Geometry
Area from the radius
The standard form. Square the radius first, then multiply by pi.
The Formula
A = pi r^2
The standard form. Square the radius first, then multiply by pi.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r | Radius of the circle | length | Centre to edge. Half the diameter. |
| pi | Ratio of circumference to diameter | dimensionless | About 3.141592653589793; irrational, so always rounded in practice. |
| A | Enclosed area | square units | Grows fourfold when the radius doubles. |
What Each Symbol Means
rlength
Radius of the circle
Centre to edge. Half the diameter.
pidimensionless
Ratio of circumference to diameter
About 3.141592653589793; irrational, so always rounded in practice.
Asquare units
Enclosed area
Grows fourfold when the radius doubles.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the area of a circle page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Area Of A Circle, filed under Math. Every number the guide produces comes from substituting into this one line.