diff --git a/lib/matplotlib/tests/test_colorbar.py b/lib/matplotlib/tests/test_colorbar.py
index 7f9b00b5e7c3..3932177565c5 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -570,3 +570,14 @@ def test_colorbar_label():
 
     cbar3 = fig.colorbar(im, orientation='horizontal', label='horizontal cbar')
     assert cbar3.ax.get_xlabel() == 'horizontal cbar'
+
+
+@pytest.mark.parametrize("clim", [(-20000, 20000), (-32768, 0)])
+def test_colorbar_int(clim):
+    # Check that we cast to float early enough to not
+    # overflow ``int16(20000) - int16(-20000)`` or
+    # run into ``abs(int16(-32768)) == -32768``.
+    fig, ax = plt.subplots()
+    im = ax.imshow([[*map(np.int16, clim)]])
+    fig.colorbar(im)
+    assert (im.norm.vmin, im.norm.vmax) == clim
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index ce517c1d00b7..3292340bf99d 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -2791,6 +2791,10 @@ def nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True):
         vmin, vmax = vmax, vmin
         swapped = True
 
+    # Expand vmin, vmax to float: if they were integer types, they can wrap
+    # around in abs (abs(np.int8(-128)) == -128) and vmax - vmin can overflow.
+    vmin, vmax = map(float, [vmin, vmax])
+
     maxabsvalue = max(abs(vmin), abs(vmax))
     if maxabsvalue < (1e6 / tiny) * np.finfo(float).tiny:
         vmin = -expander