diff --git a/src/modules/common/moduleRandom.f90 b/src/modules/common/moduleRandom.f90
index 1b8ec67..156f5e4 100644
--- a/src/modules/common/moduleRandom.f90
+++ b/src/modules/common/moduleRandom.f90
@@ -48,23 +48,24 @@ MODULE moduleRandom
     END FUNCTION randomIntAB
 
     !Returns a random number in a Maxwellian distribution of mean 0 and width 1 with the Box-Muller Method
-    function randomMaxwellian() result(rnd)
-      USE moduleConstParam, only: pi
-      implicit none
+    FUNCTION randomMaxwellian() RESULT(rnd)
+      USE moduleConstParam, ONLY: PI
+      IMPLICIT NONE
 
-      real(8):: rnd
-      real(8):: v1, v2, Rsquare
+      REAL(8):: rnd
+      REAL(8):: v1, v2, Rsquare
 
-      v1 = 0.d0
-      do while (v1 <= 0.d0)
-        v1 = random()
+      Rsquare = 1.D0
+      do while (Rsquare >= 1.D0 .and. Rsquare > 0.D0)
+        v1 = 2.D0 * random() - 1.D0
+        v2 = 2.D0 * random() - 1.D0
+        Rsquare = v1**2 + v2**2
 
       end do
-      v2 = random()
 
-      rnd = sqrt(-2.d0*log(v1))*cos(2*pi*v2)
+      rnd = v2 * sqrt(-2.D0 * log(Rsquare) / Rsquare)
 
-    end function randomMaxwellian
+    END FUNCTION randomMaxwellian
 
     !Returns a random number in a Maxwellian distribution of mean 0 and width 1
     FUNCTION randomHalfMaxwellian() RESULT(rnd)
diff --git a/src/modules/moduleInject.f90 b/src/modules/moduleInject.f90
index 099f4a7..0d761ea 100644
--- a/src/modules/moduleInject.f90
+++ b/src/modules/moduleInject.f90
@@ -257,7 +257,7 @@ MODULE moduleInject
       CLASS(velDistGeneric), ALLOCATABLE, INTENT(out):: velDist
       REAL(8), INTENT(in):: temperature, m
 
-      velDist = velDistMaxwellian(vTh = DSQRT(2.d0*temperature/m))
+      velDist = velDistMaxwellian(vTh = DSQRT(temperature/m))
 
     END SUBROUTINE initVelDistMaxwellian
 
@@ -267,7 +267,7 @@ MODULE moduleInject
       CLASS(velDistGeneric), ALLOCATABLE, INTENT(out):: velDist
       REAL(8), INTENT(in):: temperature, m
 
-      velDist = velDistHalfMaxwellian(vTh = DSQRT(2.d0*temperature/m))
+      velDist = velDistHalfMaxwellian(vTh = DSQRT(temperature/m))
 
     END SUBROUTINE initVelDistHalfMaxwellian
 
@@ -289,7 +289,7 @@ MODULE moduleInject
       REAL(8):: v
       v = 0.D0
 
-      v = self%vTh*randomMaxwellian()/sqrt(2.d0)
+      v = sqrt(2.0)*self%vTh*randomMaxwellian()
 
     END FUNCTION randomVelMaxwellian
 
@@ -302,7 +302,7 @@ MODULE moduleInject
       REAL(8):: v
       v = 0.D0
 
-      v = self%vTh*randomHalfMaxwellian()/sqrt(2.d0)
+      v = sqrt(2.0)*self%vTh*randomHalfMaxwellian()
 
     END FUNCTION randomVelHalfMaxwellian