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Radians ↔ Degrees Converter

Convert radians to degrees (and back) instantly. Supports π inputs like π/6 and shows both decimal and π-fraction forms (when possible).

Quick rule to remember

Degrees → Radians: multiply by π/180
Radians → Degrees: multiply by 180/π

Background

Degrees are common in geometry, while radians are common in calculus and trig identities. This converter helps you switch units fast — plus it recognizes the “nice angles” on the unit circle.

Convert

You can type pi or π (example: 3π/4).

Only used in Show both mode.

Rounding affects display only.

Example: 1.5708 rad → π/2

Normalization doesn’t change your original input — it just shows an equivalent angle that’s easier to use on the unit circle.

Chips prefill and calculate immediately.

Options

Result

No results yet. Enter a value and click Calculate.

How to use this converter

  • Choose a mode: Radians → Degrees, Degrees → Radians, or Show both.
  • Enter your value (supports π like 3π/4), then click Calculate.
  • Use Quick picks for common unit-circle angles.
  • Optional: turn on Normalize angle to see an equivalent angle in a standard range like [0°, 360°) or [−π, π).

How this converter works

  • It converts using the exact relationship π rad = 180°.
  • If your radian result is close to a “nice” multiple of π, the converter can show the π-fraction form.
  • If normalization is enabled, it adds or subtracts full turns (360° or 2π) to land in the chosen range.
  • It also recognizes common unit-circle angles, and shows the quadrant and reference angle.

Formula & Equation Used

Radians → Degrees: degrees = radians × (180/π)

Degrees → Radians: radians = degrees × (π/180)

Normalization idea: θ ≡ θ + 360°k or θ ≡ θ + 2πk for any integer k

Example Problem & Step-by-Step Solution

Example 1 — Convert 3π/4 to degrees

  1. Use degrees = radians × (180/π).
  2. (3π/4) × (180/π) = (3/4) × 180 = 135°.
  3. It’s a unit-circle angle in Quadrant II with reference angle 45°.

Example 2 — Convert 210° to radians (and normalize)

  1. Use radians = degrees × (π/180).
  2. 210 × (π/180) = (210/180)π = (7/6)π.
  3. So 210° = 7π/6 rad.
  4. Unit-circle insight: 210° is in Quadrant III with reference angle 30°.
  5. If you normalize to [−π, π): 7π/6 − 2π = −5π/6.

Example 3 — Convert −5π/6 to degrees (and normalize)

  1. Use degrees = radians × (180/π).
  2. (−5π/6) × (180/π) = −5 × 30 = −150°.
  3. So −5π/6 = −150°.
  4. If you normalize to [0°, 360°): −150° + 360° = 210°.
  5. Unit-circle insight: −150° (or 210°) is Quadrant III, reference angle 30°.

Frequently Asked Questions

Q: Why do radians show up so much in calculus?

Because many trig formulas (especially derivatives/integrals) work cleanly only when angles are measured in radians.

Q: What does “reference angle” mean?

It’s the acute angle between your terminal side and the x-axis. It helps you use unit-circle trig values quickly.

Q: Does normalization change my input?

No — it only shows an equivalent angle that lands in a standard range like [0°, 360°) or [−π, π).