1.5707963268
rad
0.5
π
0.25
turn
1.5707963268
rad
0.5
π
0.25
turn
The Degrees to Radians Converter converts angular measurements from degrees to radians with high precision. This is one of the most essential conversions in mathematics, physics, and programming, since most scientific calculations and programming language math libraries use radians as the standard unit for trigonometric functions.
The conversion formula is elegant and exact: radians = degrees × pi / 180. This relationship derives from the fact that a full circle contains 360 degrees and 2pi radians, so the conversion factor is 2pi/360 = pi/180. Common benchmark values include 90° = pi/2, 180° = pi, 270° = 3pi/2, and 360° = 2pi.
In physics, radians are essential for calculating angular velocity (rad/s), angular acceleration (rad/s²), torque calculations, and wave equations. The simplicity of radian measure means that the arc length formula reduces to s = r × theta (where theta is in radians), and calculus derivatives of trigonometric functions only produce clean results when angles are expressed in radians.
Our converter provides both the decimal radian value and the result expressed as a multiple of pi, making it easy to verify conversions and work with exact fractions in mathematical proofs.
The formula: radians = degrees × pi / 180. Equivalently, radians = degrees × 0.0174533.... The 'multiple of pi' output simply divides degrees by 180: pi_form = degrees / 180.
Key conversions: 30° = pi/6, 45° = pi/4, 60° = pi/3, 90° = pi/2, 180° = pi, 360° = 2pi. For programming, always convert degrees to radians before passing values to sin(), cos(), tan() functions.
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90° = pi/2 rad
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360° = 2pi rad
Radians = Degrees × pi / 180. This is derived from the fact that a full circle is 360° = 2pi radians.
45° = pi/4 radians ≈ 0.7854 radians.
180° = pi radians ≈ 3.14159265 radians.
Radians simplify mathematical formulas. The derivative of sin(x) equals cos(x) only when x is in radians. Arc length = radius × angle only works in radians.
1° = pi/180 ≈ 0.01745329 radians.
Use math.radians(degrees) or multiply by math.pi / 180. Both methods give identical results.
Multiply by Math.PI / 180. Example: var rad = degrees * Math.PI / 180.
Yes, negative radians indicate clockwise rotation (or equivalently, angles measured in the negative direction). -90° = -pi/2 radians.
The SI symbol is 'rad', though radians are dimensionless (they represent the ratio of arc length to radius). The 'rad' symbol is often omitted in mathematical contexts.
A full rotation is 2pi radians ≈ 6.28318 radians = 360 degrees.
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