Python math.tau Constant

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The Python math.tau constant represents the mathematical constant τ (tau), which is approximately equal to 6.28318.

In general mathematics, τ (tau) is a special constant that represents the ratio of the circumference of a circle to the radius (τ = circumference / radius). This makes τ particularly useful when dealing with circles and angles, as it directly relates to the concept of radians and simplifies many formulas and calculations involving circles and trigonometry.

Syntax

Following is the basic syntax of the Python math.tau constant −

math.tau

Return Value

The constant returns the value of tau, which is 6.283185307179586.

Example 1

In the following example, we are using the math.tau constant to calculate the circumference of a circle, which is twice the value of π. We simply multiply the radius of the circle by τ to obtain the circumference −

import math
radius = 4
circumference = math.tau * radius
print("The circumference of the circle with radius", radius, "is:", circumference)

Output

Following is the output of the above code −

The circumference of the circle with radius 4 is: 25.132741228718345

Example 2

Here, we calculate the length of an arc using the τ constant. We multiply the radius of the circle by the angle (in radians) to obtain the arc length −

import math
radius = 8
angle_in_radians = math.pi / 3  # 60 degrees
arc_length = radius * angle_in_radians
print("The length of the arc with radius", radius, "and angle", math.degrees(angle_in_radians), "degrees is:", arc_length)

Output

The output obtained is as follows −

The length of the arc with radius 8 and angle 59.99999999999999 degrees is: 8.377580409572781

Example 3

In this example, we calculate the volume of a cylinder using the τ constant. We apply the formula for the volume of a cylinder, which is half of τ times the square of the radius times the height −

import math
radius = 5
height = 10
volume = math.tau * (radius ** 2) * height / 2
print("The volume of the cylinder with radius", radius, "and height", height, "is:", volume)

Output

The result produced is as follows −

The volume of the cylinder with radius 5 and height 10 is: 785.3981633974483

Example 4

Now, we are calculating the surface area of a sphere using the τ constant. We simply multiply the square of the radius by τ to obtain the surface area −

import math
radius = 7
surface_area = math.tau * (radius ** 2)
print("The surface area of the sphere with radius", radius, "is:", surface_area)

Output

We get the output as shown below −

The surface area of the sphere with radius 7 is: 307.8760800517997