About the Radians to Degrees Converter
This radians to degrees converter changes an angle in radians into degrees. You can type a decimal value such as 1.5 rad, or switch to "multiple of π" mode and enter a fraction like 3π/4 or π/6 exactly as it appears in a trigonometry problem. Alongside decimal degrees you get degrees-minutes-seconds, the angle normalised to 0–360°, gradians, turns and the radian value written as a fraction of π.
It is built for students working through the unit circle, programmers whose math libraries (JavaScript, Python, C) return radians, engineers reading rotational specs and anyone checking calculator output. Seeing both the exact π form and the decimal form helps you spot mistakes such as forgetting to switch a calculator out of radian mode.
Negative angles and angles bigger than a full turn are allowed: the main result keeps your sign and size, while the normalised angle shows the equivalent direction between 0° and 360°. For extremely large inputs (beyond about 10¹⁰ rad) the DMS and normalised lines are hidden, because floating-point arithmetic can no longer resolve the leftover fraction of a turn.
With the default inputs, the degrees is 57.29578 °. Change any value above to recalculate instantly.
How to use the radians to degrees converter
- 1Choose whether you are entering decimal radians or a multiple of π.
- 2Type the radian value, or the numerator and denominator of the π fraction.
- 3Read the angle in degrees at the top.
- 4Use the DMS, normalised, gradian or turn values if you need another format.
Formula and method
A full circle is 2π radians and also 360 degrees, so one radian equals 180/π ≈ 57.29578 degrees. Multiply any radian value by 180 and divide by π to get degrees. When the input is a multiple of π, the π cancels: 3π/4 × 180/π = 3 × 180 ÷ 4 = 135°.
Degrees-minutes-seconds splits the decimal part into sixtieths: minutes = fractional degrees × 60 and seconds = fractional minutes × 60, rounded here to 0.1″. Gradians divide a circle into 400 parts (degrees × 10/9), and turns are degrees ÷ 360. The normalised angle adds or removes whole turns to land between 0° and 360°.
- π
- Pi, ≈ 3.14159265
- radians
- Angle measured as arc length divided by radius
Worked examples
One radian
1 × 180 ÷ π = 57.2958°. The 0.2958° remainder is 17′ 44.8″, so one radian is 57° 17′ 44.8″.
3π/4 radians
With π in the input it cancels: 3 × 180 ÷ 4 = 135°, which is 2.3562 rad and three-eighths of a turn.
Negative angle from code
−1.5 × 57.2958 = −85.94°. Adding a full turn gives the same direction as 274.06°.
π/6 on the unit circle
180 ÷ 6 = 30°, the angle whose sine is exactly one half.
Frequently asked questions
How do I convert radians to degrees?+
Multiply the radian value by 180 and divide by π (about 57.2958). For example 2 rad × 57.2958 = 114.59°, and π/3 rad × 180/π = 60°.
How many degrees is one radian?+
One radian is 180/π ≈ 57.2958 degrees, or 57° 17′ 44.8″. It is the angle whose arc length equals the circle’s radius.
What is π/4 in degrees?+
π/4 radians is 45°. Other common values: π/6 = 30°, π/3 = 60°, π/2 = 90°, π = 180°, 3π/2 = 270° and 2π = 360°.
Why do calculators and programming languages use radians?+
Radians make calculus formulas simple — the derivative of sin x is cos x only when x is in radians — so math libraries such as JavaScript Math.sin and Python math.sin expect radians.
How do I convert degrees back to radians?+
Multiply degrees by π/180 (about 0.0174533). For example 90° × π/180 = π/2 ≈ 1.5708 rad. Use the degrees-to-radians converter for the reverse direction.