How to set the Y-axis in radians in a Python plot?

To set the Y-axis in radians in a Python plot, we need to customize the axis ticks and labels to display radian values like ?/2, ?/4, etc. This is commonly needed when plotting trigonometric functions.

Steps to Set Y-axis in Radians

• Create data points using NumPy
• Plot the data using matplotlib
• Define custom tick positions in radian units
• Set custom tick labels using LaTeX formatting for fractions
• Apply the ticks and labels using set_yticks() and set_yticklabels()

Example

Let's plot the arctangent function and set its Y-axis in radians ?

import matplotlib.pyplot as plt
import numpy as np

# Set figure size
plt.rcParams["figure.figsize"] = [7.50, 3.50]
plt.rcParams["figure.autolayout"] = True

# Create data points
x = np.arange(-10.0, 10.0, 0.1)
y = np.arctan(x)

# Create figure and plot
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, y)

# Define radian unit and tick positions
unit = 0.25
y_tick = np.arange(-0.5, 0.5 + unit, unit)

# Custom labels in radian format
y_label = [r"$-\frac{\pi}{2}$", r"$-\frac{\pi}{4}$", r"$0$", r"$+\frac{\pi}{4}$", r"$+\frac{\pi}{2}$"]

# Set custom ticks and labels
ax.set_yticks(y_tick * np.pi)
ax.set_yticklabels(y_label, fontsize=10)

# Add labels for clarity
ax.set_xlabel('X values')
ax.set_ylabel('Y values (radians)')
ax.set_title('Arctangent Function with Y-axis in Radians')

plt.show()

Key Components

Tick Positions

The y_tick array defines where ticks appear on the Y-axis. Multiplying by np.pi converts to radian values ?

import numpy as np

unit = 0.25
y_tick = np.arange(-0.5, 0.5 + unit, unit)
print("Tick positions:", y_tick)
print("Radian positions:", y_tick * np.pi)

Tick positions: [-0.5  -0.25  0.    0.25  0.5 ]
Radian positions: [-1.57079633 -0.78539816  0.          0.78539816  1.57079633]

LaTeX Formatting

The labels use LaTeX formatting to display mathematical fractions properly ?

# Examples of LaTeX radian labels
labels = [
    r"$-\frac{\pi}{2}$",    # -?/2
    r"$-\frac{\pi}{4}$",    # -?/4  
    r"$0$",                 # 0
    r"$\frac{\pi}{4}$",     # ?/4
    r"$\frac{\pi}{2}$"      # ?/2
]

for label in labels:
    print(f"Label: {label}")

Label: $-\frac{\pi}{2}$
Label: $-\frac{\pi}{4}$
Label: $0$
Label: $\frac{\pi}{4}$
Label: $\frac{\pi}{2}$

Complete Example with Sine Function

Here's another example using a sine function with radian labeling ?

import matplotlib.pyplot as plt
import numpy as np

# Create data
x = np.linspace(-2*np.pi, 2*np.pi, 100)
y = np.sin(x)

# Create plot
fig, ax = plt.subplots(figsize=(8, 4))
ax.plot(x, y)

# Set Y-axis in radian-like fractions
y_ticks = [-1, -0.5, 0, 0.5, 1]
y_labels = [r"$-1$", r"$-\frac{1}{2}$", r"$0$", r"$\frac{1}{2}$", r"$1$"]

ax.set_yticks(y_ticks)
ax.set_yticklabels(y_labels)

# Set X-axis in radians
x_ticks = [-2*np.pi, -np.pi, 0, np.pi, 2*np.pi]
x_labels = [r"$-2\pi$", r"$-\pi$", r"$0$", r"$\pi$", r"$2\pi$"]

ax.set_xticks(x_ticks)
ax.set_xticklabels(x_labels)

ax.grid(True, alpha=0.3)
ax.set_title('Sine Function with Radian Axes')

plt.show()

Conclusion

Setting Y-axis in radians requires defining custom tick positions and using LaTeX-formatted labels with set_yticks() and set_yticklabels(). This technique is essential for displaying trigonometric functions with proper mathematical notation.