Radian measure is angle measured by arc length, and it relates to degrees by one fact: a straight angle is 180° and also π radians. These free printable worksheets ask a student to convert each way, leaving the radian answer in terms of π.
Every conversion is a single multiplication — by π/180 to go from degrees to radians, by 180/π to come back — and because the angles are the common multiples of 30° and 45°, the π cancels to a clean fraction. 90° is π/2, π/3 is 60°: no decimal appears, and none should.
Why this sheet works
Leaving π in the answer is the whole point. A student who writes 1.57 instead of π/2 has reached for a calculator the topic is built to do without, so the answers here stay exact — π/6, 3π/4, 2π — and the step-by-step walk shows the single multiplication that produced each one.
How this one works
One question from this sheet, worked through a step at a time.
Convert 5π/6 to degrees
5π/6×180/π
5π/6 in degrees=150°
π radians is 180°, so multiply radians by 180/π to get degrees.
