diff --git a/src/dimension.h b/src/dimension.h
index 92b56ac25a1027891cecaca696186c985e01a48b..11234fd2c167db8c04351aaec6537a9fefceb170 100644
--- a/src/dimension.h
+++ b/src/dimension.h
@@ -105,8 +105,15 @@ __attribute__((always_inline)) INLINE static float pow_dimension_plus_one(
 #endif
 }
 
+/* ------------------------------------------------------------------------- */
 #ifdef WITH_VECTORIZATION
 
+/**
+ * @brief Returns the argument to the power given by the dimension (vector
+ * version)
+ *
+ * Computes \f$x^d\f$.
+ */
 __attribute__((always_inline)) INLINE static vector pow_dimension_vec(
     vector x) {
 
@@ -130,6 +137,12 @@ __attribute__((always_inline)) INLINE static vector pow_dimension_vec(
 #endif
 }
 
+/**
+ * @brief Returns the argument to the power given by the dimension plus one
+ * (vector version)
+ *
+ * Computes \f$x^{d+1}\f$.
+ */
 __attribute__((always_inline)) INLINE static vector pow_dimension_plus_one_vec(
     vector x) {
 
diff --git a/src/hydro/Default/hydro.h b/src/hydro/Default/hydro.h
index 7fe78f75fc00569ee8d34ea30a822bac394531e2..7abcfefbe8d1320bce70cc4601ef7e61b696f9e5 100644
--- a/src/hydro/Default/hydro.h
+++ b/src/hydro/Default/hydro.h
@@ -173,33 +173,33 @@ __attribute__((always_inline)) INLINE static void hydro_end_density(
 
   /* Some smoothing length multiples. */
   const float h = p->h;
-  const float ih = 1.0f / h;
-  const float ih2 = ih * ih;
-  const float ih4 = ih2 * ih2;
+  const float h_inv = 1.0f / h;                       /* 1/h */
+  const float h_inv_dim = pow_dimension(h_inv);       /* 1/h^d */
+  const float h_inv_dim_plus_one = h_inv_dim * h_inv; /* 1/h^(d+1) */
 
   /* Final operation on the density (add self-contribution). */
   p->rho += p->mass * kernel_root;
-  p->rho_dh -= 3.0f * p->mass * kernel_root;
+  p->rho_dh -= hydro_dimension * p->mass * kernel_root;
   p->density.wcount += kernel_root;
 
   /* Finish the calculation by inserting the missing h-factors */
-  p->rho *= ih * ih2;
-  p->rho_dh *= ih4;
+  p->rho *= h_inv_dim;
+  p->rho_dh *= h_inv_dim_plus_one;
   p->density.wcount *= kernel_norm;
-  p->density.wcount_dh *= ih * kernel_gamma * kernel_norm;
+  p->density.wcount_dh *= h_inv * kernel_gamma * kernel_norm;
 
   const float irho = 1.f / p->rho;
 
   /* Compute the derivative term */
-  p->rho_dh = 1.f / (1.f + 0.33333333f * p->h * p->rho_dh * irho);
+  p->rho_dh = 1.f / (1.f + hydro_dimension_inv * p->h * p->rho_dh * irho);
 
   /* Finish calculation of the velocity curl components */
-  p->density.rot_v[0] *= ih4 * irho;
-  p->density.rot_v[1] *= ih4 * irho;
-  p->density.rot_v[2] *= ih4 * irho;
+  p->density.rot_v[0] *= hydro_dimension_inv * irho;
+  p->density.rot_v[1] *= hydro_dimension_inv * irho;
+  p->density.rot_v[2] *= hydro_dimension_inv * irho;
 
   /* Finish calculation of the velocity divergence */
-  p->density.div_v *= ih4 * irho;
+  p->density.div_v *= hydro_dimension_inv * irho;
 }
 
 /**
@@ -217,7 +217,7 @@ __attribute__((always_inline)) INLINE static void hydro_prepare_force(
 
