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Radian Measure

The proportionate Ratio between the length of an arc and its radius is used to define radian measure. In most areas of mathematics radian is considered as its standard unit for the measurements of the angle. “rad” is the symbol which is used for the representation of radian measures. For instance an angle of 1.5 radian can be written as “1.5 rad”.

One radian is equals to the angle subtended at the center of the Circle with help of an arc and it is equal in length with Radius of Circle. The magnitude in radian is an angle which equals to the ratio of radius of the circle to the Arc Length, such as θ (theta) = a / r; where ‘θ’ is subtended angle in the radian, ‘a’ is its arc length and ‘r’ is its radius. The magnitude in Radian Measure of the complete revolution i.e. 3600 will be the length of the whole circumference divided by the radius. This concludes 2∏ radian is equals to the 3600, which also means one radian will be equals to 180 / ∏ degrees.

Thus if we want to convert radian into degree we can multiply it by 1800 / ∏ or we can write it as:
Angle in degree = Angle in radian *(1800 / ∏).
We can even consider an example to understand it in a better way:
∏/2 rad = (∏/2) * (1800 / ∏) = 900,.


There are also several advantages in measuring in radians such as in Calculus and also other branches of mathematics which are beyond practical Geometry, radians are the pervasive measures of angle. 


Topics Covered in Radian Measure

Angle Measurement Units

Angle and angle measurement units play an important role in mathematics. An angle is a figure which is formed by two rays. The inclination of a Ray over the second ray makes a figure which is called as angle. An angle is also used in measuring the rotation of a ray around a fixed Point. These two rays which form the angle are called as sides of ray.  Ray which is...Read More

Converting Degrees to Radians

Before going in deep with converting degrees into Radians let's discuss degree and radians. Degrees are used to measure the direction and the size of an angle. Initially degree was defined in the Domain of 0 to 90 degrees but later on negative degrees also introduced. Degrees further divided into minutes and seconds. When a Ray completes 360 degrees it comp...Read More

Radian Measure of an Angle

Angle can be defined as inclination of one Ray over other ray. Angle is used in Geometry to describe inclination. There are two units which are used to measure angles; one is degree and second is radian. Generally we use unit degree to represent angle’s measurements. Let us now see Radian Measure of an angle.
Unit radian is used to denote measurement of angle...Read More

Radian Measure Chart

Angle is a quantity in mathematics which defines direction of any object or mathematical shape or figure. We consider two units for its measurement namely: degrees and the radians. Here we will discuss Radian Measure chart. In degrees angles can be written as 900, 450 and so on to 3600, that completes one cycle of all quadrants and with increase of angle above 3600,...Read More

Radian Measure of Central Angle

A central angle in a Circle can be defined as angle that subtends an arc of some arbitrary length. Total measure of central angle is 3600 i.e. 2∏ in radians. Radian measure of central angle is representation of angle as a multiple of ∏ i.e. N∏ where, N <= 2. To calculate central angle we need to find Radius of Circle and length of arc subtended by angle f...Read More

Applications of Radian Measures

Radian measure is the proportionate Ratio between the length of an arc and its radius. Some of the applications of Radian Measure are Arc Length, area of sector of a Circle, and angular velocity...Read More

Convert Radians to Degrees

Before going to discuss about how to convert radian to degree, let's discuss about radians and degrees. Radian is a Ratio of an arc of a Circle and its radius. This is a unit which is used in measuring the angle of a circle. Radian is represented by the symbol rad. For example we could write 1.6 radian as 1.6 rad.

Degree is also a unit which is used to m...Read More

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