diff --git a/src/core/include/mp-units/bits/magnitude.h b/src/core/include/mp-units/bits/magnitude.h
index 6f9e238a..c4d23b31 100644
--- a/src/core/include/mp-units/bits/magnitude.h
+++ b/src/core/include/mp-units/bits/magnitude.h
@@ -719,6 +719,16 @@ template<auto H1, auto... T1, auto H2, auto... T2>
   }
 }
 
+template<auto... Ms>
+[[nodiscard]] consteval auto common_magnitude_type_impl(magnitude<Ms...>)
+{
+  return (... * decltype(get_base(Ms)){}) * std::intmax_t{};
+}
+
+// Returns the most precise type to express the magnitude factor
+template<Magnitude auto M>
+using common_magnitude_type = decltype(common_magnitude_type_impl(M));
+
 }  // namespace detail
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -764,6 +774,7 @@ struct prime_factorization<1> {
 
 template<std::intmax_t N>
 inline constexpr auto prime_factorization_v = prime_factorization<N>::value;
+
 }  // namespace detail
 
 /**
diff --git a/src/core/include/mp-units/bits/quantity_cast.h b/src/core/include/mp-units/bits/quantity_cast.h
index 61047592..712ea041 100644
--- a/src/core/include/mp-units/bits/quantity_cast.h
+++ b/src/core/include/mp-units/bits/quantity_cast.h
@@ -22,22 +22,12 @@
 
 #pragma once
 
-#include <mp-units/bits/external/type_traits.h>
-#include <mp-units/bits/magnitude.h>
 #include <mp-units/bits/quantity_concepts.h>
-#include <mp-units/bits/reference_concepts.h>
-#include <mp-units/bits/representation_concepts.h>
-#include <mp-units/bits/unit_concepts.h>
-#include <mp-units/customization_points.h>
-#include <mp-units/dimension.h>
 #include <mp-units/reference.h>
-#include <mp-units/unit.h>
+#include <type_traits>
 
 namespace mp_units {
 
-template<Reference auto R, RepresentationOf<get_quantity_spec(R).character> Rep>
-class quantity;
-
 /**
  * @brief Explicit cast of a quantity type
  *
@@ -56,11 +46,10 @@ class quantity;
  * @tparam ToQS a quantity specification to use for a target quantity
  */
 template<QuantitySpec auto ToQS, typename Q>
-  requires Quantity<std::remove_cvref_t<Q>> && (castable(std::remove_cvref_t<Q>::quantity_spec, ToQS))
 [[nodiscard]] constexpr Quantity auto quantity_cast(Q&& q)
+  requires Quantity<std::remove_cvref_t<Q>> && (castable(q.quantity_spec, ToQS))
 {
-  constexpr reference<ToQS, std::remove_cvref_t<Q>::unit> r;
-  return std::forward<Q>(q).number() * r;
+  return make_quantity<reference<ToQS, q.unit>{}>(std::forward<Q>(q).number());
 }
 
 }  // namespace mp_units
diff --git a/src/core/include/mp-units/bits/sudo_cast.h b/src/core/include/mp-units/bits/sudo_cast.h
index 1195d309..a950ad51 100644
--- a/src/core/include/mp-units/bits/sudo_cast.h
+++ b/src/core/include/mp-units/bits/sudo_cast.h
@@ -28,67 +28,71 @@
 #include <mp-units/bits/reference_concepts.h>
 #include <mp-units/unit.h>
 
-namespace mp_units {
+namespace mp_units::detail {
 
-template<Reference auto R, RepresentationOf<get_quantity_spec(R).character> Rep>
-class quantity;
+// determines the best available representation type
+template<Quantity From, Quantity To>
+[[nodiscard]] consteval auto common_rep_type(From, To)
+{
+  if constexpr (requires { typename std::common_type_t<typename From::rep, typename To::rep>; })
+    // returns a common type of two representation types if available
+    // i.e. `double` and `int` will end up with `double` precision
+    return std::common_type_t<typename From::rep, typename To::rep>{};
+  else
+    return typename From::rep{};
+}
 