   /* Some smoothing length multiples. */
   const float h = p->h;
-  const float ih = 1.0f / h;
+  const float h_inv = 1.0f / h;
 
   /* Pre-compute some stuff for the balsara switch. */
   const float normDiv_v = fabs(p->density.div_v);
@@ -231,11 +231,11 @@ __attribute__((always_inline)) INLINE static void hydro_prepare_force(
       sqrtf(hydro_gamma * hydro_gamma_minus_one * u);
 
   /* Compute the P/Omega/rho2. */
-  xp->omega = 1.0f + 0.3333333333f * h * p->rho_dh / p->rho;
+  xp->omega = 1.0f + hydro_dimension_inv * h * p->rho_dh / p->rho;
   p->force.P_over_rho2 = u * hydro_gamma_minus_one / (p->rho * xp->omega);
 
   /* Balsara switch */
-  p->force.balsara = normDiv_v / (normDiv_v + normRot_v + 0.0001f * fc * ih);
+  p->force.balsara = normDiv_v / (normDiv_v + normRot_v + 0.0001f * fc * h_inv);
 
   /* Viscosity parameter decay time */
   const float tau = h / (2.f * const_viscosity_length * p->force.soundspeed);
@@ -309,7 +309,7 @@ __attribute__((always_inline)) INLINE static void hydro_predict_extra(
  */
 __attribute__((always_inline)) INLINE static void hydro_end_force(
     struct part *restrict p) {
-  p->force.h_dt *= p->h * 0.333333333f;
+  p->force.h_dt *= p->h * hydro_dimension_inv;
 }
 
 /**
diff --git a/src/hydro/Default/hydro_iact.h b/src/hydro/Default/hydro_iact.h
index 141ab8f884da7f120f2b636933904f0d795a5d8b..4975cac35aaa3d4b4b9f99319dfd061998014453 100644
--- a/src/hydro/Default/hydro_iact.h
+++ b/src/hydro/Default/hydro_iact.h
@@ -75,7 +75,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_density(
   kernel_deval(xi, &wi, &wi_dx);
 
   pi->rho += mj * wi;
-  pi->rho_dh -= mj * (3.0f * wi + xi * wi_dx);
+  pi->rho_dh -= mj * (hydro_dimension * wi + xi * wi_dx);
   pi->density.wcount += wi;
   pi->density.wcount_dh -= xi * wi_dx;
 
@@ -88,7 +88,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_density(
   kernel_deval(xj, &wj, &wj_dx);
 
   pj->rho += mi * wj;
-  pj->rho_dh -= mi * (3.0f * wj + xj * wj_dx);
+  pj->rho_dh -= mi * (hydro_dimension * wj + xj * wj_dx);
   pj->density.wcount += wj;
   pj->density.wcount_dh -= xj * wj_dx;
 
@@ -174,14 +174,14 @@ __attribute__((always_inline)) INLINE static void runner_iact_vec_density(
   for (k = 0; k < 3; k++) curlvr[k].v *= ri.v;
 
   rhoi.v = mj.v * wi.v;
-  rhoi_dh.v = mj.v * (vec_set1(3.0f) * wi.v + xi.v * wi_dx.v);
+  rhoi_dh.v = mj.v * (vec_set1(hydro_dimension) * wi.v + xi.v * wi_dx.v);
   wcounti.v = wi.v;
   wcounti_dh.v = xi.v * wi_dx.v;
   div_vi.v = mj.v * dvdr.v * wi_dx.v;
   for (k = 0; k < 3; k++) rot_vi[k].v = mj.v * curlvr[k].v * wi_dx.v;
 
