How many radians in a circle
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How to convert radians to degrees
1 radian to degree!
Radians
The angle made when the radius is wrapped round the circle:
1 Radian is about 57.2958 degrees . |
Why "57.2958..." degrees? We will see in a moment.
The Radian is a pure measure based on the Radius of the circle:
images/radian.js?mode=rad
Radian: the angle made when we take the radius
and wrap it round the circle.
Radians and Degrees
Let us see why 1 Radian is equal to 57.2958...
degrees:
images/radian.js?mode=circ
In a half circle there are π radians, which is also 180°
π radians =180°
So 1 radian = 180°/π
=57.2958...°
(approximately)
To go from radians to degrees: multiply by 180, divide by π
To go from degrees to radians: multiply by π, divide by 180
Here is a table of equivalent values:
| Degrees | Radians (exact) | Radians (approx) |
|---|---|---|
| 30° | π/6 | 0.524 |
| 45° | π/4 | 0.785 |
| 60° | π/3 | 1.047 |
| 90° | π/2 | 1.571 |
| 180° | π | 3.142 |
| 270° | 3π/2 | 4.712 |
| 360° | 2π | 6.283 |
Example: How Many Radians in a Full Circle?
Imagine you cut pieces of string exactly the length from the center to the circu
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