diff --git a/include/bout/coordinates.hxx b/include/bout/coordinates.hxx
index a090dcd959..cfcd9368d4 100644
--- a/include/bout/coordinates.hxx
+++ b/include/bout/coordinates.hxx
@@ -564,17 +564,26 @@ std::string parallelSliceFieldName(std::string_view field, int offset);
 /// tensor, which is multiplied by the normalisation factor.
 struct MetricNormaliser {
   std::optional<BoutReal> g = std::nullopt;
+  bool g_mul = false;
   std::optional<BoutReal> g11 = std::nullopt;
+  bool g11_mul = false;
   std::optional<BoutReal> g22 = std::nullopt;
+  bool g22_mul = false;
   std::optional<BoutReal> g33 = std::nullopt;
+  bool g33_mul = false;
   std::optional<BoutReal> g12 = std::nullopt;
+  bool g12_mul = false;
   std::optional<BoutReal> g13 = std::nullopt;
+  bool g13_mul = false;
   std::optional<BoutReal> g23 = std::nullopt;
+  bool g23_mul = false;
   std::optional<BoutReal> dx = std::nullopt;
   std::optional<BoutReal> dy = std::nullopt;
   std::optional<BoutReal> dz = std::nullopt;
   std::optional<BoutReal> J = std::nullopt;
+  bool J_mul = false;
   std::optional<BoutReal> Bxy = std::nullopt;
+  bool Bxy_mul = false;
 };
 
 #endif // BOUT_COORDINATES_H
diff --git a/src/mesh/coordinates.cxx b/src/mesh/coordinates.cxx
index bad8ebbd84..66f4195ca1 100644
--- a/src/mesh/coordinates.cxx
+++ b/src/mesh/coordinates.cxx
@@ -1313,16 +1313,32 @@ void Coordinates::normaliseMetric(const MetricNormaliser& norm) {
 
   if (norm.J.has_value()) {
     if (J().hasParallelSlices()) {
-      setJ(FieldMetricParallel{J() / *norm.J});
+      if (norm.J_mul) {
+        setJ(FieldMetricParallel{J() * *norm.J});
+      } else {
+        setJ(FieldMetricParallel{J() / *norm.J});
+      }
     } else {
-      setJ(J() / *norm.J);
+      if (norm.J_mul) {
+        setJ(J() * *norm.J);
+      } else {
+        setJ(J() / *norm.J);
+      }
     }
   }
   if (norm.Bxy.has_value()) {
     if (Bxy().hasParallelSlices()) {
-      setBxy(FieldMetricParallel{Bxy() / *norm.Bxy});
+      if (norm.Bxy_mul) {
+        setBxy(FieldMetricParallel{Bxy() * *norm.Bxy});
+      } else {
+        setBxy(FieldMetricParallel{Bxy() / *norm.Bxy});
+      }
     } else {
-      setBxy(Bxy() / *norm.Bxy);
+      if (norm.Bxy_mul) {
+        setBxy(Bxy() * *norm.Bxy);
+      } else {
+        setBxy(Bxy() / *norm.Bxy);
+      }
     }
   }
   if (norm.dx.has_value()) {
@@ -1334,7 +1350,7 @@ void Coordinates::normaliseMetric(const MetricNormaliser& norm) {
   if (norm.dz.has_value()) {
     setDz(dz() / *norm.dz);
   }
-  invalidateMetricCaches();
+  recalculateAndReset(false, false);
   if (norm.g.has_value() or norm.g22.has_value()) {
     if (Bxy().isFci()) {
       // No we compute g_22_* - they must not be cleared. If they get
@@ -1343,9 +1359,14 @@ void Coordinates::normaliseMetric(const MetricNormaliser& norm) {
       g_22_ylow();
       g_22_yhigh();
       ASSERT2(_g_22_ylow.has_value());
-      (*_g_22_ylow) /= g22;
       ASSERT2(_g_22_yhigh.has_value());
-      (*_g_22_yhigh) /= g22;
+      if (norm.g.has_value() ? norm.g_mul : norm.g22_mul) {
+        (*_g_22_ylow) *= g22;
+        (*_g_22_yhigh) *= g22;
+      } else {
+        (*_g_22_ylow) /= g22;
+        (*_g_22_yhigh) /= g22;
+      }
     }
   }
 }
diff --git a/src/mesh/metric_tensor.cxx b/src/mesh/metric_tensor.cxx
index 1347f88a7e..29b511e2cf 100644
--- a/src/mesh/metric_tensor.cxx
+++ b/src/mesh/metric_tensor.cxx
@@ -152,40 +152,56 @@ auto ContravariantMetricTensor::inverse(const std::string& region, bool communic
 template <class F>
 void MetricTensor::normaliseMetric(const MetricNormaliser& norm, const F& op) {
   if (norm.g.has_value()) {
-    op(g11_m, norm.g);
-    op(g22_m, norm.g);
-    op(g33_m, norm.g);
-    op(g12_m, norm.g);
-    op(g13_m, norm.g);
-    op(g23_m, norm.g);
+    op(g11_m, norm.g, norm.g_mul);
+    op(g22_m, norm.g, norm.g_mul);
+    op(g33_m, norm.g, norm.g_mul);
+    op(g12_m, norm.g, norm.g_mul);
+    op(g13_m, norm.g, norm.g_mul);
+    op(g23_m, norm.g, norm.g_mul);
   } else {
-    op(g11_m, norm.g11);
-    op(g22_m, norm.g22);
-    op(g33_m, norm.g33);
-    op(g12_m, norm.g12);
-    op(g13_m, norm.g13);
-    op(g23_m, norm.g23);
+    op(g11_m, norm.g11, norm.g11_mul);
+    op(g22_m, norm.g22, norm.g22_mul);
+    op(g33_m, norm.g33, norm.g33_mul);
+    op(g12_m, norm.g12, norm.g12_mul);
+    op(g13_m, norm.g13, norm.g13_mul);
+    op(g23_m, norm.g23, norm.g23_mul);
   }
 }
 
