diff --git a/stan/math/prim/constraint/sum_to_zero_constrain.hpp b/stan/math/prim/constraint/sum_to_zero_constrain.hpp
index 92fa4a2daa0..212aed2790a 100644
--- a/stan/math/prim/constraint/sum_to_zero_constrain.hpp
+++ b/stan/math/prim/constraint/sum_to_zero_constrain.hpp
@@ -25,12 +25,13 @@ namespace math {
 template <typename Vec, require_eigen_col_vector_t<Vec>* = nullptr,
           require_not_st_var<Vec>* = nullptr>
 inline plain_type_t<Vec> sum_to_zero_constrain(const Vec& y) {
-  int Km1 = y.size();
+  const auto Km1 = y.size();
   plain_type_t<Vec> x(Km1 + 1);
   // copy the first Km1 elements
-  x.head(Km1) = y;
+  auto&& y_ref = to_ref(y);
+  x.head(Km1) = y_ref;
   // set the last element to -sum(y)
-  x.coeffRef(Km1) = -sum(y);
+  x.coeffRef(Km1) = -sum(y_ref);
   return x;
 }
 
diff --git a/stan/math/rev/constraint/sum_to_zero_constrain.hpp b/stan/math/rev/constraint/sum_to_zero_constrain.hpp
index 10cbcd295de..01878004691 100644
--- a/stan/math/rev/constraint/sum_to_zero_constrain.hpp
+++ b/stan/math/rev/constraint/sum_to_zero_constrain.hpp
@@ -29,28 +29,20 @@ template <typename T, require_rev_col_vector_t<T>* = nullptr>
 inline auto sum_to_zero_constrain(const T& y) {
   using ret_type = plain_type_t<T>;
 
-  size_t N = y.size();
-  Eigen::VectorXd x_val(N + 1);
-
-  arena_t<T> arena_y = y;
-
+  const auto N = y.size();
   if (unlikely(N == 0)) {
-    x_val << 0;
-    return ret_type(x_val);
+    return ret_type(Eigen::VectorXd{{0}});
   }
-
-  x_val.head(N) = y.val();
+  Eigen::VectorXd x_val = Eigen::VectorXd::Zero(N + 1);
+  auto arena_y = to_arena(y);
+  double x_sum = -sum(arena_y.val());
+  x_val.head(N) = arena_y.val();
+  x_val(N) = x_sum;
   arena_t<ret_type> arena_x = x_val;
-
-  var x_N = -sum(y);
-
-  arena_x.coeffRef(N) = x_N;
-
-  reverse_pass_callback([arena_y, arena_x, x_N, N]() mutable {
-    arena_y.adj() += arena_x.adj().head(N);
-    x_N.adj() += arena_x.adj().coeff(N);
+  reverse_pass_callback([arena_y, arena_x, x_sum, N]() mutable {
+    arena_y.adj().array() -= arena_x.adj_op()(N);
+    arena_y.adj() += arena_x.adj_op().head(N);
   });
-
   return ret_type(arena_x);
 }
 
diff --git a/test/unit/math/mix/constraint/sum_to_zero_constrain_test.cpp b/test/unit/math/mix/constraint/sum_to_zero_constrain_test.cpp
index cec8c2cd068..ae4ce5516db 100644
--- a/test/unit/math/mix/constraint/sum_to_zero_constrain_test.cpp
+++ b/test/unit/math/mix/constraint/sum_to_zero_constrain_test.cpp
@@ -24,11 +24,11 @@ void expect_sum_to_zero_transform(const T& x) {
   auto f2 = [](const auto& x) { return g2(x); };
   auto f3 = [](const auto& x) { return g3(x); };
   stan::test::expect_ad(f1, x);
-  //   stan::test::expect_ad_matvar(f1, x);
+     stan::test::expect_ad_matvar(f1, x);
   stan::test::expect_ad(f2, x);
-  //   stan::test::expect_ad_matvar(f2, x);
+     stan::test::expect_ad_matvar(f2, x);
   stan::test::expect_ad(f3, x);
-  //   stan::test::expect_ad_matvar(f3, x);
+     stan::test::expect_ad_matvar(f3, x);
 }
 }  // namespace sum_to_zero_constrain_test