diff --git a/MapControl/Shared/PolarStereographicProjection.cs b/MapControl/Shared/PolarStereographicProjection.cs
index c3a9ee34..0f461601 100644
--- a/MapControl/Shared/PolarStereographicProjection.cs
+++ b/MapControl/Shared/PolarStereographicProjection.cs
@@ -32,6 +32,7 @@ namespace MapControl
         {
             var sign = Math.Sign(LatitudeOfOrigin);
             var phi = sign * latitude * Math.PI / 180d;
+
             var e = Math.Sqrt((2d - Flattening) * Flattening);
             var eSinPhi = e * Math.Sin(phi);
             var t = Math.Tan(Math.PI / 4d - phi / 2d)
@@ -55,7 +56,6 @@ namespace MapControl
 
             var e = Math.Sqrt((2d - Flattening) * Flattening);
             var eSinPhi = e * Math.Sin(phi);
-
             var t = Math.Tan(Math.PI / 4d - phi / 2d)
                   / Math.Pow((1d - eSinPhi) / (1d + eSinPhi), e / 2d); // p.161 (15-9)
             // ρ
diff --git a/MapControl/Shared/TransverseMercatorProjection.cs b/MapControl/Shared/TransverseMercatorProjection.cs
index 98a4dea4..c1db6dad 100644
--- a/MapControl/Shared/TransverseMercatorProjection.cs
+++ b/MapControl/Shared/TransverseMercatorProjection.cs
@@ -17,6 +17,7 @@ namespace MapControl
     public class TransverseMercatorProjection : MapProjection
     {
         private readonly double n;
+        private readonly double m;  // 2*sqrt(n)/(1+n)
         private readonly double a1; // α1
         private readonly double a2; // α2
         private readonly double a3; // α3
@@ -26,8 +27,7 @@ namespace MapControl
         private readonly double d1; // δ1
         private readonly double d2; // δ2
         private readonly double d3; // δ3
-        private readonly double f1; // A/a
-        private readonly double f2; // 2*sqrt(n)/(1+n)
+        private readonly double A;
 
         public TransverseMercatorProjection(
             double equatorialRadius, double flattening,
@@ -42,8 +42,10 @@ namespace MapControl
             FalseNorthing = falseNorthing;
 
             n = flattening / (2d - flattening);
+            m = 2d * Math.Sqrt(n) / (1d + n);
             var n2 = n * n;
             var n3 = n * n2;
+
             a1 = n / 2d - n2 * 2d / 3d + n3 * 5d / 16d;
             a2 = n2 * 13d / 48d - n3 * 3d / 5d;
             a3 = n3 * 61d / 240d;
@@ -53,8 +55,7 @@ namespace MapControl
             d1 = n * 2d - n2 * 2d / 3d - n3 * 2d;
             d2 = n2 * 7d / 3d - n3 * 8d / 5d;
             d3 = n3 * 56d / 15d;
-            f1 = (1d + n2 / 4d + n2 * n2 / 64d) / (1d + n);
-            f2 = 2d * Math.Sqrt(n) / (1d + n);
+            A = equatorialRadius / (1d + n) * (1d + n2 / 4d + n2 * n2 / 64d);
         }
 
         public TransverseMercatorProjection(
@@ -87,7 +88,7 @@ namespace MapControl
             var cosLambda = Math.Cos(lambda);
             var tanLambda = Math.Tan(lambda);
             // t
-            var t = Math.Sinh(Atanh(sinPhi) - f2 * Atanh(f2 * sinPhi));
+            var t = Math.Sinh(Atanh(sinPhi) - m * Atanh(m * sinPhi));
             var u = Math.Sqrt(1d + t * t);
             // ξ'
             var xi_ = Math.Atan2(t, cosLambda);
@@ -104,8 +105,9 @@ namespace MapControl
                 4d * a2 * Math.Sin(4d * xi_) * Math.Sinh(4d * eta_) +
                 6d * a3 * Math.Sin(6d * xi_) * Math.Sinh(6d * eta_);
 
-            var m = (1d - n) / (1d + n) * Math.Tan(phi);
-            var k = ScaleFactor * f1 * Math.Sqrt((1d + m * m) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
+            var q = (1d - n) / (1d + n) * Math.Tan(phi);
+            var k = ScaleFactor * A / EquatorialRadius
+                  * Math.Sqrt((1d + q * q) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
 
             // γ, grid convergence
             var gamma = Math.Atan2(tau * u + sigma * t * tanLambda, sigma * u - tau * t * tanLambda);
@@ -122,22 +124,20 @@ namespace MapControl
             var phi = latitude * Math.PI / 180d;
             var sinPhi = Math.Sin(phi);
             // t
-            var t = Math.Sinh(Atanh(sinPhi) - f2 * Atanh(f2 * sinPhi));
+            var t = Math.Sinh(Atanh(sinPhi) - m * Atanh(m * sinPhi));
             // λ - λ0
             var lambda = (longitude - CentralMeridian) * Math.PI / 180d;
             // ξ'
             var xi_ = Math.Atan2(t, Math.Cos(lambda));
             // η'
             var eta_ = Atanh(Math.Sin(lambda) / Math.Sqrt(1d + t * t));
-            // k0 * A
-            var k0A = ScaleFactor * EquatorialRadius * f1;
 
-            var x = FalseEasting + k0A * (eta_ +
+            var x = FalseEasting + ScaleFactor * A * (eta_ +
                 a1 * Math.Cos(2d * xi_) * Math.Sinh(2d * eta_) +
                 a2 * Math.Cos(4d * xi_) * Math.Sinh(4d * eta_) +
                 a3 * Math.Cos(6d * xi_) * Math.Sinh(6d * eta_));
 
-            var y = FalseNorthing + k0A * (xi_ +
+            var y = FalseNorthing + ScaleFactor * A * (xi_ +
                 a1 * Math.Sin(2d * xi_) * Math.Cosh(2d * eta_) +
                 a2 * Math.Sin(4d * xi_) * Math.Cosh(4d * eta_) +
                 a3 * Math.Sin(6d * xi_) * Math.Cosh(6d * eta_));
@@ -147,12 +147,10 @@ namespace MapControl
 
         public override Location MapToLocation(double x, double y)
         {
-            // k0 * A
-            var k0A = ScaleFactor * EquatorialRadius * f1;
             // ξ
-            var xi = (y - FalseNorthing) / k0A;
+            var xi = (y - FalseNorthing) / (ScaleFactor * A);
             // η
-            var eta = (x - FalseEasting) / k0A;
+            var eta = (x - FalseEasting) / (ScaleFactor * A);
             // ξ'
             var xi_ = xi -
                 b1 * Math.Sin(2d * xi) * Math.Cosh(2d * eta) -