Convert radian to degree

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.

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.

How to Convert radians to degrees

In multiplication to utilizing online instruments, there are further methods to convert radians to degrees:

  • Instructions: to modification rad to deg = rad * (180/π). Here π (pi) is the digit π reached by 3.14159, and 180 is the numeral of phases in a total circle.
  • Operating a plain: You might construct a plain including the elements of grades in rad and their connected values in deg. This can be practical if you conduct regular modifications of radians to degrees for straightforward steps.
  • Graphical radian to degree calculator technique: You can mark a circle, calculate the arc length in rad, and then relate it to the size of the entire process (360 deg).
1 rad
57.296 deg
1 deg
0.0175 rad
Example: convert 15 rad to deg:
15 rad
57.296 deg
859.44 deg

How many radian in a degree

1 deg includes about 0.01745 rad. Radians and degrees are two distinct elements of angle measure. Deg is commonly employed in the day-to-day and represents 1/360 of a full circle. On the further pointer, the rad is employed in calculation and explains the size of an angle via the ratio of the arc size of a process to its radius.

radian (rad)
degree (deg)
0.01 rad0.572957795 deg
0.1 rad5.729577951 deg
1 rad57.29577951 deg
2 rad114.591559 deg
3 rad171.8873385 deg
5 rad286.4788976 deg
10 rad572.9577951 deg
20 rad1145.91559 deg
50 rad2864.788976 deg
100 rad5729.577951 deg
1000 rad57295.77951 deg

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