   rhoj.v = mi.v * wj.v;
-  rhoj_dh.v = mi.v * (vec_set1(3.0f) * wj.v + xj.v * wj_dx.v);
+  rhoj_dh.v = mi.v * (vec_set1(hydro_dimension) * wj.v + xj.v * wj_dx.v);
   wcountj.v = wj.v;
   wcountj_dh.v = xj.v * wj_dx.v;
   div_vj.v = mi.v * dvdr.v * wj_dx.v;
@@ -250,7 +250,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_density(
   kernel_deval(xi, &wi, &wi_dx);
 
   pi->rho += mj * wi;
-  pi->rho_dh -= mj * (3.0f * wi + xi * wi_dx);
+  pi->rho_dh -= mj * (hydro_dimension * wi + xi * wi_dx);
   pi->density.wcount += wi;
   pi->density.wcount_dh -= xi * wi_dx;
 
@@ -327,7 +327,7 @@ runner_iact_nonsym_vec_density(float *R2, float *Dx, float *Hi, float *Hj,
   for (k = 0; k < 3; k++) curlvr[k].v *= ri.v;
 
   rhoi.v = mj.v * wi.v;
-  rhoi_dh.v = mj.v * (vec_set1(3.0f) * wi.v + xi.v * wi_dx.v);
+  rhoi_dh.v = mj.v * (vec_set1(hydro_dimension) * wi.v + xi.v * wi_dx.v);
   wcounti.v = wi.v;
   wcounti_dh.v = xi.v * wi_dx.v;
   div_vi.v = mj.v * dvdr.v * wi_dx.v;
@@ -358,8 +358,8 @@ __attribute__((always_inline)) INLINE static void runner_iact_force(
 
   float r = sqrtf(r2), ri = 1.0f / r;
   float xi, xj;
-  float hi_inv, hi2_inv;
-  float hj_inv, hj2_inv;
+  float hi_inv, hid_inv;
+  float hj_inv, hjd_inv;
   float wi, wj, wi_dx, wj_dx, wi_dr, wj_dr, w, dvdr;
   float mi, mj, POrho2i, POrho2j, rhoi, rhoj;
   float v_sig, omega_ij, Pi_ij, alpha_ij, tc, v_sig_u;
@@ -376,17 +376,17 @@ __attribute__((always_inline)) INLINE static void runner_iact_force(
 
   /* Get the kernel for hi. */
   hi_inv = 1.0f / hi;
-  hi2_inv = hi_inv * hi_inv;
+  hid_inv = pow_dimension_plus_one(hi_inv); /* 1/h^(d+1) */
   xi = r * hi_inv;
   kernel_deval(xi, &wi, &wi_dx);
-  wi_dr = hi2_inv * hi2_inv * wi_dx;
+  wi_dr = hid_inv * wi_dx;
 
   /* Get the kernel for hj. */
   hj_inv = 1.0f / hj;
-  hj2_inv = hj_inv * hj_inv;
+  hjd_inv = pow_dimension_plus_one(hj_inv); /* 1/h^(d+1) */
   xj = r * hj_inv;
   kernel_deval(xj, &wj, &wj_dx);
-  wj_dr = hj2_inv * hj2_inv * wj_dx;
+  wj_dr = hjd_inv * wj_dx;
 
   /* Compute dv dot r. */
   dvdr = (pi->v[0] - pj->v[0]) * dx[0] + (pi->v[1] - pj->v[1]) * dx[1] +
@@ -457,7 +457,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_vec_force(
   vector r, r2, ri;
   vector xi, xj;
   vector hi, hj, hi_inv, hj_inv;
-  vector hi2_inv, hj2_inv;
+  vector hid_inv, hjd_inv;
   vector wi, wj, wi_dx, wj_dx, wi_dr, wj_dr, dvdr;
   vector w;
   vector piPOrho2, pjPOrho2, pirho, pjrho, piu, pju;
@@ -564,19 +564,19 @@ __attribute__((always_inline)) INLINE static void runner_iact_vec_force(
   hi.v = vec_load(Hi);
   hi_inv.v = vec_rcp(hi.v);
   hi_inv.v = hi_inv.v - hi_inv.v * (hi.v * hi_inv.v - vec_set1(1.0f));
-  hi2_inv.v = hi_inv.v * hi_inv.v;
+  hid_inv = pow_dimension_plus_one_vec(hi_inv);
   xi.v = r.v * hi_inv.v;
   kernel_deval_vec(&xi, &wi, &wi_dx);
-  wi_dr.v = hi2_inv.v * hi2_inv.v * wi_dx.v;
+  wi_dr.v = hid_inv.v * wi_dx.v;
 
