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Use Axes.secondary_yaxis() when the right axis should show converted values of the same quantity as the left axis. Provide forward and inverse conversion functions, then set the logarithmic scale on the primary axis—and on the secondary axis too if you want logarithmic ticks there. For independent data series with separate scales, use twinx() instead.
Plot a converted secondary y-axis on a log scale
This runnable example plots distance in meters on the left and the corresponding values in kilometers on the right. The data are strictly positive so they can be displayed on logarithmic scales.
import matplotlib.pyplot as plt
import numpy as np
# Primary values are meters; secondary values are kilometers.
def meters_to_kilometers(meters):
return np.asarray(meters) / 1000
def kilometers_to_meters(kilometers):
return np.asarray(kilometers) * 1000
x = np.linspace(0, 10, 100)
y_meters = np.geomspace(100, 100_000, x.size)
fig, ax = plt.subplots()
ax.plot(x, y_meters)
ax.set_xlabel("x")
ax.set_ylabel("Distance (m)")
ax.set_yscale("log")
secax = ax.secondary_yaxis(
"right",
functions=(meters_to_kilometers, kilometers_to_meters),
)
secax.set_ylabel("Distance (km)")
secax.set_yscale("log")
plt.show()The first function converts primary-axis values to secondary-axis values; the second converts them back. The API requires both functions to accept NumPy arrays, and they should be mutually consistent across the displayed range. Matplotlib’s Axes.secondary_yaxis API reference documents the method and its requirements.
Why the secondary axis needs a conversion
secondary_yaxis("right", functions=(forward, inverse)) creates an axis whose values are derived from the parent axis through the supplied transformation. It is intended for alternate units or representations of the same quantity, not for plotting another dataset. Its limits follow the parent through the conversion; to change the displayed range, adjust the primary axis limits rather than treating the secondary axis as independently scaled.
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The secondary axis is an overlaid axis, not a data-bearing plotting area. Keep plotting calls on the parent axes. A positive unit conversion such as meters to kilometers preserves positivity, which is necessary for a logarithmic display.
Choose where to apply the logarithmic scale
Use ax.set_yscale("log") to make the primary y-axis logarithmic. Matplotlib uses base 10 by default; pass a different base to set_yscale if another logarithm base is needed. The Matplotlib log-scale guide documents the scale options and how nonpositive values are handled.
To show logarithmic ticks on the right as well, call secax.set_yscale("log"). If you omit that call, the secondary axis does not explicitly receive a logarithmic scale setting. Matplotlib’s secondary-axis gallery example demonstrates a logarithmic parent axis and a child axis that is also made logarithmic.
Check the domain of the data and conversion
Nonpositive values cannot be displayed on a logarithmic scale. Matplotlib masks or clips such values, depending on the configured behavior; choose handling that matches what the data mean rather than silently changing values. Also check the conversion’s output: if it can produce zero or negative values, those values cannot appear on a logarithmic secondary axis.
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If the right axis represents a different quantity or an independent dataset, use a twinned axis such as ax.twinx() rather than supplying a conversion. A twin can plot a separate series and use its own y scale. Label both axes and the plotted series clearly so readers do not mistake the scales for two units of one quantity. Matplotlib distinguishes transformed secondary axes from plots using different scales in its secondary-axis gallery.
Version note
The API reference labels secondary_yaxis experimental as of Matplotlib 3.1 and warns that the API may change. Check the documentation for the Matplotlib version used by your environment when maintaining long-lived code.
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