Degrees to radians converter
Convert between degrees and radians, showing the result both as a decimal and as an exact multiple of pi.
How it works
A degree is an arbitrary unit — someone decided a full turn should be cut into 360 parts, and 360 was chosen because it divides so cleanly. A radian is not arbitrary at all. It is the angle you get when the arc you have walked around a circle is exactly as long as its radius, which means it is defined by the circle itself rather than by a convention. Since the whole circumference is 2π radii long, a full turn is 2π radians, a half turn is π, and the conversion factor π/180 is just that relationship rearranged. This is why the exact form above matters more than the decimal: 45° is precisely π/4, and 0.7853981634 is a rounded shadow of that fact. It is also why calculus and physics work in radians throughout — the derivative of sin(x) is only cos(x) when x is measured this way, and in degrees an awkward π/180 turns up in every result.