Area Calculator
Choose a shape, enter dimensions, and instantly get area and perimeter with the full formula.
📐 What is an Area Calculator?
Area is the measure of the two-dimensional space enclosed within a shape, expressed in square units such as square metres, square centimetres, square feet, or square inches. Calculating area correctly requires knowing the right formula for each shape, because the formulas differ significantly: a circle uses the radius and the constant pi, while a trapezoid needs two parallel sides and a perpendicular height.
This calculator covers eight of the most common 2D shapes used in practice: rectangles (floors, walls, screens), triangles (roof cross-sections, land parcels, sail shapes), circles (pipes, wheels, circular garden beds), trapezoids (drainage channels, retaining walls, architectural features), parallelograms (tile layouts, slanted surfaces), ellipses (oval tracks, swimming pools, elliptical windows), sectors (pie charts, sprinkler coverage zones, clock hands), and regular polygons (hexagonal tiles, octagonal stop signs, polygonal floor plans).
A common mistake is confusing area with perimeter. Area answers "how much space is inside?" while perimeter answers "how long is the boundary?" Painting a wall requires area (litres of paint per square metre). Fencing a garden requires perimeter (metres of fence per linear metre). Another frequent error is using the slant side instead of the perpendicular height for triangles and parallelograms: the height in the formula always refers to the perpendicular distance between the base and the opposite vertex or side.
This calculator shows both area and perimeter (or equivalent boundary measure) together for each shape, using the geometry utility functions that power all shape calculators on this site. All formulas are exact except the ellipse perimeter, which uses the Ramanujan approximation accurate to within 0.02% for typical aspect ratios.
📐 Formulas
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Rectangle (living room floor)
A living room 8 m wide and 5 m long
Example 2 - Circle (circular garden bed, radius 7 m)
Circular garden bed with radius 7 metres
Example 3 - Triangle (roof cross-section)
Triangular roof cross-section with base 10 m and height 4 m
Example 4 - Sector (90-degree pizza slice from a 10 m radius)
A 90-degree sector of a circle with radius 10 m
Example 5 - Regular Hexagon (honeycomb cell, side 5 cm)
Regular hexagon with side length 5 cm
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the area of a rectangle?
Area of a rectangle = length times width (A = l times w). For example, a rectangle 8 m long and 5 m wide has area 8 times 5 = 40 square metres. The perimeter is 2 times (l + w) = 2 times (8 + 5) = 26 m. Both area and perimeter are shown together in the Rectangle mode of this calculator.
How do you calculate the area of a triangle?
Area of a triangle = half times base times height (A = 0.5 times b times h). The height must be perpendicular to the base. For example, a triangle with base 10 cm and perpendicular height 6 cm has area 0.5 times 10 times 6 = 30 square centimetres. If you know all three sides, use Heron's formula instead.
How do you calculate the area of a circle?
Area of a circle = pi times radius squared (A = pi times r squared). Using pi = 3.14159, a circle with radius 7 m has area 3.14159 times 49 = 153.94 square metres. The circumference is 2 times pi times r = 43.98 m. Enter the radius in the Circle mode to get both values instantly.
How do you calculate the area of a trapezoid?
Area of a trapezoid = half times (parallel side a + parallel side b) times height h (A = 0.5 times (a + b) times h). For example, a trapezoid with parallel sides 6 m and 10 m and a height of 4 m has area 0.5 times 16 times 4 = 32 square metres. The height must be perpendicular to the parallel sides.
How do you calculate the area of an ellipse?
Area of an ellipse = pi times semi-major axis a times semi-minor axis b (A = pi times a times b). For example, an ellipse with a = 8 cm and b = 5 cm has area 3.14159 times 8 times 5 = 125.66 square centimetres. The semi-major axis is half the longest diameter; the semi-minor axis is half the shortest diameter.
How do you calculate the area of a sector?
Area of a sector = 0.5 times r squared times theta, where theta is the central angle in radians. In degrees: A = (theta / 360) times pi times r squared. For example, a sector with radius 10 m and central angle 90 degrees has area (90/360) times pi times 100 = 78.54 square metres. The arc length is (theta / 360) times 2 times pi times r = 15.71 m.
How do you calculate the area of a regular polygon?
Area of a regular n-gon with side length s = (n times s squared) divided by (4 times tan(pi/n)). For example, a regular hexagon (n=6) with side length 5 cm has area (6 times 25) / (4 times tan(30 degrees)) = 150 / (4 times 0.5774) = 64.95 square centimetres. The perimeter is simply n times s = 30 cm.
What is the difference between area and perimeter?
Area measures the space enclosed inside a 2D shape, expressed in square units (square metres, square feet, etc.). Perimeter measures the total length of the boundary around the shape, expressed in linear units (metres, feet, etc.). For a rectangle 4 m by 3 m: area = 12 square metres (the floor space inside) and perimeter = 14 m (the length of fencing around it).
How do you find the area of an irregular shape?
For irregular shapes, the most common methods are: (1) divide the shape into regular sub-shapes (rectangles, triangles) and sum their areas; (2) use the Shoelace formula if you know the coordinates of all vertices: A = 0.5 times the absolute value of the sum of (x_i times y_{i+1} minus x_{i+1} times y_i); (3) use graph paper and count squares. For curved irregular shapes, numerical integration (Simpson's rule) or planimeters are used.
What units does this area calculator use?
The calculator is unit-agnostic. If you enter dimensions in metres, the area result is in square metres and the perimeter in metres. If you enter in centimetres, results are in square centimetres and centimetres. No unit conversion is performed, so ensure all inputs use the same unit. To convert square metres to square feet, multiply by 10.764. To convert square feet to square metres, multiply by 0.0929.
How do you calculate the area of a parallelogram?
Area of a parallelogram = base times perpendicular height (A = b times h). The perpendicular height is the distance between the two parallel sides, measured at a right angle, NOT the length of the slanted side. For a parallelogram with base 9 m and perpendicular height 4 m: area = 36 square metres. Note that a rectangle is a special case of a parallelogram where the slant side equals the perpendicular height.
How does a sector area compare to the full circle area?
A sector with central angle theta (in degrees) covers (theta / 360) of the full circle area. So a 180-degree sector (semicircle) has half the circle area, a 90-degree sector (quarter circle) has one quarter, and a 60-degree sector has one sixth. For a circle of radius r, the full area is pi times r squared, and the sector area is (theta / 360) times pi times r squared. This proportional relationship is why sectors are often called pie slices.