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.
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 deg0.000174533 rad
0.1 deg0.001745329 rad
1 deg0.017453293 rad
2 deg0.034906585 rad
3 deg0.052359878 rad
5 deg0.087266463 rad
10 deg0.174532925 rad
20 deg0.34906585 rad
50 deg0.872664626 rad
100 deg1.745329252 rad
1000 deg17.45329252 rad

Popular Unit Conversions Angel

The most used and popular units of angel conversions are presented for quick and free access.

grad to deg
OneConvert Logotype

OneConvert - online calculator and file converter. Provides free unit conversion, convert PDF files, and other documents to help you solve problems of all types.

  • Navigation

    HomeUnit ConvertersContact Us

Share us

2023 OneConvert
  • Privacy Policy
  • Terms of Use
  • Cookie Policy
  • DMCA