About Radians (rad)

The radian (symbol: rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle; one radian is just under 57.3 degrees.

One radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Since the circumference of a circle is 2πr, there are 2π radians in a full circle (or 360 degrees).

Radians are extensively used in:

• Mathematics (calculus, trigonometry, geometry).
• Physics (angular velocity, angular frequency, rotational motion).
• Engineering and computer graphics.
• Navigation and astronomy (though degrees, arcminutes, and arcseconds are also common).

• 1 radian (rad) ≈ 57.2958 degrees (°)
• π radians = 180 degrees (°)
• 2π radians = 360 degrees (°) = 1 full circle/revolution/turn
• π/2 radians = 90 degrees (°) = 1 right angle = 1 quadrant
• 1 radian (rad) ≈ 63.662 gradians (gon)

Using radians simplifies many mathematical formulas, especially in calculus. For example, the derivative of sin(x) is cos(x) only when x is in radians. Radian measure is also more "natural" in geometric contexts involving circles and spheres.