Degrees to Radians Calculator
Convert degrees to radians or radians to degrees, with the answer also expressed as a clean multiple of π.
How it works
radians = degrees × π ÷ 180 · degrees = radians × 180 ÷ π
A radian is the angle that wraps one radius-length of arc around the circle, and there are exactly 2π radians in a full 360° turn. That makes the conversion a single scale factor: π ÷ 180 going from degrees to radians, or 180 ÷ π going back. Radians are the natural unit for calculus and physics because they make arc length and angular speed formulas drop the extra constants.
Worked example
180°: multiply by π ÷ 180 to get 180 × π ÷ 180 = π ≈ 3.141593 radians, shown as 1.0000 π. Reversing it, π radians × 180 ÷ π = 180°, confirming a straight angle either way.
Sources: Radian — Wikipedia
Frequently asked questions
Why use radians instead of degrees?
In radians, arc length is simply r × θ and the derivative of sin θ is cos θ with no conversion factor. Degrees are a human convention; radians are the unit the math itself prefers, so calculus and physics default to them.
How many degrees is one radian?
About 57.2958° (180 ÷ π). One full circle is 2π ≈ 6.2832 radians, a right angle is π ÷ 2 ≈ 1.5708 radians, and a straight angle is π radians.
What does the multiple of π mean?
Many common angles are neat fractions of π: 90° = 0.5 π, 60° = 0.3333 π, 45° = 0.25 π. Expressing the answer this way keeps it exact and easy to recognise instead of a long decimal.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.