diff --git a/CHANGELOG.md b/CHANGELOG.md
index e3945d1a..3d1795ff 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 * Multi-iterator constructors now return a status corresponding to allocation success or failure, and raise `MemoryError` instead of `ValueError` [gh-373](https://github.com/IntelPython/mkl_fft/pull/373)
 * `_direct_fftnd` now also checks the status returned by the backend instead of discarding it [gh-373](https://github.com/IntelPython/mkl_fft/pull/373)
 * Pinned Cython in the Coverity Scan workflow so generated code stays stable between scans, and added `coverity/README.md` documenting the known false-positive families and the scan review checklist [gh-374](https://github.com/IntelPython/mkl_fft/pull/374)
+* Reduced Python overhead in `norm="forward"`/`"ortho"` scaling by computing the scale factor without `numpy.prod` [gh-384](https://github.com/IntelPython/mkl_fft/pull/384)
 
 ### Fixed
 * Fixed `norm="forward"`/`"ortho"` scaling in `fftn`, `ifftn`, `rfftn`, `irfftn` and the `fft2` family when only a subset of axes is transformed: the scale used the full array shape instead of the transformed axes [gh-336](https://github.com/IntelPython/mkl_fft/issues/336), [gh-370](https://github.com/IntelPython/mkl_fft/pull/370)
diff --git a/mkl_fft/_fft_utils.py b/mkl_fft/_fft_utils.py
index 9681adcb..8e2fb505 100644
--- a/mkl_fft/_fft_utils.py
+++ b/mkl_fft/_fft_utils.py
@@ -23,6 +23,8 @@
 # OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
+import math
+
 import numpy as np
 
 # pylint: disable=no-name-in-module
@@ -70,7 +72,15 @@ def _compute_fwd_scale(norm, n, shape):
         return 1.0
 
     ss = n if n is not None else shape
-    nn = np.prod(ss)
+    # Avoid np.prod's array-creation overhead on the hot scalar (1-D) and
+    # sequence (N-D) paths; np.prod stays as the fallback for array-like
+    # `n`/`s` (e.g. np.array(8)) that math.prod can't handle.
+    if isinstance(ss, (int, np.integer)):
+        nn = ss
+    elif isinstance(ss, (list, tuple)):
+        nn = math.prod(ss)
+    else:
+        nn = np.prod(ss)
     fsc = 1 / nn if nn != 0 else 1
     if norm == "forward":
         return fsc