Area Calculator
Calculate the area of circles, rectangles, triangles, trapezoids, ellipses, and sectors.
Area Formulas Reference
| Shape | Formula | Variables |
|---|---|---|
| Circle | A = π r² | r = radius |
| Rectangle | A = l × w | l = length, w = width |
| Triangle | A = ½ b h | b = base, h = height |
| Trapezoid | A = ½ (a + b) h | a, b = parallel bases, h = height |
| Ellipse | A = π a b | a, b = semi-axes |
| Sector | A = ½ r² θ | r = radius, θ = angle in radians |
Frequently Asked Questions
What is the formula for the area of a circle?
The area of a circle is A = π × r², where r is the radius. For example, a circle with radius 5 cm has area π × 25 ≈ 78.54 cm². If you know the diameter instead, divide it by 2 to get the radius first.
How do I find the area of a triangle?
The most common formula is A = ½ × base × height, where height is the perpendicular distance from the base to the opposite vertex. For a right triangle, the two legs serve as the base and height. For other triangles, you may need to calculate the height from the known side lengths using trigonometry.
What is a trapezoid and how is its area calculated?
A trapezoid (or trapezium) is a quadrilateral with exactly one pair of parallel sides, called the bases. Its area formula is A = ½ × (a + b) × h, where a and b are the lengths of the two parallel bases and h is the perpendicular height between them.
What is the area of an ellipse?
An ellipse is like a stretched circle. Its area is A = π × a × b, where a and b are the lengths of the semi-major and semi-minor axes (half the width and half the height of the ellipse). A circle is a special case of an ellipse where a = b = r.
What is a sector and how do I calculate its area?
A sector is a 'pie slice' of a circle, defined by a radius and a central angle. Its area is A = ½ × r² × θ, where θ is the angle in radians. To convert degrees to radians, multiply by π/180. A 90° sector of a circle with radius 4 has area ½ × 16 × (π/2) ≈ 12.57 square units.