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Python - math.atan2() method example

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The math.atan2() function returns the angle in radians in the range -math.pi/2 to +math.pi/2 between the positive x-axis and the ray to the point (x, y) ‚Ȇ (0, 0).

import math

#                y    x         angle in radians
print(math.atan2(2,   4))     # 0.4636476090008061  <-   ~26.6 degrees
print(math.atan2(4,  -2))     # 2.0344439357957027  <-  ~116.6 degrees
print(math.atan2(-2, -4))     # -2.677945044588987  <- ~-153.4 degrees
print(math.atan2(-4,  2))     # -1.1071487177940904 <-  ~-63.4 degrees

atan2() method has been visualized on below image:

atan2(y, x) function visualization - Python math module.
Atan2(y, x) function visualization - Python math module.

1. Documentation

Syntax
math.atan2(y, x)
Parametersy, x - double values that are coordinates of the point.
Result

number value of the angle between two lines OP and OX in radians in the range -math.pi/2 to +math.pi/2.

Where:

  • O=(0, 0)¬†- intersection point of coordinate system axes,
  • P=(x, y)¬†- out point,
  • OX - positive part of x-axis.

If point is in the 1st (I) or 2nd (II) quadrant angle is measured in a counterclockwise direction.

If point is in the 3rd (III) or 4th (IV) quadrant angle is measured in a clockwise direction.

Note: angle arrows show measured angles for points located in different quadrants.

Description

atan2 is a method that takes two parameters and returns an approximation of the arctangent(y/x) function taking into account quadrants of a point location (P=(x, y)).

2. Working with degrees

import math


def calculate_angle(x, y):
    angle = math.atan2(x, y)
    return (180 / math.pi) * angle


#                     y    x       degrees
print(calculate_angle(2,   4))   # 26.56505117707799
print(calculate_angle(4,  -2))   # 116.56505117707799
print(calculate_angle(-2, -4))   # -153.434948822922
print(calculate_angle(-4,  2))   # -63.43494882292201

3.  Conversion to only clockwise angles in degrees

This section shows how to convert angles to clockwise angles (from 0 to 360 degrees).

import math


def calculate_angle(x, y):
    angle = math.atan2(x, y)

    if angle < 0:
        angle += 2 * math.pi
    return (180 / math.pi) * angle


#                     y    x        degrees
print(calculate_angle(2,   4))    # 26.56505117707799
print(calculate_angle(4,  -2))    # 116.56505117707799
print(calculate_angle(-2, -4))    # 206.565051177078
print(calculate_angle(-4,  2))    # 296.565051177078

4.  Conversion to only counterclockwise angles in degrees

This section shows how to convert angles to counterclockwise angles (from -360 to 0 degrees).

import math


def calculate_angle(x, y):
    angle = math.atan2(x, y)

    if angle > 0:
        angle -= 2 * math.pi
    return (180 / math.pi) * angle  # rad to deg conversion


#                     y   x        degrees
print(calculate_angle(2,   4))    # -333.434948822922
print(calculate_angle(4,  -2))    # -243.434948822922
print(calculate_angle(-2, -4))    # -153.434948822922
print(calculate_angle(-4,  2))    # -63.43494882292201

References

  1. atan2 - Wikipedia
  2. Inverse trigonometric functions - Wikipedia

Python - math module

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