 void ContravariantMetricTensor::normaliseMetric(const MetricNormaliser& norm) {
-  MetricTensor::normaliseMetric(norm, [](FieldMetric& f, auto fac) {
+  MetricTensor::normaliseMetric(norm, [](FieldMetric& f, auto fac, bool fac_mul) {
     if (fac.has_value()) {
       if (f.hasParallelSlices()) {
-        f.asField3DParallel() *= fac.value();
+        if (fac_mul) {
+          f.asField3DParallel() /= fac.value();
+        } else {
+          f.asField3DParallel() *= fac.value();
+        }
       } else {
-        f *= fac.value();
+        if (fac_mul) {
+          f /= fac.value();
+        } else {
+          f *= fac.value();
+        }
       }
     }
   });
 }
 void CovariantMetricTensor::normaliseMetric(const MetricNormaliser& norm) {
-  MetricTensor::normaliseMetric(norm, [](FieldMetric& f, auto fac) {
+  MetricTensor::normaliseMetric(norm, [](FieldMetric& f, auto fac, bool fac_mul) {
     if (fac.has_value()) {
       if (f.hasParallelSlices()) {
-        f.asField3DParallel() /= fac.value();
+        if (fac_mul) {
+          f.asField3DParallel() *= fac.value();
+        } else {
+          f.asField3DParallel() /= fac.value();
+        }
       } else {
-        f /= fac.value();
+        if (fac_mul) {
+          f *= fac.value();
+        } else {
+          f /= fac.value();
+        }
       }
     }
   });
diff --git a/src/mesh/tokamak_coordinates.cxx b/src/mesh/tokamak_coordinates.cxx
index 8f651eec23..dd5e2f0bf2 100644
--- a/src/mesh/tokamak_coordinates.cxx
+++ b/src/mesh/tokamak_coordinates.cxx
@@ -81,14 +81,18 @@ MetricNormaliser TokamakOrFCIMetricNormaliser(const Mesh* mesh, BoutReal Bnorm,
   if (mesh->isFci()) {
     return {.g{SQ(rho_s0)}, .J{rho_s0 * rho_s0 * rho_s0}, .Bxy{Bnorm}};
   }
-  return {.g11{1 / SQ(Bnorm * rho_s0)},
+  return {.g11{SQ(Bnorm * rho_s0)},
+          .g11_mul{true},
           .g22{SQ(rho_s0)},
           .g33{SQ(rho_s0)},
-          .g12{1 / Bnorm},
-          .g13{1 / Bnorm},
+          .g12{Bnorm},
+          .g12_mul{true},
+          .g13{Bnorm},
+          .g13_mul{true},
           .g23{SQ(rho_s0)},
           .dx{rho_s0 * rho_s0 * Bnorm},
-          .J{rho_s0 / Bnorm},
+          .J{Bnorm / rho_s0},
+          .J_mul{true},
           .Bxy{Bnorm}};
 }