Converting angles in geometry from degrees to radians is a common practice. Measurement units for angles are the same as those for quantities. Degrees and radians are the standard units of measurement for angles. Since radians are more often used to measure angles than degrees, understanding how to convert degrees to radians is critical. The radian measure may be used to calculate the area of a sector of a circle, the length of an arc, and the speed of an object's rotation. When working with circular pathways, radians are the most appropriate unit of measurement. Before doing any computations, we should convert any angles given in degrees to radians, regardless of how they appear in the issue statement.
If you want to go from one unit of measurement to another, you may use this formula to convert degrees to radians. In order to convert degrees to radians, we double the angle by /180.
Radians = Degrees × π / 180
To convert a negative degree back to its original form, the same procedure that we used for positive degrees must be followed. To get the radian angle, multiply the degree value by /180. Suppose, -180 degrees has to be converted into radian, then,
Radian = (π/180) x (degrees)
Radian = (π/180) x (-180°)
Angle in radian = – π
Angle in Degrees |
Angle in Radians |
0° |
0 |
30° |
π/6 = 0.524 Rad |
45° |
π/4 = 0.785 Rad |
60° |
π/3 = 1.047 Rad |
90° |
π/2 = 1.571 Rad |
120° |
2π/3 = 2.094 Rad |
150° |
5π/6 = 2.618 Rad |
180° |
π = 3.14 Rad |
210° |
7π/6 = 3.665 Rad |
270° |
3π/2 = 4.713 Rad |
360° |
2π = 6.283 Rad |
Turns |
Radian Measure |
Degree Measure |
0 turn |
0 rad |
0° |
1/24 turn |
π/12 rad |
15° |
1/16 turn |
π/8 rad |
22.5° |
1/12 turn |
π/6 |
30° |
1/10 turn |
π/5 rad |
36° |
⅛ turn |
π/4 rad |
45° |
1/2π turn |
1 rad |
57.3° |
⅙ turn |
π/3 rad |
60° |
⅕ turn |
2π/5 rad |
72° |
¼ turn |
π/2 rad |
90° |
⅓ turn |
2π/3 rad |
120° |
⅖ turn |
4π/5 rad |
144° |
½ turn |
π rad |
180° |
¾ turn |
3π/2 rad |
270° |
1 turn |
2π rad |
360° |
Degrees to Radians Examples
Solution:
We have, ∠AOB = 60°.
Degrees to radians conversion formula is given as (Degrees × π)/180°
Thus converting the given angle we get,
∠AOB in Radians = ∠AOB in degrees × (π/180°)
∠AOB in Radians = 60° × (π/180°)
∠AOB in Radians = π/3
Answer: ∠AOB = π/3 rad.
Solution:
Here, the portion Katie got = (1/4)th of the complete pizza. Since the shape of a pizza is circular, and the angle for a complete circle = 360°, thus we can conclude that:
Angle for the complete pizza = 360°
The angle for the (1/4)th slice = 360°/4 = 90°
We know,
The value of this angle in radians = value in degrees × (π/180°)
= 90° × (π/180°) = π/2 rad
Answer: The angle of Katie's slice in degrees is 90°, and when it is converted from degrees to radians, its measure is π/2 rad.
Solution: To convert the following degree measure to radians we will use the following steps:
Radians may be calculated by taking the reciprocal of the square root of the degree
In order to convert degrees to radians, we must multiply the supplied angle (which is in degrees) by /180 degrees. Radians are calculated by multiplying degrees by a factor of 180°.
Degrees To Radians Formula: What Is It?
The formula for converting a given angle's degree measure to radians equivalent is known as the "conversion factor." As a general rule, degrees to radians equals degrees divided by 180° = radians.
30 degrees to radians conversion is what I'm looking for.
Using the formula Radians = Degrees /180°, we must first convert the provided degrees (30°) into radians using the formula. Radians = 30° /180° = /6 rad. As a result, 30 degrees may be expressed as a fraction of a degree.
180 degrees is equivalent to how many pi radians?
A 360-degree counterclockwise rotation of an XY plane is equivalent to 2 (in radians) (in degrees). As a result, we may say:
= 2 = 360°
Or
* = 180o
This means that the value of pi is equal to 180
One degree is equal to how many radians?
0.0174533 radians is equivalent to one degree of angle.
One radian is equivalent to how many degrees?
57.2958 degrees is the value of one radian.
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