Degrees to Radians Converter

A degrees-to-radians converter switches an angle between the two standard units used in mathematics, physics, and programming. Degrees split a full turn into 360 equal parts; radians measure an angle by the length of arc it cuts on a unit circle. Both describe the same rotation — they're just different scales, like inches versus centimeters.

The relationship is fixed and exact: 180° equals π radians, which means a full circle of 360° equals 2π radians ≈ 6.2832. This calculator does the conversion in both directions and, when the result lands on a recognizable fraction of π (like π/4 or 2π/3), shows that exact form alongside the decimal.

Convert 135° to radians:

• radians = 135 × π / 180 = 135π/180 = 3π/4
• Decimal: 3 × 3.14159 / 4 ≈ 2.3562 rad

Now convert 1 radian to degrees:

• degrees = 1 × 180 / π ≈ 57.2958°

And going the other way for a "round" radian value: π/3 in degrees = (π/3) × (180/π) = 180/3 = 60°. Notice how the π cancels — that's typical when the radian input is already a clean fraction of π.

• Calculus and physics — derivatives, integrals, and angular velocity formulas all assume radians.
• Programming — Math.sin, Math.cos and friends in JavaScript, Python, C, Java, and most languages take radian inputs.
• Reading textbook answers — if a problem gives an answer like π/6 and you're working in degrees, convert to compare.
• Engineering drawings vs. simulation code — the drawing might list 45°, but the simulation expects 0.7854 rad.
• Trigonometry homework — quickly check whether sin(π/4) and sin(45°) agree (they should both be ≈ 0.7071).

• Forgetting your calculator mode. A scientific calculator in radian mode evaluating sin(30) returns -0.988 instead of 0.5. Always check the DEG/RAD indicator.
• Mixing units mid-calculation. If a formula already has π in it, adding more degree-to-radian factors usually means converting twice.
• Treating π as exactly 3.14. That's only good to three digits. Use 3.14159 or, in code, the language's built-in (Math.PI, math.pi).
• Confusing radians with revolutions. One revolution is 2π radians, not 1 — don't drop the 2π factor in angular velocity.
• Negative angles. -90° = -π/2, not π/2. Direction matters; the calculator preserves the sign.