diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index dd7f43d16..ec4c53b43 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -1029,7 +1029,10 @@ struct npy_format_descriptor_name<T, enable_if_t<std::is_integral<T>::value>> {
 
 template <typename T>
 struct npy_format_descriptor_name<T, enable_if_t<std::is_floating_point<T>::value>> {
-    static constexpr auto name = _<std::is_same<T, float>::value || std::is_same<T, double>::value>(
+    static constexpr auto name = _<std::is_same<T, float>::value
+                                   || std::is_same<T, const float>::value
+                                   || std::is_same<T, double>::value
+                                   || std::is_same<T, const double>::value>(
         _("numpy.float") + _<sizeof(T)*8>(), _("numpy.longdouble")
     );
 };
@@ -1037,7 +1040,9 @@ struct npy_format_descriptor_name<T, enable_if_t<std::is_floating_point<T>::valu
 template <typename T>
 struct npy_format_descriptor_name<T, enable_if_t<is_complex<T>::value>> {
     static constexpr auto name = _<std::is_same<typename T::value_type, float>::value
-                                   || std::is_same<typename T::value_type, double>::value>(
+                                   || std::is_same<typename T::value_type, const float>::value
+                                   || std::is_same<typename T::value_type, double>::value
+                                   || std::is_same<typename T::value_type, const double>::value>(
         _("numpy.complex") + _<sizeof(typename T::value_type)*16>(), _("numpy.longcomplex")
     );
 };
diff --git a/tests/test_numpy_array.cpp b/tests/test_numpy_array.cpp
index dca7145f9..204ea8367 100644
--- a/tests/test_numpy_array.cpp
+++ b/tests/test_numpy_array.cpp
@@ -437,4 +437,10 @@ TEST_SUBMODULE(numpy_array, sm) {
     sm.def("accept_double_f_style_forcecast_noconvert",
            [](py::array_t<double, py::array::forcecast | py::array::f_style>) {},
            "a"_a.noconvert());
+
+    // Check that types returns correct npy format descriptor
+    sm.def("test_fmt_desc_float", [](py::array_t<float>) {});
+    sm.def("test_fmt_desc_double", [](py::array_t<double>) {});
+    sm.def("test_fmt_desc_const_float", [](py::array_t<const float>) {});
+    sm.def("test_fmt_desc_const_double", [](py::array_t<const double>) {});
 }
diff --git a/tests/test_numpy_array.py b/tests/test_numpy_array.py
index 02f3ecfc0..548c84bab 100644
--- a/tests/test_numpy_array.py
+++ b/tests/test_numpy_array.py
@@ -482,6 +482,19 @@ def test_index_using_ellipsis():
     assert a.shape == (6,)
 
 
+@pytest.mark.parametrize(
+    "test_func",
+    [
+        m.test_fmt_desc_float,
+        m.test_fmt_desc_double,
+        m.test_fmt_desc_const_float,
+        m.test_fmt_desc_const_double,
+    ],
+)
+def test_format_descriptors_for_floating_point_types(test_func):
+    assert "numpy.ndarray[numpy.float" in test_func.__doc__
+
+
 @pytest.mark.parametrize("forcecast", [False, True])
 @pytest.mark.parametrize("contiguity", [None, "C", "F"])
 @pytest.mark.parametrize("noconvert", [False, True])