Degrees to radians conversion
Degrees to radians and back, with the exact π/180 factor, the notable values and the calculator’s angle mode.
Result
0.017 453 3 rad
- Formula
- 1 ° = 0.017 453 292 52 rad
Calculation, assumptions and sources
OverviewDegrees to radians and back, by the exact factor π/180 (one turn is 2π radians), as well as to gradians, turns, arcminutes and arcseconds, with the factor shown under the result.
Degrees to radians and back, by the exact factor π/180 (one turn is 2π radians), as well as to gradians, turns, arcminutes and arcseconds, with the factor shown under the result.
Method & formulasradians = degrees × π / 180
The π/180 factor is exact: the degree is 1/360 of a turn, the radian is the angle whose arc equals the radius, and the turn is 2π radians. Only the decimal writing of π is approximate; the calculation uses double precision.
- 30°
- π/6 ≈ 0.5236 rad; the sine is 1/2.
- 45°
- π/4 ≈ 0.7854 rad; sine and cosine equal, √2/2.
- 60°
- π/3 ≈ 1.0472 rad; the cosine is 1/2.
- 90°
- π/2 ≈ 1.5708 rad: the right angle.
- 180°
- π ≈ 3.1416 rad: the straight angle.
- 1 rad
- ≈ 57.296°: the angle whose arc equals the radius.
Validity domainA calculator set to the wrong angle mode returns a wrong result with no warning: sin(30) computed in radian mode gives −0.988 instead of 0.5.
A calculator set to the wrong angle mode returns a wrong result with no warning: sin(30) computed in radian mode gives −0.988 instead of 0.5. In degrees, sin(180) returns 0, which checks the mode.
Radians in calculusCalculus formulas assume angles in radians: the derivative of sin x is cos x, arc length is r × θ, and sin θ ≈ θ for small angles.
Calculus formulas assume angles in radians: the derivative of sin x is cos x, arc length is r × θ, and sin θ ≈ θ for small angles. The degree serves descriptive geometry and instrument readings.