The circle constant (tau) is a geometric constant that appears in numerous math formulas relating to circles and angles. The numeric value of is defined as the length of the circumference of a circle divided by the length of its radius and is approximately equal to .
In the radian angle system the circle constant is equal to a full rotation in radains. Measured angles are represented as fractions of the circle constant . For example, shown below are two angles measured using the circle constant.
Here are some traditional geometric formulas in terms of the circle constant.
Calculate the area of a circle given the radius.
Calculate the circumference of a circle given the radius.
Calculate the volume of a sphere given the radius.
Calculate the volume of a cylinder given the radius and height.
The circle constant also appears in advanced applications such as the normal distribution, Fourier transform, and more.
Approximate the Circle ConstantWumbo (internal)
No, really, pi is wrong: The Tau ManifestoMichael Hartl