   /* Get the kernel for hj. */
   hj.v = vec_load(Hj);
   hj_inv.v = vec_rcp(hj.v);
   hj_inv.v = hj_inv.v - hj_inv.v * (hj.v * hj_inv.v - vec_set1(1.0f));
-  hj2_inv.v = hj_inv.v * hj_inv.v;
+  hjd_inv = pow_dimension_plus_one_vec(hj_inv);
   xj.v = r.v * hj_inv.v;
   kernel_deval_vec(&xj, &wj, &wj_dx);
-  wj_dr.v = hj2_inv.v * hj2_inv.v * wj_dx.v;
+  wj_dr.v = hjd_inv.v * wj_dx.v;
 
   /* Compute dv dot r. */
   dvdr.v = ((vi[0].v - vj[0].v) * dx[0].v) + ((vi[1].v - vj[1].v) * dx[1].v) +
@@ -659,8 +659,8 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_force(
 
   float r = sqrtf(r2), ri = 1.0f / r;
   float xi, xj;
-  float hi_inv, hi2_inv;
-  float hj_inv, hj2_inv;
+  float hi_inv, hid_inv;
+  float hj_inv, hjd_inv;
   float wi, wj, wi_dx, wj_dx, wi_dr, wj_dr, w, dvdr;
   float /*mi,*/ mj, POrho2i, POrho2j, rhoi, rhoj;
   float v_sig, omega_ij, Pi_ij, alpha_ij, tc, v_sig_u;
@@ -677,17 +677,17 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_force(
 
   /* Get the kernel for hi. */
   hi_inv = 1.0f / hi;
-  hi2_inv = hi_inv * hi_inv;
+  hid_inv = pow_dimension_plus_one(hi_inv); /* 1/h^(d+1) */
   xi = r * hi_inv;
   kernel_deval(xi, &wi, &wi_dx);
-  wi_dr = hi2_inv * hi2_inv * wi_dx;
+  wi_dr = hid_inv * wi_dx;
 
   /* Get the kernel for hj. */
   hj_inv = 1.0f / hj;
-  hj2_inv = hj_inv * hj_inv;
+  hjd_inv = pow_dimension_plus_one(hj_inv); /* 1/h^(d+1) */
   xj = r * hj_inv;
   kernel_deval(xj, &wj, &wj_dx);
-  wj_dr = hj2_inv * hj2_inv * wj_dx;
+  wj_dr = hjd_inv * wj_dx;
 
   /* Compute dv dot r. */
   dvdr = (pi->v[0] - pj->v[0]) * dx[0] + (pi->v[1] - pj->v[1]) * dx[1] +
@@ -752,7 +752,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_vec_force(
   vector r, r2, ri;
   vector xi, xj;
   vector hi, hj, hi_inv, hj_inv;
-  vector hi2_inv, hj2_inv;
+  vector hid_inv, hjd_inv;
   vector wi, wj, wi_dx, wj_dx, wi_dr, wj_dr, dvdr;
   vector w;
   vector piPOrho2, pjPOrho2, pirho, pjrho, piu, pju;
@@ -856,19 +856,19 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_vec_force(
   hi.v = vec_load(Hi);
   hi_inv.v = vec_rcp(hi.v);
   hi_inv.v = hi_inv.v - hi_inv.v * (hi.v * hi_inv.v - vec_set1(1.0f));
-  hi2_inv.v = hi_inv.v * hi_inv.v;
+  hid_inv = pow_dimension_plus_one_vec(hi_inv);
   xi.v = r.v * hi_inv.v;
   kernel_deval_vec(&xi, &wi, &wi_dx);
-  wi_dr.v = hi2_inv.v * hi2_inv.v * wi_dx.v;
+  wi_dr.v = hid_inv.v * wi_dx.v;
 
