diff --git a/mlx/primitives.cpp b/mlx/primitives.cpp
index 027f6bb48b..a4fa011d51 100644
--- a/mlx/primitives.cpp
+++ b/mlx/primitives.cpp
@@ -510,7 +510,27 @@ std::vector<array> ArcTan2::vjp(
     const std::vector<array>& cotangents,
     const std::vector<int>& argnums,
     const std::vector<array>&) {
-  return jvp(primals, cotangents, argnums);
+  assert(primals.size() == 2);
+  assert(argnums.size() == 2);
+
+  const auto& s = stream();
+  const array& x1 = primals[0];
+  const array& x2 = primals[1];
+  const array& dy = cotangents[0];
+
+  std::vector<array> grads;
+  array dy_over_x1_x2_squared =
+      divide(dy, add(square(x1, s), square(x2, s)), s);
+
+  for (auto arg : argnums) {
+    if (arg == 0) {
+      grads.emplace_back(multiply(x2, dy_over_x1_x2_squared, s));
+    } else {
+      grads.emplace_back(multiply(negative(x1, s), dy_over_x1_x2_squared, s));
+    }
+  }
+
+  return grads;
 }
 
 std::vector<array> ArcTan2::jvp(
@@ -519,11 +539,17 @@ std::vector<array> ArcTan2::jvp(
     const std::vector<int>& argnums) {
   assert(primals.size() == 2);
   assert(argnums.size() == 2);
-  array t =
-      add(square(primals[0], stream()), square(primals[1], stream()), stream());
-  return {
-      divide(tangents[0], t, stream()),
-      divide(negative(tangents[1], stream()), t, stream())};
+
+  const auto& s = stream();
+  const array& x1 = primals[0];
+  const array& x2 = primals[1];
+  const array& dx1 = tangents[0];
+  const array& dx2 = tangents[1];
+
+  return {divide(
+      subtract(multiply(x2, dx1, s), multiply(x1, dx2, s), s),
+      add(square(x1, s), square(x2, s), s),
+      s)};
 }
 
 std::pair<std::vector<array>, std::vector<int>> ArcTan2::vmap(
diff --git a/tests/autograd_tests.cpp b/tests/autograd_tests.cpp
index 5b3454bfce..3a373fb18b 100644
--- a/tests/autograd_tests.cpp
+++ b/tests/autograd_tests.cpp
@@ -413,6 +413,25 @@ TEST_CASE("test op vjps") {
     CHECK(out.second.item<float>() == doctest::Approx(-std::sin(1.0f)));
   }
 
+  // Test arctan
+  {
+    auto out = vjp(
+        [](array input) { return arctan(input); }, array(2.0f), array(1.0f));
+    CHECK(out.second.item<float>() == doctest::Approx(0.2f));
+  }
+
+  // Test arctan2
+  {
+    auto out = vjp(
+        [](const std::vector<array>& xs) {
+          return std::vector<array>{arctan2(xs[0], xs[1])};
+        },
+        {array(2.0f), array(3.0f)},
+        {array(1.0f)});
+    CHECK(out.second[0].item<float>() == doctest::Approx(3.0f / 13.0f));
+    CHECK(out.second[1].item<float>() == doctest::Approx(-2.0f / 13.0f));
+  }
+
   // Test log
   {
     auto out = vjp([](array in) { return log(in); }, array(2.0f), array(1.0f));