diff --git a/docs/release.md b/docs/release.md
index 78e8901c..780a8bfb 100644
--- a/docs/release.md
+++ b/docs/release.md
@@ -14,6 +14,12 @@
 
 ## Unreleased
 
+### Bug fixes
+
+* Preserve multidimensional array shapes in `FixedScaleOffset` and preserve logical
+  coordinates when copying equally shaped arrays across different memory orders.
+  By {user}`shixi-li <shixi-li>`, {issue}`852`
+
 ### Maintenance
 
 * **Migrate build system from setuptools/setup.py to meson-python.** This replaces the
diff --git a/src/numcodecs/compat.py b/src/numcodecs/compat.py
index d1844e10..dd3dbe93 100644
--- a/src/numcodecs/compat.py
+++ b/src/numcodecs/compat.py
@@ -185,13 +185,18 @@ def ndarray_copy(src, dst) -> NDArrayLike:
     src = ensure_ndarray_like(src)
     dst = ensure_ndarray_like(dst)
 
-    # flatten source array
-    src = src.reshape(-1, order="A")
-
     # ensure same data type
     if dst.dtype != object:
         src = src.view(dst.dtype)
 
+    # preserve logical coordinates when equally shaped arrays use different memory orders
+    if src.shape == dst.shape:
+        np.copyto(dst, src)
+        return dst
+
+    # flatten source array
+    src = src.reshape(-1, order="A")
+
     # reshape source to match destination
     if src.shape != dst.shape:
         if dst.flags.f_contiguous:
diff --git a/src/numcodecs/fixedscaleoffset.py b/src/numcodecs/fixedscaleoffset.py
index b1db5205..9b4b9cc1 100644
--- a/src/numcodecs/fixedscaleoffset.py
+++ b/src/numcodecs/fixedscaleoffset.py
@@ -84,8 +84,9 @@ def encode(self, buf):
         # normalise input
         arr = ensure_ndarray(buf).view(self.dtype)
 
-        # flatten to simplify implementation
-        arr = arr.reshape(-1, order='A')
+        # preserve the historical one-element shape for scalar inputs
+        if arr.ndim == 0:
+            arr = arr.reshape(-1)
 
         # compute scale offset
         enc = (arr - self.offset) * self.scale
@@ -100,8 +101,9 @@ def decode(self, buf, out=None):
         # interpret buffer as numpy array
         enc = ensure_ndarray(buf).view(self.astype)
 
-        # flatten to simplify implementation
-        enc = enc.reshape(-1, order='A')
+        # preserve the historical one-element shape for scalar inputs
+        if enc.ndim == 0:
+            enc = enc.reshape(-1)
 
         # decode scale offset
         dec = (enc / self.scale) + self.offset
diff --git a/tests/test_compat.py b/tests/test_compat.py
index 0d5f2d74..ec81b8a0 100644
--- a/tests/test_compat.py
+++ b/tests/test_compat.py
@@ -4,7 +4,7 @@
 import numpy as np
 import pytest
 
-from numcodecs.compat import ensure_bytes, ensure_contiguous_ndarray, ensure_text
+from numcodecs.compat import ensure_bytes, ensure_contiguous_ndarray, ensure_text, ndarray_copy
 
 
 def test_ensure_text():
@@ -109,3 +109,20 @@ def test_ensure_contiguous_ndarray_max_buffer_size():
         for buf in buffers:
             with pytest.raises(ValueError):
                 ensure_contiguous_ndarray(buf, max_buffer_size=max_buffer_size)
+
+
+@pytest.mark.parametrize(("source_order", "destination_order"), [("C", "F"), ("F", "C")])
+@pytest.mark.parametrize("destination_type", ["ndarray", "memoryview"])
+def test_ndarray_copy_same_shape_preserves_logical_coordinates(
+    source_order, destination_order, destination_type
+):
+    shape = (2, 3, 4)
+    source = np.arange(np.prod(shape), dtype="<f4").reshape(shape, order=source_order)
+    destination_array = np.empty(shape, dtype="<f4", order=destination_order)
+    destination = (
+        memoryview(destination_array) if destination_type == "memoryview" else destination_array
+    )
+
+    ndarray_copy(source, destination)
+
+    np.testing.assert_array_equal(destination_array, source)
diff --git a/tests/test_fixedscaleoffset.py b/tests/test_fixedscaleoffset.py
index 343d3026..911594fb 100644
--- a/tests/test_fixedscaleoffset.py
+++ b/tests/test_fixedscaleoffset.py
@@ -1,8 +1,9 @@
 import itertools
+from typing import Literal
 
