How To: Degree to Radian Conversion

Technical drawings of circles
••• cookelma/iStock/Getty Images

The radian is an angular unit of measurement. Also a ratio, a given number of radians is the arc length associated with a given plane angle divided by the radius of the circle. Therefore, 1 radian (180 degrees/pi) is when an arc length of a circle defined by a central angle is equal to the circle's radius. Given this relationship, you can simply convert between degrees and radians.

    Determine the measurement of your angle in degrees. For example, suppose you have a 90-degree angle.

    Convert from degrees to radians by multiplying the number of degrees by pi/180. For a 90-degree angle, multiply 90 by pi/180 to get pi/2. Or, if you had an angle of 270 degrees, you would multiply 270 by pi/180 to get 3*pi/2 radians.

    Convert from radians to degrees by multiplying the number of radians by 180/pi. For example, in the example of pi/2 radians, you would multiply pi/2 by 180/pi to get 90 degrees. Or, if you had an angle of pi radians, you would multiply pi by 180/pi to get 180 degrees.

    Tips

    • If you forget whether to multiply by 180/pi or pi/180 to properly convert, memorize one of the relationships in the previous examples, pi radians = 180 degrees. Then check your work and see if your answer makes sense.

Related Articles

How to Calculate the Angle of a Sector
What is a Radian?
How to Find the Number of Sides of a Polygon
How to Use Trigonometry in Carpentry
How to Calculate Triangle Dimensions
How to Find the Cross Sectional Area of a Pipe
How to Convert Degrees into Inches or Millimeters
How to Solve a Hexagon
How to Find the Radius of a Sector
How to Calculate the Arc Length, Central Angle, and...
How to Find Degrees in Polygons
How to Calculate the Chord of a Circle
How to Convert Latitude & Longtitude Into Feet
How to Calculate the Linear Footage in a Radius
How to Calculate Arctan
What Is the Equator's Latitude?
How to Use the TI-84 Plus Calculator to Convert Sine,...
How to Calculate the Winter Solstice Sun Angle
How to Calculate Arc Area
How to Find a Missing Angle

Dont Go!

We Have More Great Sciencing Articles!