Complete Lesson on Degrees to Radians

Degrees to Radians

Like every other quantity, angles likewise have systems for measurement. Degrees and Radians are two basic units for measuring the angles. There are various other devices to gauge the angles (like gradians and MRADs), yet you will only see these two units in secondary school. Let’s understand more about Degrees to Radians.

Understanding more about Degrees to Radians

One of the most popular units for gauging angles that many people recognize is the level is written ( °). The degree’s subunits are minutes and also secs. There are 360 levels, 180 levels for a half-circle (semi-circle), and even 90 levels for a right triangle or quarter circle in a full circle or one total rotation.

Degrees essentially specify instructions and angle size. Looking North means you are facing the direction of 0 levels. If you turn in the order of South, you are encountering the instructions of 90 levels. If you return to North after complete rotation, you have transformed through 360 levels. Usually, the anticlockwise instructions are thought about the positive. If you turn towards West from North, the angle will undoubtedly be either -90 levels of +270 degrees.

There is another system for measuring angles in geometry, referred to as the radian (Rad).

Currently, why do we need radians when we are presently comfortable with angles?

Most calculation in math includes numbers. Considering that degrees are not numbers, then the radians step is preferred and commonly called to fix troubles.

A fine example that resembles this principle is using decimals when we have percentages. Although we can reveal a rate with a number complied with by a % sign, we convert it to a decimal (or portion).

Made the principle of discovering angle by the size of the arc used long ago. The radian was presented a lot later on. Roger Cotes offered radians’ principle in 1714, yet he didn’t give it this name and called it around the step of an angle.

The term “radians” was first utilized in 1873. This name, later, got global attention as well as got permission.

In this article, you will discover just how to transform degrees to radians and the other way around (radians to levels). Let’s have a look.

How to convert degrees to radians?

To convert levels to radians, we multiply the given angle (in levels) by π/ 180.

Angle in levels ( °) x π/ 180 = Angle in radian (Rad).

Where, π = 22/7 or 3.14.


Convert the following angles from levels to radians.

0 °.

30 °

45 °. Service. Angle in levels( ° )x π/ 180 =Angle in radian (Rad).


0 ° x π/ 180.

= 0 Rad.

  1. 30 ° x π/ 180.

= π/ 6.

= 0.5 Rad.

  1. 45 ° x π/ 180.= π/ 4.= 0.785 Rad.

Solving the Degrees to Radians

To convert radians to levels, multiply the radian by 180/ π. So, the formula is provided by.

Angle in radian x 180/ π = Angle in degrees.


Convert the angle π/ 5 radians right into degrees.


Angle in radian x 180/ π = Angle in degrees.

By replacement.

π/ 5 x 180/ π = 36 levels.

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