 import numpy as np
 import pytest
-from numpy.testing import assert_array_equal
+from numpy.testing import assert_array_almost_equal, assert_array_equal
 
 from numcodecs.fixedscaleoffset import FixedScaleOffset
 from tests.common import (
@@ -55,9 +56,80 @@ def test_encode(offset: float, scale: float, expected: list[int]):
     assert np.dtype(astype) == actual.dtype
 
 
+@pytest.mark.parametrize("order", ["C", "F"])
+def test_preserves_dimensions(order: Literal["C", "F"]):
+    shape = (8, 4, 5)
+    arr = 200.0 + np.arange(np.prod(shape), dtype="<f4").reshape(shape, order=order) * 0.001
+    codec = FixedScaleOffset(
+        offset=200.0,
+        scale=1000.0,
+        dtype="<f4",
+        astype="<u2",
+    )
+
+    encoded = codec.encode(arr)
+    decoded = codec.decode(encoded)
+
+    assert encoded.shape == shape
+    assert decoded.shape == shape
+    assert_array_almost_equal(arr, decoded, decimal=3)
+
+    serialized = encoded.tobytes(order="A")
+    decoded_serialized = codec.decode(serialized)
+    assert decoded_serialized.shape == (arr.size,)
+    assert_array_almost_equal(arr.reshape(-1, order="A"), decoded_serialized, decimal=3)
+
+    out = np.empty_like(arr)
+    decoded_out = codec.decode(serialized, out=out)
+    assert decoded_out is out
+    assert_array_almost_equal(arr, decoded_out, decimal=3)
+
+    legacy_encoded = np.around((arr.reshape(-1, order="A") - codec.offset) * codec.scale).astype(
+        codec.astype,
+        copy=False,
+    )
+    assert encoded.tobytes(order="A") == legacy_encoded.tobytes(order="A")
+
+
+@pytest.mark.parametrize(("input_order", "out_order"), [("C", "F"), ("F", "C")])
+def test_decode_out_preserves_logical_coordinates(
+    input_order: Literal["C", "F"], out_order: Literal["C", "F"]
+):
+    shape = (2, 3, 4)
+    arr = np.arange(np.prod(shape), dtype="<f4").reshape(shape, order=input_order)
+    codec = FixedScaleOffset(
+        offset=0,
+        scale=1,
+        dtype="<f4",
+        astype="<i4",
+    )
+    encoded = codec.encode(arr)
+    out = np.empty(shape, dtype="<f4", order=out_order)
+
+    decoded = codec.decode(encoded, out=out)
+
+    assert decoded is out
+    assert decoded.shape == shape
+    assert decoded.dtype == arr.dtype
+    assert_array_equal(decoded, arr)
+
+
+def test_scalar_preserves_legacy_shape():
+    arr = np.array(3.5, dtype="<f4")
+    codec = FixedScaleOffset(offset=0, scale=10, dtype="<f4")
+
+    encoded = codec.encode(arr)
+    decoded = codec.decode(encoded)
+
+    assert encoded.shape == (1,)
+    assert decoded.shape == (1,)
+    assert_array_equal(decoded, arr.reshape(-1))
+
+
 def test_config():
     codec = FixedScaleOffset(dtype='<f8', astype='<i4', scale=10, offset=100)
     check_config(codec)
+    assert "keep_dimensions" not in codec.get_config()
 
 
 def test_repr():