How do I find the area of a circle?

Multiply pi by the radius squared. If you have the diameter, halve it first — squaring the diameter by mistake gives four times the true area, which is the single most common error with this formula.

What is the difference between an arc and a chord?

The arc is the curved edge of a slice; the chord is the straight line joining its two ends. The arc is always longer. This page gives the arc, which is what you need for edging, trim or a curved wall.

Is a bigger pizza better value?

Almost always, and by more than it looks. Area scales with the square of the radius, so an 18-inch pizza has 2.25 times the area of a 12-inch one. If it costs less than 2.25 times as much, it is the better buy.

Math

Circle Calculator

Enter a radius. Everything else about the circle follows from it.

The formula

area = π × radius²

circumference = 2 × π × radius

sector area = area × angle ÷ 360

arc length = circumference × angle ÷ 360

Worked example

A circle of radius 5, with a 90° quarter

area = π × 25 = 78.5398
circumference = 2 × π × 5 = 31.4159
quarter sector = 78.5398 ÷ 4 = 19.6350

Where this goes wrong

Expecting twice the radius to give twice the area

It gives four times. Area grows with the square of the radius, so a 12-inch pizza has 1.44 times the area of a 10-inch one, not 1.2 times — which is why the larger size is nearly always better value per square inch. The same trap turns up in pipes, tanks and circular slabs: doubling a pipe’s diameter quadruples what flows through its cross-section.

Questions

How do I find the area of a circle?: Multiply pi by the radius squared. If you have the diameter, halve it first — squaring the diameter by mistake gives four times the true area, which is the single most common error with this formula.
What is the difference between an arc and a chord?: The arc is the curved edge of a slice; the chord is the straight line joining its two ends. The arc is always longer. This page gives the arc, which is what you need for edging, trim or a curved wall.
Is a bigger pizza better value?: Almost always, and by more than it looks. Area scales with the square of the radius, so an 18-inch pizza has 2.25 times the area of a 12-inch one. If it costs less than 2.25 times as much, it is the better buy.