diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0583fec45c..ea837e3d0b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,9 +5,9 @@ This project adheres to [Semantic Versioning](http://semver.org/).
 ## Unreleased
 
 ### Fixed
-- Fix concurrent first access to lazily initialized graph object properties, which could raise `ValueError("Invalid value")` [[#3441](https://github.com/plotly/plotly.py/issues/3441)], with thanks to @hb1915 for the contribution!
-- Fix `px.sunburst`, `px.treemap` and `px.icicle` listing sectors in a different order on every run when `path` is used with a Polars DataFrame; sectors now follow their order of first appearance for all dataframe backends [[#5765](https://github.com/plotly/plotly.py/issues/5765)], with thanks to @Irahan2 for the contribution!
-
+- Fix concurrent first access to lazily initialized graph object properties, which could raise `ValueError("Invalid value")` [[#5691](https://github.com/plotly/plotly.py/pull/5691)], with thanks to @hb1915 for the contribution!
+- Fix `mpl_to_plotly` crashing on touching bars (such as `plt.hist`) due to floating-point noise producing negative `bargap` values by clamping `bargap` to `[0, 1]` [[#5696](https://github.com/plotly/plotly.py/pull/5696)], with thanks to @robertoffmoura for the contribution!
+- Fix `px.sunburst`, `px.treemap` and `px.icicle` listing sectors in a different order on every run when `path` is used with a Polars DataFrame; sectors now follow their order of first appearance for all dataframe backends [[#5766](https://github.com/plotly/plotly.py/pull/5766)], with thanks to @Irahan2 for the contribution!
 
 ## [7.1.0] - 2026-09-15
 
diff --git a/plotly/matplotlylib/mpltools.py b/plotly/matplotlylib/mpltools.py
index ad01b37520..e1198c9792 100644
--- a/plotly/matplotlylib/mpltools.py
+++ b/plotly/matplotlylib/mpltools.py
@@ -269,7 +269,13 @@ def get_bar_gap(bar_starts, bar_ends, tol=1e-10):
         gap0 = gaps[0]
         uniform = all([abs(gap0 - gap) < tol for gap in gaps])
         if uniform:
-            return gap0
+            # Plotly's `bargap` is a fraction of the distance between bar positions, not a gap in data units
+            # so we need to normalize `gap0` with `bar_delta`
+            bar_delta = bar_starts[1] - bar_starts[0]
+            if bar_delta <= 0:
+                return None
+            # Clamp to guard against floating point noise, such as -8.9e-16 for touching bars
+            return min(max(gap0 / bar_delta, 0.0), 1.0)
 
 
 def convert_rgba_array(color_list):
diff --git a/plotly/matplotlylib/tests/test_renderer.py b/plotly/matplotlylib/tests/test_renderer.py
index 18ce2d02b3..02dd6cf34a 100644
--- a/plotly/matplotlylib/tests/test_renderer.py
+++ b/plotly/matplotlylib/tests/test_renderer.py
@@ -235,6 +235,21 @@ def test_semitransparent_axes_background_preserved():
     assert plotly_fig.layout.plot_bgcolor == "rgba(26, 51, 76, 0.4)"
 
 
+def test_histogram_converts():
+    """Histograms must convert without error and keep bargap in plotly's
+    valid [0, 1] range; get_bar_gap can return a gap with floating point
+    noise for touching bars, which plotly rejects."""
+    # Seed 0 makes the first gap slightly negative (-4.4e-16)
+    rng = np.random.RandomState(0)
+    fig, ax = plt.subplots()
+    ax.hist(rng.randn(10000), 30)
+
+    plotly_fig = tls.mpl_to_plotly(fig)
+
+    assert len(plotly_fig.data) == 1
+    assert plotly_fig.layout.bargap == 0
+
+
 def test_line_color_is_valid_plotly_color():
     """Converted line colors are valid plotly color strings: plotly rejects
     a space between 'rgba' and the opening parenthesis."""