Geometry
Sector area in radians
The same result with the angle in radians, which removes the division by 360.
The Formula
sector area = 0.5 x r^2 x theta, where theta = angle x pi / 180
The same result with the angle in radians, which removes the division by 360.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| theta | Angle in radians | radians | angle x pi / 180. |
| r | Radius | any length unit | Distance from the centre to the arc. |
| A | Sector area | square length units | The area of the wedge. |
| 0.5 | Half | unitless | The constant that makes the units come out right. |
What Each Symbol Means
thetaradians
Angle in radians
angle x pi / 180.
rany length unit
Radius
Distance from the centre to the arc.
Asquare length units
Sector area
The area of the wedge.
0.5unitless
Half
The constant that makes the units come out right.
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.