Converting 225 Degrees to Radians: How-To & Steps

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

How do you change from an angle measured in degrees to an angle measured in radians? Find out what a radian is and how to convert between the two units by reading this step by step lesson.

Steps to Solving the Problem

Olivia is fascinated by computer games and wants to go to college to become a game designer. She's joined an after school robotics club because she feels it will be good experience for her. Plus, it's a lot of fun. Today though, she's run into a problem when trying to get Steve, her robot, to dance.

When she types in 225 degrees into the software program hooked up to Steve she's expecting him to lift his arm until it goes all the way over his head and then behind him at an angle of 45 degrees to the ground. However, whenever she enters 225 into the input box, Steve spins his arm in a bunch of circles and ends up pointing in front himself at about a 20 degree angle. The move causes her to laugh, but it's not what she's trying to get him to do. She wonders what the problem might be.

Olivia consults the online manual for Steve's programming and finds the answer: She's been using degrees to enter the angle she wants his arm to point, but Steve's software only accepts radian measure for input. Radians are a way of measuring angles: one radian is the distance on the outside of the circle equal to the same length as the radius.

Radian Angle Measurement
radian measure

Now that she knows this, Olivia needs to convert her angle of 225 degrees into radians. Let's take a closer look at how to do this.

A full circle measures 2pi radians and also 360 degrees. This leads to a conversion factor of (pi/180) for converting from an angle measured in degrees to an angle measured in radians, as you can see from the equations below.

conversion factor

Now that we have the conversion factor, how does Olivia use the conversion factor to get from the 225 degrees that she has to the angle measurement in radians that she needs to get Steve to do his move? Simple, all she has to do is multiply the degrees she has by the conversion factor:

Convert 225 to radians

There is no pi button on her keyboard and when Olivia tries putting 1.25 into the program it still doesn't work - Steve's arm stopped before getting fully overhead.

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