Area Calculator

About Area Calculator

Calculate the area and perimeter of six common 2D shapes: rectangle, triangle, circle, trapezoid, parallelogram, and ellipse. Select a shape tab, enter the dimensions, and see the result with the formula and step-by-step working shown instantly.

Area Formulas at a Glance

Shape	Area Formula	Perimeter Formula
Rectangle	A = l x w	P = 2(l + w)
Triangle	A = (1/2) x b x h	P = a + b + c
Circle	A = πr²	C = 2πr
Trapezoid	A = (1/2)(a + b) x h	P = a + b + c + d
Parallelogram	A = b x h	P = 2(a + b)
Ellipse	A = πab	P ≈ Ramanujan approximation

Worked Examples

Rectangle (l=12, w=8):

• Area = 12 x 8 = 96 square units
• Perimeter = 2(12 + 8) = 40 units

Triangle (base=10, height=6):

• Area = (1/2) x 10 x 6 = 30 square units

Trapezoid (parallel sides 8 and 14, height 5):

• Area = (1/2)(8 + 14) x 5 = (1/2)(22)(5) = 55 square units

Circle (r=7):

• Area = π x 49 = 153.94 square units
• Circumference = 2π x 7 = 43.98 units

Area Comparison Between Shapes

Different shapes enclose different areas for the same perimeter. The circle is the most efficient:

Shape	Perimeter = 40 units	Area	% of Circle
Circle	C = 40, r = 6.366	127.32	100%
Square	s = 10	100.00	78.5%
Equilateral triangle	s = 13.33	77.00	60.5%
Rectangle (2:1 ratio)	l=13.33, w=6.67	88.89	69.8%
Rectangle (4:1 ratio)	l=16, w=4	64.00	50.3%

The more "stretched" a rectangle becomes, the less area it encloses for the same perimeter. This is why efficient buildings tend toward square floor plans and why circular tanks and silos use minimal material for maximum volume.

Common Real-World Areas

Item	Shape	Dimensions	Area
A4 paper	Rectangle	21 x 29.7 cm	623.7 cm²
US Letter paper	Rectangle	8.5 x 11 in	93.5 in²
Football pitch (soccer)	Rectangle	105 x 68 m	7,140 m²
Tennis court	Rectangle	23.77 x 10.97 m	260.8 m²
Large pizza (14")	Circle	r = 17.78 cm	993 cm²
Basketball court	Rectangle	28.65 x 15.24 m	436.6 m²

Unit Conversion for Area

From	To	Multiply by
cm²	m²	0.0001
m²	ft²	10.764
ft²	m²	0.0929
in²	cm²	6.4516
acres	m²	4,046.86
hectares	m²	10,000

The Ellipse Perimeter Problem

Unlike every other shape on this list, there is no exact closed-form formula for the perimeter of an ellipse. This calculator uses Ramanujan's approximation (1914):

P ≈ π(3(a+b) - √((3a+b)(a+3b)))

Where a is the semi-major axis and b is the semi-minor axis. This approximation is accurate to within 0.04% for most practical ellipses. The area, however, is exact: A = πab.

For circle-specific calculations including arc length and sector area, the circumference calculator provides extra detail. For 3D shape volumes, the volume calculator covers spheres, cylinders, cones, and more.

All calculations run entirely in your browser. No data is sent to any server.