The area calculator computes area and perimeter for 7 geometric shapes. Select a shape, enter dimensions in metric or imperial units, and get instant results with a visual SVG diagram and the formula used.
Select Shape
How to Calculate Area for Any Shape
This area calculator supports 7 common geometric shapes. Each uses a proven formula — select your shape, enter the known dimensions, and get the area instantly along with a visual diagram.
Rectangle and Square
Area = length × width. A 12 × 9 ft living room has 108 sq ft. For flooring at $4/sq ft = $432 material cost. A square is a rectangle where length = width — a 10 ft square room = 100 sq ft.
Triangle
Area = ½ × base × height. A triangular garden bed with 8 ft base and 6 ft height has 24 sq ft. The height must be perpendicular to the base (not a slant side). For oddly shaped triangles where only the three sides are known, use Heron's formula: Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.
Circle
Area = π × r². A circular patio with 5 ft radius = π × 25 = 78.54 sq ft. To convert from diameter: radius = diameter / 2. Circumference = 2πr = 31.42 ft (for fencing or edging calculations).
Trapezoid
Area = ½ × (base₁ + base₂) × height. An A-frame window with parallel sides 4 ft (top) and 8 ft (bottom) and 3 ft height: ½ × (4+8) × 3 = 18 sq ft. Both parallel sides (bases) and the perpendicular distance between them (height) are required.
Ellipse and Parallelogram
Ellipse: Area = π × a × b, where a and b are the semi-axes (half the major and minor diameters). A 10 × 6 ft elliptical garden: π × 5 × 3 = 47.12 sq ft. Parallelogram: Area = base × height (perpendicular height, not the slant side). A 10 ft base with 4 ft perpendicular height = 40 sq ft.
FAQ
What shapes does this area calculator support?
This calculator handles 7 shapes: rectangle (length × width), triangle (base × height ÷ 2 or Heron's formula), circle (πr²), trapezoid (½(a+b)×h), ellipse (πab), parallelogram (base × height), and regular polygon (¼ns² cot(π/n)).
What is the formula for circle area?
Circle area = π × r², where r is the radius. For a circle with radius 5 ft: area = π × 25 = 78.54 sq ft. The circumference is 2πr = 31.42 ft. If you know the diameter d, the radius is d/2.
How do you calculate the area of a trapezoid?
Trapezoid area = ½ × (base₁ + base₂) × height. For a trapezoid with parallel sides 6 and 10 and height 4: Area = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 sq units. The two parallel sides are the 'bases' regardless of their orientation.
What is the area of an ellipse?
Ellipse area = π × a × b, where a is the semi-major axis (half the longer diameter) and b is the semi-minor axis (half the shorter diameter). For an ellipse with semi-axes 5 and 3: area = π × 5 × 3 = 47.12 sq units. A circle is a special ellipse where a = b = r.
Is this tool free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is sent to any server.
Does the calculator support metric and imperial units?
Yes. Toggle between imperial (inches, feet, yards) and metric (centimeters, meters) using the switch. All inputs and outputs update to the selected unit system.
How do you find the area of a regular polygon?
Regular polygon area = (n × s²) / (4 × tan(π/n)), where n is the number of sides and s is the side length. For a regular hexagon (n=6) with side 5: area = (6 × 25) / (4 × tan(30°)) = 150 / (4 × 0.5774) = 64.95 sq units.