How do I calculate the area of a circle?

Multiply pi by the radius squared. Remember the radius is half the diameter; using the diameter gives four times the correct answer.

Is a 16-inch pizza twice a 12-inch one?

No, considerably less than twice. Area scales with the square of diameter, so a 16-inch pizza has about 1.8 times the area of a 12-inch.

What is the volume of a cone?

One third of pi times radius squared times height, exactly a third of the cylinder that would enclose it.

Why do my units come out wrong?

Almost always from mixing units before calculating. Convert everything to the same unit first, and remember areas come out squared and volumes cubed.

Geometry Calculator - Area, Perimeter and Volume

Geometry Calculator

Area, perimeter and volume formulas for the shapes that come up most often, whether you are tiling a floor, sizing a tank or checking homework.

Formula

Circle: A = πr², C = 2πr · Triangle: A = ½bh · Rectangle: A = lw

Pythagoras: a² + b² = c² for a right-angled triangle
Keep every measurement in the same unit before calculating

A circle of radius 5: A = π × 25 = 78.54, C = 2π × 5 = 31.42

Two-Dimensional Shapes

Rectangle: area = length × width; perimeter = 2(l + w)
Triangle: area = ½ × base × height
Circle: area = πr²; circumference = 2πr
Trapezium: area = ½(a + b) × height

The radius trips people up more than anything else: it is half the diameter. Using the diameter in πr² gives four times the true area.

Three-Dimensional Shapes

Cuboid: volume = l × w × h
Cylinder: volume = πr²h
Sphere: volume = (4/3)πr³; surface area = 4πr²
Cone: volume = (1/3)πr²h

A cone holds exactly one third of the cylinder that encloses it, and a pyramid one third of its prism — a relationship worth remembering because it saves looking anything up.

Scaling Is Not Linear

Doubling the dimensions of a shape does not double its area or volume.

Lengths scale by the factor
Areas scale by the factor squared
Volumes scale by the factor cubed

A pizza of twice the diameter has four times the area, which is why the larger size is usually far better value than it looks. And keep every measurement in the same unit before calculating: mixing centimetres with metres is the most frequent source of wrong answers.

Quick Reference

Area and perimeter for the common plane shapes.
Shape	Area	Perimeter
Rectangle	l × w	2(l + w)
Square	s²	4s
Triangle	½ × base × height	a + b + c
Circle	πr²	2πr
Trapezium	½(a + b) × h	sum of sides
Parallelogram	base × height	2(a + b)

Frequently Asked Questions

How do I calculate the area of a circle?: Multiply pi by the radius squared. Remember the radius is half the diameter; using the diameter gives four times the correct answer.
Is a 16-inch pizza twice a 12-inch one?: No, considerably less than twice. Area scales with the square of diameter, so a 16-inch pizza has about 1.8 times the area of a 12-inch.
What is the volume of a cone?: One third of pi times radius squared times height, exactly a third of the cylinder that would enclose it.
Why do my units come out wrong?: Almost always from mixing units before calculating. Convert everything to the same unit first, and remember areas come out squared and volumes cubed.