How many radians are in a full circle?

• A. 2π
• B. π
• C. π/2
• D. 3π

Answer: (A)

Radians measure an angle by comparing the length of the intercepted arc to the circle’s radius. One radian is the angle whose arc length equals the radius. For a full circle, the intercepted arc is the circumference, which is 2πr. Dividing by the radius r gives 2π radians for a complete rotation. Equivalently, π radians corresponds to 180 degrees, so a full 360-degree turn is 2π radians. The other values match smaller or larger rotations: π is a straight angle (180°), π/2 is a quarter turn (90°), and 3π is 540°, which is more than a full circle. Therefore, the full circle equals 2π radians.