Convert degree to radian

What is a degree?

Degrees are depicted by the symbol ° and utilized for the determination of angles. The word itself comes from Latin and designates the part of the scale. When we think about 360°, we imagine a full rotation and 90° are perceived as the right angle.

There is no one opinion on the question of why a degree was chosen as a unit and why it has such values. Most of the explanations refer to ancient times and systems that were utilized by our predecessors. Thus, the Persians used a calendar with 360 days and the similar system was also common in Babylon. Another interesting fact is that 1 deg is almost equal to 1 cm in the circle with a 57 cm radius.

Nowadays degrees are not a standard unit. However, they are widely used and have an easy relation to radians. Thus, one deg corresponds to π/180 radians.

What is a radians?

Humans were fascinated by circles since ancient times. Looking at the sun and the moon our predecessors wanted to create something similar. Thus, plates, baskets and wheels appeared.

A full rotation was given a value of 360 degrees. Later it was noted that the circumference and diameter of the circle always have the same ratio. This fact led to the introduction of π value, the calculation of the circumference as 2πr and the appearance of a radian.

Radians are modern standard units without dimensions. One rad corresponds to approximately 57 deg. The definition says that it is the angle on a circle, on which the arc lies the radius of that circle.

When you encounter an angle of 2 rad, then you should imagine one of 114 deg. If there is π rad, it means 180 deg. At last, a full circle corresponds to 2π radians.

How to Convert degrees to radians

A straightforward instruction is used to convert degrees to radians founded on the connection among deg and rad on an orbit:

  • The instruction is as ensues: rad = deg * (π/180)
  • Here, π (pi) is the numeral π, compared to 3.14159, and 180 is the digit of deg in a whole circle.
  • Illustration of modification degrees to radians: To correct an inclination of 45 deg to rad, do the following plan to remake degree to radian: radians = 45 * (π/180) ≈ 0.7854 radians.
  • Accordingly, an inclination of 45 degrees = about 0.7854 rad.
To convert degree to radian , the formula is used,
r = πd / 180
where the deg to rad value is substituted to get the answer from Angle Converter.
1 deg
0.0175 rad
1 rad
57.296 deg
Example: convert 15 deg to rad:
15 deg
0.0175 rad
0.2618 rad

How many degrees are in a radian

Remember that 1 rad includes around 57.2958 deg to transform degrees to radians. Degrees and radians are two distinct elements for calculating inclinations. Deg is typically operated daily and separates a circle into 360 similar components. The rad, on the other pointer, is utilized in computation and is connected to the size of the arc of a process.

degree (deg) radian (rad)
0.01 deg 0.000174533 rad
0.1 deg 0.001745329 rad
1 deg 0.017453293 rad
2 deg 0.034906585 rad
3 deg 0.052359878 rad
5 deg 0.087266463 rad
10 deg 0.174532925 rad
20 deg 0.34906585 rad
50 deg 0.872664626 rad
100 deg 1.745329252 rad
1000 deg 17.45329252 rad

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