Radians to Degrees Converter
To convert radians to degrees, multiply by 180/π (≈57.296°). To convert degrees to radians, multiply by π/180. For example, π/2 radians = 90°, and 180° = π radians.
Convert angles between radians and degrees, both directions, with the π-based steps shown.
How to use this calculator
Enter an angle value, pick the direction, and press Calculate. The converter applies the π-based factor and shows the substitution, so you see exactly where the π comes from instead of getting a bare decimal.
The two facts worth memorizing: π radians = 180°, so 1° = π/180 rad and 1 rad = 180/π ≈ 57.296°.
The converter shows both the exact pi-multiple form and the decimal, because teachers expect the exact form while applied work needs the decimal.
How it works
A full circle is 360° and also 2π radians, the same angle measured in two units. Dividing both sides: 180° = π rad. That single equation gives both directions:
Degrees → radians: multiply by π/180. So 90° = 90 × π/180 = π/2 ≈ 1.5708 rad.
Radians → degrees: multiply by 180/π. So π/4 rad = π/4 × 180/π = 45°.
The calculator shows the exact multiple-of-π form where it is clean (e.g. 180° = 1π rad) alongside the decimal.
Pro tips
Memorize the circle: 0° = 0, 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π. These seven cover 90% of problems. Negative angles: −90° = −π/2, the formulas handle signs naturally. Beyond 360°: 450° = 450 − 360 = 90° = π/2; subtract full turns first.
Worked example
Example: 60° to radians, and 2 rad to degrees
60° → rad: 60 × π ÷ 180 = π/3 ≈ 1.0472 rad.
2 rad → °: 2 × 180 ÷ π ≈ 114.59°.
Check: 1.0472 × 180/π = 60. ✓ Round-trip conversions must return the starting value.
More examples: 90° → π/2 ≈ 1.5708 rad; 1 rad → 57.2958°; 270° → 3π/2 ≈ 4.7124 rad.
Common mistakes
- Calculator in the wrong mode: the #1 trig error in history, computing sin(30) in radian mode gives −0.988 instead of 0.5. Convert first, then set the mode.
- Memorizing 57.3° without understanding: 1 rad ≈ 57.296° is a consequence of 180/π, not a definition, derive it when unsure.
- Mixing units inside one problem: pick one unit for the whole problem. Formulas in calculus assume radians.
- Forgetting π is a number: “π/3 radians” and “1.047 radians” are the same answer; the first is exact, the second is rounded.
When to use it
Trigonometry homework, physics (angular velocity is rad/s), programming (most math libraries use radians), and reading solutions that mix notations. For computing the trig ratios themselves, use the sin cos tan calculator; for length units, the unit converter.
Full walkthrough: wheel speed
A wheel spins at 3 rad/s – in degrees? 3 x 180 div pi = 171.887 deg/s. A 135-degree angle to radians: 135 x pi div 180 = 2.3562 rad (3pi/4 exact).
Key takeaway: 180 degrees equals pi radians. Multiply by pi/180 for radians, by 180/pi for degrees. For angles beyond one full turn, subtract multiples of 360 degrees (or 2 pi) first, then convert. Standard angles (30, 45, 60, 90 degrees) convert to clean pi-multiples worth memorizing. These four angles appear so often that recognizing them on sight repays the memorization.
Frequently asked questions
Multiply by 180/π (≈57.296). So 1 radian ≈ 57.296°, and π/2 radians = 90°. The converter above shows the substitution for any value.
Multiply by π/180 (≈0.01745). So 180° = π radians ≈ 3.1416 rad, and 90° = π/2 ≈ 1.5708 rad.
Radians make calculus clean: the derivative of sin(x) is cos(x) only when x is in radians. They also simplify arc-length (s = rθ) and sector-area formulas.
Yes, exactly. A full circle is 360° = 2π rad, so half a circle is 180° = π rad. Every conversion here is just scaling from that identity.
About 57.2958°. From 180/π. A handy check: π/2 rad ≈ 1.5708 × 57.2958 ≈ 90°.
π/4 ≈ 0.7854 rad. 45 × π/180 = π/4. One of the standard angles worth memorizing alongside 30° (π/6) and 60° (π/3).
Multiply by 180/π: 2.5 × 57.2958 ≈ 143.24°. Enter 2.5 with radians → degrees selected above to see the substitution steps.