rectangle: A = l × w | Circle: A = πr² | Triangle: A = ½bh
Additional inputs: Base B (bottom), Height, Semi-major Axis (a), Semi-minor Axis (b).
Worked example — Area: 180 sq ft | Perimeter: 54 ft
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 P = 2(12 + 15) = 54 ft (for baseboards) Diagonal = √(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 C = 2πr = 2 × π × 6 ≈ 37.70 m Diameter = 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.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
Related Calculators
🧮Annulus Area Calculator
Calculate annulus area with inputs, formulas, and instant results.
🧮Area of a Rectangle Calculator
Calculate the area, perimeter, and diagonal of a rectangle. Find missing sides from known area. Convert between metric and imperial area units.
🧮Area of Crescent Calculator
Calculate area of crescent with inputs, formulas, and instant results.
🧮Cross Sectional Area Calculator
Calculate cross sectional area with inputs, formulas, and instant results.
🧮Shoelace Formula Polygon Area Calculator
Calculate shoelace formula polygon area with inputs, formulas, and instant results.
🧮Lateral Area Trapezoidal Prism Calculator
Calculate lateral area trapezoidal prism with inputs, formulas, and instant results.
🧮Surface Area of a Hemisphere Calculator
Calculate surface area of ahemisphere with inputs, formulas, and instant results.
🧮Area of a Circle Calculator
Calculate area of acircle with inputs, formulas, and instant results.