diff --git a/dlib/cuda/cpu_dlib.cpp b/dlib/cuda/cpu_dlib.cpp
index 252cb9413..b1ba41a83 100644
--- a/dlib/cuda/cpu_dlib.cpp
+++ b/dlib/cuda/cpu_dlib.cpp
@@ -1711,7 +1711,7 @@ namespace dlib
             const tensor& gradient_input
         )
         {
-            const float beta = 1.0f / std::sqrt(pi) / sqrt_2;
+            const float beta = 1.0f / std::sqrt(2.0f * pi);
             const auto compute_gradient = [beta](float x)
             {
                 const float cdf = 0.5f*(1.0f + std::erf(x/sqrt_2));
diff --git a/dlib/cuda/cuda_dlib.cu b/dlib/cuda/cuda_dlib.cu
index 7ac740d63..9f4cc9287 100644
--- a/dlib/cuda/cuda_dlib.cu
+++ b/dlib/cuda/cuda_dlib.cu
@@ -4,6 +4,7 @@
 #include "cuda_utils.h"
 #include "cuda_dlib.h"
 #include "cudnn_dlibapi.h"
+#include <math_constants.h>
 
 
 namespace dlib 
@@ -1501,7 +1502,7 @@ namespace dlib
 
         __device__ float gelu_compute_gradient(float x)
         {
-                const float beta = 1.0f / std::sqrt(pi) / sqrt_2;
+                const float beta = 1.0f / CUDART_SQRT_2PI;
                 const float cdf = normcdf(x);
                 const float pdf = beta*std::exp(-0.5f*x*x);
                 return cdf + x * pdf;