Area of a square

How the Area Calculator Works

Select a geometric shape and enter its dimensions. The calculator applies the correct formula automatically and displays the result with the formula used. Supports 7 common shapes: square, rectangle, triangle, circle, trapezoid, parallelogram and rhombus.

Area Formulas - Complete Reference

Every 2D shape has a specific area formula. The table below shows what dimensions you need for each:

Shape	Formula	Dimensions	Example
Square	a^2	Side (a)	a=5 -> 25
Rectangle	a x b	Length (a), Width (b)	8x3 = 24
Triangle	(base x height) / 2	Base, Height	10x6/2 = 30
Circle	pi x r^2	Radius (r)	r=7 -> 153.94
Trapezoid	(a + b) x h / 2	Base 1, Base 2, Height	(6+10)x4/2 = 32
Parallelogram	base x height	Base, Height	12x5 = 60
Rhombus	(d1 x d2) / 2	Diagonal 1, Diagonal 2	10x8/2 = 40

Unit Conversion for Area

Area is always in square units. Converting between units requires squaring the linear conversion factor:

From	To	Multiply by
m2	cm2	10,000
m2	ft2	10.764
ft2	m2	0.0929
acres	m2	4,047
hectares	m2	10,000

Practical Examples

Example 1: Square with side 5 m - area = 5^2 = 25 m2

Example 2: Rectangle 8 x 3 cm - area = 8 x 3 = 24 cm2

Example 3: Triangle with base 10, height 6 - area = (10 x 6) / 2 = 30 sq. units

Example 4: Circle with radius 7 - area = pi x 49 = 153.94 sq. units

Example 5: Trapezoid with bases 6 and 10, height 4 - area = (6+10) x 4 / 2 = 32 sq. units

Example 6: Parallelogram base 12, height 5 - area = 12 x 5 = 60 sq. units

Example 7: Rhombus diagonals 10 and 8 - area = (10 x 8) / 2 = 40 sq. units

FAQ

What units does the calculator use?

The calculator works with any unit you enter. If dimensions are in centimeters, the area is in square centimeters (cm2). If in meters, the result is in square meters (m2). Just be consistent - do not mix cm and m in the same calculation.

How do I find the area of an irregular shape?

Break the irregular shape into simpler shapes (rectangles, triangles, circles), calculate each area separately, then add them together. For truly irregular shapes, methods like the shoelace formula (for polygons with known vertices) or numerical integration are needed.

What is the difference between area and perimeter?

Area measures the surface inside a shape (in square units). Perimeter measures the total length of the boundary (in linear units). A 5x3 rectangle has area 15 sq. units and perimeter 16 units. Two shapes can have the same perimeter but very different areas.

What is the height of a triangle?

The height (altitude) is the perpendicular distance from the base to the opposite vertex. It is NOT the length of a side (unless the triangle is right-angled and you use the two legs as base and height). For obtuse triangles, the height may fall outside the triangle.

Which dimensions are the diagonals of a rhombus?

The diagonals of a rhombus are the two lines connecting opposite corners. They always cross at right angles and bisect each other. Enter the full length of each diagonal. The order does not matter for the area calculation since multiplication is commutative.

How accurate is pi in circle calculations?

This calculator uses JavaScript's Math.PI which provides 15 decimal places of precision (3.141592653589793). For practical purposes this is more than sufficient. Even NASA uses only 15 digits of pi for interplanetary navigation calculations.

What is the difference between a parallelogram and a trapezoid?

A parallelogram has two pairs of parallel sides (opposite sides are equal and parallel). A trapezoid (trapezium in British English) has exactly one pair of parallel sides (the bases). Area formula differs: parallelogram uses base x height, trapezoid uses (base1 + base2) x height / 2.

Can I calculate the area of a semicircle or quarter circle?

Calculate the full circle area (pi x r^2), then divide by 2 for a semicircle or by 4 for a quarter circle. For a semicircle with radius 10: area = pi x 100 / 2 = 157.08 sq. units.

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