diff --git a/src/math/transform.cpp b/src/math/transform.cpp
index e98bff1..43fb93e 100644
--- a/src/math/transform.cpp
+++ b/src/math/transform.cpp
@@ -15,6 +15,26 @@ void axis_ends(Range r, bool log, f64& lo, f64& hi) noexcept {
   }
 }
 
+/// Scale mapping `[lo,hi]` (transform space, already widened by `axis_ends`)
+/// onto the pixel interval `[p0,p1]`.
+///
+/// A collapsed pixel span (`|p1 - p0| <= kMinPixelSpan`, e.g. a zero-height
+/// panel or an untouched layout) would yield a zero scale, so `to_data_*` would
+/// divide by zero and return NaN or +/-inf. Instead the span is substituted by
+/// the unit span `p0 -> p0 + 1`: the scale is then finite and non-zero and the
+/// mapping stays invertible (`to_data_x(to_screen_x(v)) == v`), the axis simply
+/// occupying one pixel rather than none. Non-collapsed spans are used verbatim,
+/// so ordinary ranges are unaffected.
+f64 axis_scale(f64 lo, f64 hi, f64 p0, f64 p1) noexcept {
+  /// Pixel coordinates in this library are O(1e3), so 1e-12 is
+  /// indistinguishable from zero while staying far below any span a real
+  /// viewport can produce.
+  constexpr f64 kMinPixelSpan = 1e-12;
+  const f64 span = p1 - p0;
+  const f64 effective_span = std::fabs(span) <= kMinPixelSpan ? 1.0 : span;
+  return effective_span / (hi - lo);
+}
+
 }  // namespace
 
 f64 Transform::log10_positive(f64 v) noexcept {
@@ -30,12 +50,12 @@ Transform Transform::from_range(Range x, Range y, f64 px0, f64 px1, f64 py0, f64
 
   f64 x_lo = 0.0, x_hi = 0.0;
   axis_ends(x, lx, x_lo, x_hi);
-  t.sx = (px1 - px0) / (x_hi - x_lo);
+  t.sx = axis_scale(x_lo, x_hi, px0, px1);
   t.tx = px0 - x_lo * t.sx;
 
   f64 y_lo = 0.0, y_hi = 0.0;
   axis_ends(y, ly, y_lo, y_hi);
-  t.sy = (py1 - py0) / (y_hi - y_lo);
+  t.sy = axis_scale(y_lo, y_hi, py0, py1);
   t.ty = py0 - y_lo * t.sy;
 
   return t;
diff --git a/tests/test_transform.cpp b/tests/test_transform.cpp
index 1180a34..2b960dd 100644
--- a/tests/test_transform.cpp
+++ b/tests/test_transform.cpp
@@ -29,3 +29,65 @@ PLOT_TEST(zoom_anchor_is_invariant) {
   t.tx = before - anchor_data * t.sx;
   PLOT_CHECK_NEAR(t.to_screen_x(anchor_data), before, 1e-12);
 }
+PLOT_TEST(from_range_linear) {
+  const Transform t =
+      Transform::from_range({0.0, 10.0}, {-1.0, 1.0}, 0.0, 100.0, 0.0, 200.0, false, false);
+  PLOT_CHECK_NEAR(t.to_screen_x(0.0), 0.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_x(10.0), 100.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_y(-1.0), 0.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_y(1.0), 200.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_data_x(t.to_screen_x(3.5)), 3.5, 1e-12);
+  PLOT_CHECK_NEAR(t.to_data_y(t.to_screen_y(0.25)), 0.25, 1e-12);
+}
+
+PLOT_TEST(from_range_flipped_pixel_axis) {
+  // px0 > px1 reverses the direction of the axis; the round trip must survive.
+  const Transform t =
+      Transform::from_range({0.0, 10.0}, {0.0, 10.0}, 100.0, 0.0, 200.0, 0.0, false, false);
+  PLOT_CHECK_NEAR(t.to_screen_x(0.0), 100.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_x(10.0), 0.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_y(0.0), 200.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_y(10.0), 0.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_data_x(t.to_screen_x(2.5)), 2.5, 1e-12);
+  PLOT_CHECK_NEAR(t.to_data_y(t.to_screen_y(7.5)), 7.5, 1e-12);
+}
+
+PLOT_TEST(from_range_log_x) {
+  const Transform t =
+      Transform::from_range({1.0, 1000.0}, {0.0, 1.0}, 0.0, 300.0, 0.0, 100.0, true, false);
+  PLOT_CHECK(t.log_x);
+  PLOT_CHECK(!t.log_y);
+  PLOT_CHECK_NEAR(t.to_screen_x(1.0), 0.0, 1e-12);
+  PLOT_CHECK_NEAR(t.to_screen_x(1000.0), 300.0, 1e-12);
+  // log10(31.6227766) == 1.5 lands exactly halfway along the axis.
+  PLOT_CHECK_NEAR(t.to_screen_x(31.6227766), 150.0, 1e-6);
+  PLOT_CHECK_NEAR(t.to_data_x(t.to_screen_x(31.6227766)), 31.6227766, 1e-9);
+}
+
+PLOT_TEST(from_range_degenerate_data_range) {
+  // min == max: the range is widened, so the mapping stays finite and invertible.
+  const Transform t =
+      Transform::from_range({5.0, 5.0}, {2.0, 2.0}, 0.0, 100.0, 0.0, 200.0, false, false);
+  PLOT_CHECK(std::isfinite(t.sx) && t.sx != 0.0);
+  PLOT_CHECK(std::isfinite(t.sy) && t.sy != 0.0);
+  PLOT_CHECK_NEAR(t.to_data_x(t.to_screen_x(5.0)), 5.0, 1e-9);
+  PLOT_CHECK_NEAR(t.to_data_y(t.to_screen_y(2.0)), 2.0, 1e-9);
+}
+
+PLOT_TEST(from_range_collapsed_pixel_span) {
+  // px0 == px1 previously gave sx == 0, so to_data_x returned NaN/inf.
+  const Transform t =
+      Transform::from_range({0.0, 10.0}, {0.0, 10.0}, 50.0, 50.0, 25.0, 25.0, false, false);
+  PLOT_CHECK(std::isfinite(t.sx) && t.sx != 0.0);
+  PLOT_CHECK(std::isfinite(t.sy) && t.sy != 0.0);
+  PLOT_CHECK_NEAR(t.to_data_x(t.to_screen_x(4.0)), 4.0, 1e-9);
+  PLOT_CHECK_NEAR(t.to_data_y(t.to_screen_y(7.0)), 7.0, 1e-9);
+  PLOT_CHECK(std::isfinite(t.to_data_x(t.to_screen_x(0.0))));
+  PLOT_CHECK(std::isfinite(t.to_data_y(t.to_screen_y(10.0))));
+}
+
+PLOT_TEST(log10_positive_clamps_non_positive) {
+  PLOT_CHECK(std::isfinite(Transform::log10_positive(0.0)));
+  PLOT_CHECK(std::isfinite(Transform::log10_positive(-5.0)));
+  PLOT_CHECK_NEAR(Transform::log10_positive(1.0), 0.0, 1e-12);
+}