Geometry
Sector area from the angle fraction
The wedge's share of the circle, taken straight from the angle as a fraction of a full turn.
The Formula
sector area = (angle / 360) x pi x r^2
The wedge's share of the circle, taken straight from the angle as a fraction of a full turn.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| angle | Central angle | degrees | The angle at the centre, in degrees. |
| r | Radius | any length unit | Distance from the centre to the arc. |
| A | Sector area | square length units | The area of the wedge. |
| 360 | Full turn | degrees | The degrees in one complete circle. |
What Each Symbol Means
angledegrees
Central angle
The angle at the centre, in degrees.
rany length unit
Radius
Distance from the centre to the arc.
Asquare length units
Sector area
The area of the wedge.
360degrees
Full turn
The degrees in one complete circle.
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 sector 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 Sector, filed under Math. Every number the guide produces comes from substituting into this one line.