   /* Get the kernel for hj. */
   hj.v = vec_load(Hj);
   hj_inv.v = vec_rcp(hj.v);
   hj_inv.v = hj_inv.v - hj_inv.v * (hj.v * hj_inv.v - vec_set1(1.0f));
-  hj2_inv.v = hj_inv.v * hj_inv.v;
+  hjd_inv = pow_dimension_plus_one_vec(hj_inv);
   xj.v = r.v * hj_inv.v;
   kernel_deval_vec(&xj, &wj, &wj_dx);
-  wj_dr.v = hj2_inv.v * hj2_inv.v * wj_dx.v;
+  wj_dr.v = hjd_inv.v * wj_dx.v;
 
   /* Compute dv dot r. */
   dvdr.v = ((vi[0].v - vj[0].v) * dx[0].v) + ((vi[1].v - vj[1].v) * dx[1].v) +
diff --git a/src/hydro/Minimal/hydro.h b/src/hydro/Minimal/hydro.h
index 444920ab2bec940af9c10ea0a6ba471b2ab79762..1433136ad906beba491636716f38b98da2699b26 100644
--- a/src/hydro/Minimal/hydro.h
+++ b/src/hydro/Minimal/hydro.h
@@ -182,25 +182,25 @@ __attribute__((always_inline)) INLINE static void hydro_end_density(
 
   /* Some smoothing length multiples. */
   const float h = p->h;
-  const float ih = 1.0f / h;
-  const float ih2 = ih * ih;
-  const float ih4 = ih2 * ih2;
+  const float h_inv = 1.0f / h;                       /* 1/h */
+  const float h_inv_dim = pow_dimension(h_inv);       /* 1/h^d */
+  const float h_inv_dim_plus_one = h_inv_dim * h_inv; /* 1/h^(d+1) */
 
   /* Final operation on the density (add self-contribution). */
   p->rho += p->mass * kernel_root;
-  p->rho_dh -= 3.0f * p->mass * kernel_root;
+  p->rho_dh -= hydro_dimension * p->mass * kernel_root;
   p->density.wcount += kernel_root;
 
   /* Finish the calculation by inserting the missing h-factors */
-  p->rho *= ih * ih2;
-  p->rho_dh *= ih4;
+  p->rho *= h_inv_dim;
+  p->rho_dh *= h_inv_dim_plus_one;
   p->density.wcount *= kernel_norm;
-  p->density.wcount_dh *= ih * kernel_gamma * kernel_norm;
+  p->density.wcount_dh *= h_inv * kernel_gamma * kernel_norm;
 
   const float irho = 1.f / p->rho;
 
   /* Compute the derivative term */
-  p->rho_dh = 1.f / (1.f + 0.33333333f * p->h * p->rho_dh * irho);
+  p->rho_dh = 1.f / (1.f + hydro_dimension_inv * p->h * p->rho_dh * irho);
 }
 
 /**
@@ -281,7 +281,7 @@ __attribute__((always_inline)) INLINE static void hydro_predict_extra(
 __attribute__((always_inline)) INLINE static void hydro_end_force(
     struct part *restrict p) {
 
-  p->force.h_dt *= p->h * 0.333333333f;
+  p->force.h_dt *= p->h * hydro_dimension_inv;
 }
 