-namespace detail {
+// determines the value type used by the representation type
+template<typename Rep>
+[[nodiscard]] consteval auto rep_value_type(Rep)
+{
+  if constexpr (requires { typename Rep::value_type; })
+    return typename Rep::value_type{};
+  else if constexpr (requires { typename Rep::element_type; })
+    return typename Rep::element_type{};
+  else
+    return Rep{};
+}
 
 /**
- * @brief Explicit cast of entire quantity
+ * @brief Explicit cast between different quantity types
  *
- * @note This is too powerful to be used by users.
+ * @note This is a low-level facility and is too powerful to be used by the users directly. They should either use
+ * `value_cast` or `quantity_cast`.
  *
  * @tparam To a target quantity type to cast to
  */
-template<Quantity To, auto R, typename Rep>
-  requires(castable(get_quantity_spec(R), To::quantity_spec)) &&
-          ((get_unit(R) == To::unit && std::constructible_from<typename To::rep, Rep>) ||
-           (get_unit(R) != To::unit))  // && scalable_with_<typename To::rep>))
+template<Quantity To, typename From>
+  requires Quantity<std::remove_cvref_t<From>> &&
+           (castable(std::remove_reference_t<From>::quantity_spec, To::quantity_spec)) &&
+           ((std::remove_reference_t<From>::unit == To::unit &&
+             std::constructible_from<typename To::rep, typename std::remove_reference_t<From>::rep>) ||
+            (std::remove_reference_t<From>::unit != To::unit))  // && scalable_with_<typename To::rep>))
 // TODO how to constrain the second part here?
-[[nodiscard]] constexpr Quantity auto sudo_cast(const quantity<R, Rep>& q)
+[[nodiscard]] constexpr Quantity auto sudo_cast(From&& q)
 {
-  if constexpr (get_unit(R) == To::unit) {
+  if constexpr (q.unit == To::unit) {
     // no scaling of the number needed
-    return static_cast<TYPENAME To::rep>(q.number()) * To::reference;  // this is the only (and recommended) way to do
+    return make_quantity<To::reference>(
+      static_cast<TYPENAME To::rep>(std::forward<From>(q).number()));  // this is the only (and recommended) way to do
                                                                        // a truncating conversion on a number, so we are
                                                                        // using static_cast to suppress all the compiler
                                                                        // warnings on conversions
   } else {
     // scale the number
-    using rep_type = decltype([] {
-      // determines the best representation type
-      if constexpr (requires { typename std::common_type_t<Rep, typename To::rep>; })
-        // returns a common type of two representation types if available
-        // i.e. `double` and `int` will end up with `double` precision
-        return std::common_type_t<Rep, typename To::rep>{};
-      else
-        return Rep{};
-    }());
-    using multiplier_type = decltype([] {
-      // widen the type to prevent overflows
-      using wider_type = decltype(rep_type{} * std::intmax_t{});
-      // check if `wider_type` supports scaling operations
-      if constexpr (requires(wider_type v) { v* v / v; })
-        // if the `wider_type` can handle scaling operations then use it to improve accuracy
-        return wider_type{};
-      else
-        // needed for example for linear algebra where `op/` on matrix types is not available
-        return std::intmax_t{};
-    }());
-
-    constexpr Magnitude auto c_mag =
-      detail::get_canonical_unit(get_unit(R)).mag / detail::get_canonical_unit(To::unit).mag;
+    constexpr Magnitude auto c_mag = get_canonical_unit(q.unit).mag / get_canonical_unit(To::unit).mag;
     constexpr Magnitude auto num = numerator(c_mag);
     constexpr Magnitude auto den = denominator(c_mag);
     constexpr Magnitude auto irr = c_mag * (den / num);
-
+    using c_mag_type = common_magnitude_type<c_mag>;
+    using c_rep_type = decltype(common_rep_type(q, To{}));
+    using v_type = decltype(rep_value_type(c_rep_type{}));
+    using multiplier_type = decltype(v_type{} * c_mag_type{});
     constexpr auto val = [](Magnitude auto m) { return get_value<multiplier_type>(m); };
-    return static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.number()) * val(num) / val(den) * val(irr)) *
+    return static_cast<TYPENAME To::rep>(static_cast<c_rep_type>(std::forward<From>(q).number()) * val(num) / val(den) *
+                                         val(irr)) *
            To::reference;
   }
 }
 
