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
Rectangle: A = l × w | P = 2(l + w)
l = length (longer side)
w = width (shorter side)
Triangle: A = ½ × b × h
b = base
h = perpendicular height from base to opposite vertex
Circle: A = πr² | C = 2πr
r = radius
C = circumference
Trapezoid: A = ½(a + b) × h
a, b = the two parallel sides
h = perpendicular height between the parallel sides
Parallelogram: A = b × h
b = base
h = perpendicular height (NOT the slant side)
Ellipse: A = πab
a = semi-major axis (half the longest diameter)
b = semi-minor axis (half the shortest diameter)
Sector: A = ½r²θ | Arc = rθ
r = radius of the full circle
θ = central angle in radians (degrees × π ÷ 180)
Regular Polygon: A = (n × s²) ÷ (4 × tan(π/n))
n = number of sides
s = side length
P = perimeter = n × s
📖 How to Use This Calculator
Steps
1
Select a shape - Click one of the eight shape tabs at the top: Rectangle, Triangle, Circle, Trapezoid, Parallelogram, Ellipse, Sector, or Polygon.
2
Enter dimensions - Type values into the number inputs or drag the sliders. Keep all dimensions in the same unit.
3
Click Calculate - Press the Calculate button to compute area and perimeter (or circumference/arc length) for your shape.
4
Read the results - Area is shown in square units in the primary box. The secondary box shows the perimeter, circumference, or arc length.
5
Try an example - Click any Try this example link below to pre-fill inputs and see the calculation instantly.
💡 Example Calculations
Example 1 - Rectangle (living room floor)
A living room 8 m wide and 5 m long
1
Area = length × width = 8 × 5 = 40 square metres. This is how much flooring you need.
2
Perimeter = 2 × (8 + 5) = 2 × 13 = 26 m. This is the total length of skirting boards required.
Area = 40.0000 sq units | Perimeter = 26.0000 units
Try this example →Example 2 - Circle (circular garden bed, radius 7 m)
Circular garden bed with radius 7 metres
1
Area = π × 7² = 3.14159 × 49 = 153.94 sq m. This is the area of soil to be prepared.
2
Circumference = 2 × π × 7 = 43.98 m. This is the length of edging required around the bed.
Area = 153.9380 sq units | Circumference = 43.9823 units
Try this example →Example 3 - Triangle (roof cross-section)
Triangular roof cross-section with base 10 m and height 4 m
1
Area = 0.5 × base × height = 0.5 × 10 × 4 = 20 sq m. This is the cross-sectional area of the roof space.
Area = 20.0000 sq units
Try this example →Example 4 - Sector (90-degree pizza slice from a 10 m radius)
A 90-degree sector of a circle with radius 10 m
1
Convert angle: 90 degrees = 90 × π / 180 = 1.5708 radians.
2
Area = 0.5 × 10² × 1.5708 = 78.54 sq m. This is one quarter of the full circle area (π × 100 = 314.16).
3
Arc length = 10 × 1.5708 = 15.71 m.
Area = 78.5398 sq units | Arc Length = 15.7080 units
Try this example →Example 5 - Regular Hexagon (honeycomb cell, side 5 cm)
Regular hexagon with side length 5 cm
1
Area = (6 × 5²) / (4 × tan(180/6)) = 150 / (4 × tan(30°)) = 150 / (4 × 0.5774) = 64.95 sq cm.
2
Perimeter = 6 × 5 = 30 cm.
Area = 64.9519 sq units | Perimeter = 30.0000 units
Try this example →❓ Frequently Asked Questions
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 40 square metres. The perimeter is 2 times (l + w) = 26 m. A square is a special rectangle where l = w, giving area = side squared.
How do you calculate the area of a triangle from base and height?
Area of a triangle = half times base times height (A = 0.5 times b times h). The height must be perpendicular to the base, which means it forms a 90-degree angle. For a triangle with base 10 cm and height 6 cm: area = 0.5 times 10 times 6 = 30 square centimetres. If you know all three sides instead, use Heron's formula: area = square root of (s times (s minus a) times (s minus b) times (s minus c)), where s = (a + b + c) divided by 2.
How do you calculate the area of a circle?
Area = pi times radius squared (A = pi r squared). With pi approximately 3.14159, a circle of radius 7 m has area 153.94 square metres. The circumference is 2 times pi times r = 43.98 m. If you know the diameter d instead of the radius, use r = d divided by 2. Doubling the radius quadruples the area because area is proportional to r squared.
How do you calculate the area of a trapezoid?
Area of a trapezoid = half times (a plus b) times h, where a and b are the two parallel sides and h is the perpendicular height between them. For a trapezoid with parallel sides 6 m and 10 m and height 4 m: area = 0.5 times 16 times 4 = 32 square metres. The height must be perpendicular to both parallel sides, not the length of the slant sides.
What is the difference between area and perimeter?
Area measures the enclosed space inside a shape, expressed in square units (square metres, square feet). Perimeter measures the total length of the boundary around the shape, expressed in linear units (metres, feet). For a rectangle 4 m by 3 m: area = 12 square metres (enough to tile the floor) and perimeter = 14 m (enough to frame the edge). You need area for painting, flooring, and land calculation; you need perimeter for fencing, framing, and edging.
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 right angles, not the length of the slant side. A parallelogram with base 9 m and perpendicular height 4 m has area 36 square metres. A rectangle is a special parallelogram where the slant side equals the perpendicular height, making both formulas identical.
How do you calculate the area of an ellipse?
Area of an ellipse = pi times a times b, where a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest diameter). An ellipse with a = 8 cm and b = 5 cm has area 3.14159 times 8 times 5 = 125.66 square centimetres. The perimeter of an ellipse has no simple exact formula; this calculator uses the Ramanujan approximation, accurate to within 0.02% for most shapes.
How do you calculate the area of a sector of a circle?
Sector area = (theta divided by 360) times pi times r squared, where theta is the central angle in degrees. Equivalently, area = 0.5 times r squared times theta in radians. A 90-degree sector of radius 10 m has area (90/360) times pi times 100 = 78.54 square metres, which is exactly one quarter of the full circle. The arc length = (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 a regular hexagon (n = 6) with side 5 cm: area = (6 times 25) / (4 times tan(30 degrees)) = 150 / 2.309 = 64.95 square centimetres. The perimeter is n times s = 30 cm. As n increases, the polygon approaches a circle with the same circumradius.
What units should I use for area calculations?
This calculator is unit-agnostic. Enter all dimensions in the same unit (all metres, all centimetres, all feet, etc.) and the area result is in that unit squared (square metres, square centimetres, square feet). To convert: 1 square metre = 10.764 square feet; 1 square foot = 0.0929 square metres; 1 acre = 4,047 square metres; 1 hectare = 10,000 square metres. Always ensure consistency, since mixing metres and centimetres in the same calculation produces a wrong answer.
How does a sector compare to the full circle in area?
A sector's area is proportional to its central angle. A 360-degree sector equals the full circle. A 180-degree sector (semicircle) has exactly half the circle area. A 90-degree sector (quarter circle) has one quarter of the circle area. A 60-degree sector has one sixth of the circle area. The formula (theta / 360) times pi times r squared captures this linear proportionality between angle and area.
How do you find the area of an L-shaped or irregular room?
Divide the irregular shape into regular sub-shapes. For an L-shaped room, split it into two rectangles, calculate each rectangle's area using A = l times w, then add the results. For more complex shapes, keep subdividing into triangles and rectangles. Always measure dimensions at right angles. Alternatively, subtract: treat the shape as a large rectangle and subtract the missing corner rectangle. Both methods give the same total area.