diff --git a/include/gul14/num_util.h b/include/gul14/num_util.h
index 63ddadf3..ba6c78ae 100644
--- a/include/gul14/num_util.h
+++ b/include/gul14/num_util.h
@@ -4,7 +4,7 @@
  * \authors \ref contributors
  * \date    Created on 7 Feb 2019
  *
- * \copyright Copyright 2019-2023 Deutsches Elektronen-Synchrotron (DESY), Hamburg
+ * \copyright Copyright 2019-2024 Deutsches Elektronen-Synchrotron (DESY), Hamburg
  *
  * This program is free software: you can redistribute it and/or modify
  * it under the terms of the GNU Lesser General Public License as published
@@ -29,9 +29,48 @@
 #include <type_traits>
 
 #include "gul14/internal.h"
+#include "gul14/traits.h"
 
 namespace gul14 {
 
+/// \cond HIDE_SYMBOLS
+namespace detail{
+
+template <typename T, typename = void>
+class CanCallStdAbsOn
+    : public std::false_type {};
+
+template <typename T>
+class CanCallStdAbsOn<T, gul14::void_t<decltype(std::abs(std::declval<T>()))>>
+    : public std::true_type {};
+
+// abs() for unsigned integers
+template<typename ValueT>
+constexpr auto abs_impl(ValueT n) noexcept -> std::enable_if_t<
+    std::is_unsigned<ValueT>::value, ValueT>
+{
+    return n;
+}
+
+// abs() for types supported by std::abs()
+template<typename ValueT>
+constexpr auto abs_impl(ValueT n) noexcept -> std::enable_if_t<
+    not std::is_unsigned<ValueT>::value and CanCallStdAbsOn<ValueT>::value, ValueT>
+{
+    return std::abs(n);
+}
+
+// Fallback: Try to find a user-supplied abs() via ADL
+template<typename ValueT>
+constexpr auto abs_impl(ValueT n) noexcept -> std::enable_if_t<
+    not std::is_unsigned<ValueT>::value and not CanCallStdAbsOn<ValueT>::value, ValueT>
+{
+    return abs(n);
+}
+
+} // namespace detail
+/// \endcond
+
 /**
  * \addtogroup num_util_h gul14/num_util.h
  * \brief Numerical utility functions.
@@ -41,27 +80,20 @@ namespace gul14 {
 /**
  * Compute the absolute value of a number.
  *
- * This function is almost equal to std::abs() with the exception of unsigned integral
- * types, which are returned unchanged and in their original type. This is especially
- * useful in templates, where std::abs() cannot be used for all arithmetic types.
+ * This function makes three attempts at compile time to determine the absolute value of
+ * the given number. First, if the value is of an unsigned integer type, it is returned
+ * unmodified. Second, if std::abs() can be called on the value, its result is returned.
+ * In the third and last attempt, abs() is called on the value in the hope that a suitable
+ * user-supplied function can be found via argument-dependent lookup.
  *
  * \param n  The number whose absolute value should be determined.
  *
  * \returns the absolute value of n.
  */
 template<typename ValueT>
-constexpr auto abs(ValueT n) noexcept -> std::enable_if_t<std::is_unsigned<ValueT>::value, ValueT>
-{
-    return n;
-}
-
-/**
- * \overload
- */
-template<typename ValueT>
-constexpr auto abs(ValueT n) noexcept -> std::enable_if_t<not std::is_unsigned<ValueT>::value, ValueT>
+constexpr auto abs(ValueT n) noexcept
 {
-    return std::abs(n);
+    return detail::abs_impl(n);
 }
 
 /**
@@ -114,6 +146,10 @@ bool within_orders(const NumT a, const NumT b, const OrderT orders) noexcept(fal
  * \param tol   The absolute tolerance
  *
  * \returns true if the absolute difference between a and b is smaller than tol.
+ *
+ * \note
+ * This function supports user-defined numeric types as long as they provide an
+ * implementation of abs() that can be found via argument-dependent lookup.
  */
 template<typename NumT>
 bool within_abs(NumT a, NumT b, NumT tol) noexcept {
diff --git a/tests/test_num_util.cc b/tests/test_num_util.cc
index 288736a1..99c5ffc7 100644
--- a/tests/test_num_util.cc
+++ b/tests/test_num_util.cc
@@ -4,7 +4,7 @@
  * \date   Created on 7 Feb 2019
  * \brief  Unit tests for within_orders(), within_abs(), and within_ulp().
  *
- * \copyright Copyright 2019 Deutsches Elektronen-Synchrotron (DESY), Hamburg
+ * \copyright Copyright 2019-2024 Deutsches Elektronen-Synchrotron (DESY), Hamburg
  *
  * This program is free software: you can redistribute it and/or modify
  * it under the terms of the GNU Lesser General Public License as published
@@ -25,6 +25,30 @@
 #include "gul14/catch.h"
 #include "gul14/num_util.h"
 
+namespace {
+
+// Simple physical unit class for meters
+class Meters {
+    double value_{ 0.0 };
+public:
+    explicit Meters(double value) : value_{ value } {}
+    double value() const { return value_; }
+    bool operator==(const Meters& other) const { return value_ == other.value_; }
+    bool operator!=(const Meters& other) const { return value_ != other.value_; }
+    bool operator<(const Meters& other) const { return value_ < other.value_; }
+    bool operator>(const Meters& other) const { return value_ > other.value_; }
+    bool operator<=(const Meters& other) const { return value_ <= other.value_; }
+    bool operator>=(const Meters& other) const { return value_ >= other.value_; }
+    Meters operator-() const { return Meters{ -value_ }; }
+    Meters operator+(const Meters& other) const { return Meters{ value_ + other.value_ }; }
+    Meters operator-(const Meters& other) const { return Meters{ value_ - other.value_ }; }
+};
+
+// abs() implementation, usable via ADL
+Meters abs(Meters m) { return Meters(std::abs(m.value())); }
+
+} // anonymous namespace
+
 TEST_CASE("test within_orders()", "[num_util]")
 {
     REQUIRE(gul14::within_orders(1.0, 101.0, 2) == false);
@@ -272,6 +296,10 @@ TEST_CASE("test within_abs()", "[num_util]")
     auto i2 = i1 - 1;
     auto i3 = 60;
     REQUIRE(gul14::within_abs(i1, i2, i3) == true);
+
+    // Physical units
+    REQUIRE(gul14::within_abs(Meters{ 1.0 }, Meters{ 1.01 }, Meters{ 0.02 }));
+    REQUIRE(gul14::within_abs(Meters{ 42.0 }, Meters{ 42.5 }, Meters{ 0.4 }) == false);
 }
 
 TEST_CASE("test within_ulp()", "[num_util]")