Degree to Radian Measure

How to Convert Degrees to Radians

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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.

Degree to Radian Formula

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

Negative Degrees to Radian

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

Degrees to Radians Chart

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

Degree to radian of some common angles

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

Example 1: In a circle with center O, points A and B are two points on the circle. ∠AOB = 60°. Convert ∠AOB's angle measure from degrees to radians.

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.

Example 2: Katie bought a pizza from a nearby store. Her mother gave her a slice that measured (1/4)th of the complete pizza. Katie asked her mother about the central angle that her slice of pizza made. Can you help Katie find the measurement of the angle in degree and radian?

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.

Example 3: Convert the following degree measure to radian measure.

a) 20 degrees b) 28 degrees

Solution: To convert the following degree measure to radians we will use the following steps:

a) 20° × (π/180°) = π/9 Radians.
b) 28° × (π/180°) = 7π/45 Radians.

Frequently Asked Questions by Students

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°

* = 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.