# Radians to Degrees Conversion Calculator

Home Converter

=

Enter either radian or degree and calculate the equivalent

## Formula to convert between Radians and Degrees

### How many Radians to Degrees?

• To convert degree to radians, multiply the degrees with π/180
• rad = π/180 * degree = 0.0174 * degrees, where π = 3.14
For example, to convert 90 degrees to radians, multiply degrees by π/180
radians = π/180 * 90 = 0.0174 * 90 = 1.57 radians
• Therefore, 90 degrees = 1.57 radians

• ### How many Degrees in a Radian?

• To convert radian to degrees, multiple radian value with 180 / π
• degree = 180 / π * radians = 57.32 * radians, where π = 3.14
For example, to convert 0.5 radians to degrees:
degrees = 180 / π * 0.5 = 57.32 * 0.5 = 28.65 degrees
• Therefore, 0.5 radians = 28.65 degrees.

## What are Radians and Degrees?

• Radians and Degrees are units of measurement of an angle. The SI Unit of an angle is 'Radians'.
• A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
• A degree is defined as the angle subtended at the center of a circle by an arc whose length is equal to 1/360th of the circumference of the circle. The full circle is 360 degrees
• A radian is a bigger unit than a degree. 1 radian is equal to 57.2958 degrees.
• Symbol of a degree is 'θ'. Symbol of a Radian is 'rad'
• Degrees are simpler and easy to visualize with a circle of 360 degrees. Degrees are used in any exterior activities such as surveying, construction work, drawing arcs and circles on paper using protractor and in maps and clocks
• Radians are more precise than degrees and used in calculations such as in trignometry, physics angular and rotational motion.

## How is Pi related to Radians and Degrees?

• The ratio of Circumference of a Circle to the Diameter (C/D) is a fixed value and it is always equal to 22/7 which is 3.14159. This fixed value for C/D = 3.141 holds good for any type of circle
• This ratio is defined as Pi represented by the symbol π which represents the value 3.14.
• We know that the diameter of any circle is twice of the radius.
Therefore, Circumference/Diameter = Circumference/(2 * Radius) = π
• Circumference = 2* π * Radius = 2πR
• As we know a Radian is defined as the angle formed by the arc of a circle with the radius.
A circumference is a full arc of 360 degrees. Therefore, radian of a full circle = circumference/radius = 2*π = 2 * 3.14 = 6.14 radians
• The angle formed by the full circle is 360 degrees. Therefore 360 degrees = 2π radians. which forms the basis for the conversion between the 2 units

Quarter Pi / 0.25 rad 45 degrees
Half Pi / 0.5 rad 90 degrees (Quarter Circle)
1 rad 180 degrees (Half Circle)
2 rad 360 degrees (One Circle)
3 rad 540 degrees (One and Half Circle)
4 rad 720 degrees (Two Circle)
5 rad 900 degrees (Two and Half Circle)
6 rad 1080 degrees (Three Circle)
7 rad 1260 degrees (Three and Half Circle)
8 rad 1440 degrees (Four Circle)
9 rad 1620 degrees (Four and Half Circle)
10 rad 1800 degrees (Five Circle)