diff --git a/src/modules/common/moduleRandom.f90 b/src/modules/common/moduleRandom.f90
index 7d9cec6..156f5e4 100644
--- a/src/modules/common/moduleRandom.f90
+++ b/src/modules/common/moduleRandom.f90
@@ -47,22 +47,23 @@ MODULE moduleRandom
 
     END FUNCTION randomIntAB
 
-    !Returns a random number in a Maxwellian distribution of mean 0 and width 1
+    !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
 
       REAL(8):: rnd
-      REAL(8):: x, y
+      REAL(8):: v1, v2, Rsquare
 
-      rnd = 0.D0
-      x = 0.D0
-      DO WHILE (x == 0.D0)
-        CALL RANDOM_NUMBER(x)
-      END DO
-      CALL RANDOM_NUMBER(y)
+      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
 
-      rnd = DSQRT(-2.D0*DLOG(x))*DCOS(2.D0*PI*y)
+      end do
+
+      rnd = v2 * sqrt(-2.D0 * log(Rsquare) / Rsquare)
 
     END FUNCTION randomMaxwellian
 
diff --git a/src/modules/moduleInject.f90 b/src/modules/moduleInject.f90
index 4fb855a..5e72835 100644
--- a/src/modules/moduleInject.f90
+++ b/src/modules/moduleInject.f90
@@ -289,7 +289,7 @@ MODULE moduleInject
       REAL(8):: v
       v = 0.D0
 
-      v = self%vTh*randomMaxwellian()
+      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()
+      v = sqrt(2.0)*self%vTh*randomHalfMaxwellian()
 
     END FUNCTION randomVelHalfMaxwellian