 /**
diff --git a/src/hydro/Minimal/hydro_iact.h b/src/hydro/Minimal/hydro_iact.h
index 311bdc90744059ea1272c2ca6cf419e5fbc1ba82..9eda45760248ebc0dde18e503abe0b1288659518 100644
--- a/src/hydro/Minimal/hydro_iact.h
+++ b/src/hydro/Minimal/hydro_iact.h
@@ -48,7 +48,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_density(
   kernel_deval(xi, &wi, &wi_dx);
 
   pi->rho += mj * wi;
-  pi->rho_dh -= mj * (3.f * wi + xi * wi_dx);
+  pi->rho_dh -= mj * (hydro_dimension * wi + xi * wi_dx);
   pi->density.wcount += wi;
   pi->density.wcount_dh -= xi * wi_dx;
 
@@ -58,7 +58,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_density(
   kernel_deval(xj, &wj, &wj_dx);
 
   pj->rho += mi * wj;
-  pj->rho_dh -= mi * (3.f * wj + xj * wj_dx);
+  pj->rho_dh -= mi * (hydro_dimension * wj + xj * wj_dx);
   pj->density.wcount += wj;
   pj->density.wcount_dh -= xj * wj_dx;
 }
@@ -93,7 +93,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_density(
   kernel_deval(xi, &wi, &wi_dx);
 
   pi->rho += mj * wi;
-  pi->rho_dh -= mj * (3.f * wi + xi * wi_dx);
+  pi->rho_dh -= mj * (hydro_dimension * wi + xi * wi_dx);
   pi->density.wcount += wi;
   pi->density.wcount_dh -= xi * wi_dx;
 }
@@ -128,19 +128,19 @@ __attribute__((always_inline)) INLINE static void runner_iact_force(
 
   /* Get the kernel for hi. */
   const float hi_inv = 1.0f / hi;
-  const float hi2_inv = hi_inv * hi_inv;
+  const float hid_inv = pow_dimension_plus_one(hi_inv); /* 1/h^(d+1) */
   const float xi = r * hi_inv;
   float wi, wi_dx;
   kernel_deval(xi, &wi, &wi_dx);
-  const float wi_dr = hi2_inv * hi2_inv * wi_dx;
+  const float wi_dr = hid_inv * wi_dx;
 
   /* Get the kernel for hj. */
   const float hj_inv = 1.0f / hj;
-  const float hj2_inv = hj_inv * hj_inv;
+  const float hjd_inv = pow_dimension_plus_one(hj_inv); /* 1/h^(d+1) */
   const float xj = r * hj_inv;
   float wj, wj_dx;
   kernel_deval(xj, &wj, &wj_dx);
-  const float wj_dr = hj2_inv * hj2_inv * wj_dx;
+  const float wj_dr = hjd_inv * wj_dx;
 
   /* Compute gradient terms */
   const float P_over_rho_i = pressurei / (rhoi * rhoi) * pi->rho_dh;
@@ -211,19 +211,19 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_force(
 
   /* Get the kernel for hi. */
   const float hi_inv = 1.0f / hi;
-  const float hi2_inv = hi_inv * hi_inv;
+  const float hid_inv = pow_dimension_plus_one(hi_inv); /* 1/h^(d+1) */
   const float xi = r * hi_inv;
   float wi, wi_dx;
   kernel_deval(xi, &wi, &wi_dx);
-  const float wi_dr = hi2_inv * hi2_inv * wi_dx;
+  const float wi_dr = hid_inv * wi_dx;
 
   /* Get the kernel for hj. */
   const float hj_inv = 1.0f / hj;
-  const float hj2_inv = hj_inv * hj_inv;
+  const float hjd_inv = pow_dimension_plus_one(hj_inv); /* 1/h^(d+1) */
   const float xj = r * hj_inv;
   float wj, wj_dx;
   kernel_deval(xj, &wj, &wj_dx);
-  const float wj_dr = hj2_inv * hj2_inv * wj_dx;
+  const float wj_dr = hjd_inv * wj_dx;
 
   /* Compute gradient terms */
   const float P_over_rho_i = pressurei / (rhoi * rhoi) * pi->rho_dh;