About the Degrees to Radians
This degrees to radians converter changes any angle in degrees into radians two ways: as a decimal (0.7854 rad) and as an exact fraction of π (π/4), which is the form maths teachers and textbooks expect. It also shows the angle in turns (fractions of a full circle) and gradians, and tells you which quadrant the angle falls in.
It is useful for trigonometry and calculus homework, for programmers passing angles to Math.sin() or CSS rotate() functions that expect radians, and for engineers and game developers switching between a protractor-friendly unit and the one formulas use. Negative angles and angles larger than 360° work too.
The conversion is exact because a full circle is both 360° and 2π radians, so 1° = π/180 rad. The π-fraction is reduced to lowest terms for any angle with up to four decimal places; for other inputs the tool shows a decimal multiple of π instead.
With the default inputs, the radians is 0.785398 rad. Change any value above to recalculate instantly.
How to use the degrees to radians
- 1Type the angle in degrees (decimals and negatives are fine).
- 2Read the decimal radian value for calculators and code.
- 3Use the "in terms of π" result for exact maths answers.
- 4Check the table for the standard unit-circle angles.
Formula and method
A full circle measures 360 degrees or 2π radians, so one degree equals π/180 ≈ 0.0174533 radians. Multiply the angle by π and divide by 180 to convert. For the exact form, the ratio degrees/180 is reduced to lowest terms and written as a multiple of π — for example 135/180 = 3/4, so 135° = 3π/4.
Turns divide the angle by 360 (one revolution), and gradians multiply by 400/360 because a right angle is 100 gradians. The quadrant is found after reducing the angle to the range 0–360°.
- π
- Pi, ≈ 3.14159265
- rad
- Radian — the angle whose arc length equals the radius
- °
- Degree — 1/360 of a full circle
Worked examples
45 degrees
45 × π/180 = π/4 because 45/180 reduces to 1/4. As a decimal that is 3.14159 ÷ 4 ≈ 0.7854 rad, one-eighth of a full turn.
270 degrees
270/180 reduces to 3/2, so 270° = 3π/2 ≈ 4.7124 rad — three quarters of a circle, pointing straight down on the unit circle.
30 degrees
30/180 = 1/6, so 30° is π/6 ≈ 0.5236 rad. This is the angle whose sine is exactly 0.5.
A negative angle: −22.5°
−22.5/180 = −225/1800 = −1/8, so −22.5° = −π/8 ≈ −0.3927 rad. Negative angles are measured clockwise.
Frequently asked questions
How do you convert degrees to radians?+
Multiply the number of degrees by π and divide by 180. For example, 60° × π/180 = π/3 ≈ 1.0472 radians.
How many radians is 1 degree?+
One degree is π/180 radians, which is about 0.0174533 rad. Conversely, one radian is about 57.2958 degrees.
What is 180 degrees in radians?+
180 degrees is exactly π radians (≈ 3.14159). A full 360° circle is 2π radians and a right angle of 90° is π/2.
Why do calculators and programming languages use radians?+
Radians make calculus formulas clean — the derivative of sin(x) is cos(x) only when x is in radians — so JavaScript Math.sin, Python math.sin and Excel SIN all expect radians.
How do I write radians in terms of π?+
Divide the degrees by 180 and reduce the fraction, then attach π. For 150°, 150/180 = 5/6, so the answer is 5π/6.