diff --git a/jax/_src/numpy/fft.py b/jax/_src/numpy/fft.py
index d365506be..cbb50be44 100644
--- a/jax/_src/numpy/fft.py
+++ b/jax/_src/numpy/fft.py
@@ -86,7 +86,8 @@ def _fft_core(func_name, fft_type, a, s, axes, norm):
         s += [max(0, 2 * (a.shape[axes[-1]] - 1))]
     else:
       s = [a.shape[axis] for axis in axes]
-  transformed = lax.fft(a, fft_type, tuple(s)) * _fft_norm(jnp.array(s), func_name, norm)
+  transformed = lax.fft(a, fft_type, tuple(s))
+  transformed *= _fft_norm(jnp.array(s, dtype=transformed.real.dtype), func_name, norm)
 
   if orig_axes is not None:
     transformed = jnp.moveaxis(transformed, axes, orig_axes)
diff --git a/tests/fft_test.py b/tests/fft_test.py
index 83e512946..8b15276f9 100644
--- a/tests/fft_test.py
+++ b/tests/fft_test.py
@@ -138,6 +138,11 @@ class FftTest(jtu.JaxTestCase):
       tol = 0.15
       jtu.check_grads(jnp_fn, args_maker(), order=2, atol=tol, rtol=tol)
 
+    # check dtypes
+    dtype = jnp_fn(rng(shape, dtype)).dtype
+    expected_dtype = jnp.promote_types(float if inverse and real else complex, dtype)
+    self.assertEqual(dtype, expected_dtype)
+
   def testIrfftTranspose(self):
     # regression test for https://github.com/google/jax/issues/6223
     def build_matrix(linear_func, size):