Use Axes.secondary_yaxis() when the right-hand axis is a conversion of the left-hand axis, such as meters to kilometers. Provide forward and inverse conversion functions, then set the logarithmic scale on the parent axis and, if you want logarithmic tick spacing on the right, on the secondary axis too. For a separate dataset with its own scale, use twinx() instead.
Plot a converted secondary y-axis on a logarithmic scale
This runnable example plots distance in meters on the left and the equivalent distance in kilometers on the right. The values are strictly positive so they can be shown 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()How the conversion pair works
The first function in functions=(forward, inverse) converts values from the parent axis into the secondary axis’s units; the second converts them back. Here, meters become kilometers and kilometers become meters. Matplotlib requires both functions to accept NumPy arrays, so np.asarray() makes the arithmetic work for array input. The functions need to be mutually consistent across the displayed range. See the official Axes.secondary_yaxis API reference.
Why set the scale on both axes?
ax.set_yscale("log") makes the parent y-axis logarithmic; base 10 is the default, and the base parameter can select another base. Set secax.set_yscale("log") as well when you want logarithmic ticks on the right-hand axis. The Matplotlib log-scale guide documents the scale and its treatment of nonpositive values.
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Keep all displayed values positive
Nonpositive values cannot be displayed on a logarithmic scale. Matplotlib documents masking or clipping such values, but neither should be used as a substitute for deciding what those values mean in your data. Check the plotted data and any converted values; if a conversion produces zero or a negative result, that value cannot appear on the logarithmic secondary axis. For meters-to-kilometers, positive inputs remain positive.
Choose the axis type that matches the data
| What the right axis represents | Use | What it means |
|---|---|---|
| A converted version of the left-axis quantity, such as meters and kilometers | secondary_yaxis() with forward and inverse functions |
The secondary limits are derived from the parent limits through the conversion; this axis is not intended to hold a separate plotted dataset. |
| A distinct series with its own independent y scale | twinx() |
The axes can show different data and scales. Label them clearly so the right-hand scale is not mistaken for a unit conversion. |
Matplotlib’s secondary-axis gallery illustrates transformed axes and points to different-scale plotting as a separate use case. Do not call plotting methods on the secondary axis: plot the data on the parent axis and use the secondary axis to show its transformed values.
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Control the range through the parent axis
The secondary axis’s limits are linked to the parent through the conversion rather than controlled as an independent range. To change the visible range, set the parent axis limits, for example with ax.set_ylim(lower, upper), using positive bounds for a logarithmic axis.
Version note
The Matplotlib API reference labels secondary_yaxis() experimental and notes that the API may change. The stable API and log-scale documentation identify Matplotlib 3.11.2, while a versioned example for 3.11.0 shows a logarithmic parent and child axis. If maintaining code across releases, check the documentation for the Matplotlib version in your environment.
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