Enter a value and instantly convert between degrees and radians — with the exact fraction of π shown, not just a decimal.
Degrees ↔ Radians Converter
How It’s Calculated
The conversion rests on one fact: 180° = π radians. To go from degrees to radians, multiply by π/180. To go from radians to degrees, multiply by 180/π. This tool also reduces the degrees-to-radians result to its simplest π fraction, since that’s the form used throughout the Trigonometric Functions chapter — not the decimal.
Reference Angles Worth Memorising
0° = 0 · 30° = π/6 · 45° = π/4 · 60° = π/3 · 90° = π/2 · 180° = π · 270° = 3π/2 · 360° = 2π
Frequently Asked Questions
Q: Why does mathematics use radians instead of degrees?
Radians make calculus on trigonometric functions work cleanly — derivatives and integrals of sin, cos and tan only take their simple standard forms when the angle is measured in radians.
Q: Is π radians the same as 180 degrees exactly?
Yes, always — that equivalence is the definition the whole conversion is built on.
Radian measure trips up more 1st PUC students than almost anything else in the Trigonometric Functions chapter. Read the full chapter guide →