-}  // namespace detail
-}  // namespace mp_units
+}  // namespace mp_units::detail
diff --git a/src/core/include/mp-units/bits/value_cast.h b/src/core/include/mp-units/bits/value_cast.h
index 249d4629..92880e16 100644
--- a/src/core/include/mp-units/bits/value_cast.h
+++ b/src/core/include/mp-units/bits/value_cast.h
@@ -23,16 +23,13 @@
 #pragma once
 
 #include <mp-units/bits/quantity_concepts.h>
-#include <mp-units/bits/reference_concepts.h>
 #include <mp-units/bits/representation_concepts.h>
 #include <mp-units/bits/sudo_cast.h>
 #include <mp-units/bits/unit_concepts.h>
+#include <mp-units/reference.h>
 
 namespace mp_units {
 
-template<Reference auto R, RepresentationOf<get_quantity_spec(R).character> Rep>
-class quantity;
-
 /**
  * @brief Explicit cast of a quantity's unit
  *
@@ -43,17 +40,19 @@ class quantity;
  *
  * @tparam ToU a unit to use for a target quantity
  */
-template<Unit auto ToU, auto R, typename Rep>
-  requires(convertible(get_unit(R), ToU))
-[[nodiscard]] constexpr Quantity auto value_cast(const quantity<R, Rep>& q)
+template<Unit auto ToU, typename Q>
+[[nodiscard]] constexpr Quantity auto value_cast(Q&& q)
+  requires Quantity<std::remove_cvref_t<Q>> && (convertible(q.reference, ToU))
 {
-  if constexpr (detail::is_specialization_of_reference<std::remove_const_t<decltype(R)>> ||
-                !AssociatedUnit<std::remove_const_t<decltype(ToU)>>) {
-    constexpr reference<quantity<R, Rep>::quantity_spec, ToU> r;
-    return detail::sudo_cast<quantity<r, Rep>>(q);
-  } else {
-    return detail::sudo_cast<quantity<ToU, Rep>>(q);
-  }
+  using q_type = std::remove_reference_t<Q>;
+  constexpr auto r = [] {
+    if constexpr (detail::is_specialization_of_reference<std::remove_const_t<decltype(q_type::reference)>> ||
+                  !AssociatedUnit<std::remove_const_t<decltype(ToU)>>)
+      return reference<q_type::quantity_spec, ToU>{};
+    else
+      return ToU;
+  }();
+  return detail::sudo_cast<quantity<r, typename q_type::rep>>(std::forward<Q>(q));
 }
 
 /**
@@ -66,11 +65,13 @@ template<Unit auto ToU, auto R, typename Rep>
  *
  * @tparam ToRep a representation type to use for a target quantity
  */
-template<Representation ToRep, auto R, typename Rep>
-  requires RepresentationOf<ToRep, get_quantity_spec(R).character> && std::constructible_from<ToRep, Rep>
-[[nodiscard]] constexpr Quantity auto value_cast(const quantity<R, Rep>& q)
+template<Representation ToRep, typename Q>
+  requires Quantity<std::remove_cvref_t<Q>> &&
+           RepresentationOf<ToRep, std::remove_reference_t<Q>::quantity_spec.character> &&
+           std::constructible_from<ToRep, typename std::remove_reference_t<Q>::rep>
+[[nodiscard]] constexpr quantity<std::remove_reference_t<Q>::reference, ToRep> value_cast(Q&& q)
 {
-  return detail::sudo_cast<quantity<R, ToRep>>(q);
+  return detail::sudo_cast<quantity<q.reference, ToRep>>(std::forward<Q>(q));
 }
 
 }  // namespace mp_units