diff --git a/gtsam/linear/GaussianBayesNet.h b/gtsam/linear/GaussianBayesNet.h
index 9da7a1609..3f6d69e91 100644
--- a/gtsam/linear/GaussianBayesNet.h
+++ b/gtsam/linear/GaussianBayesNet.h
@@ -143,7 +143,7 @@ namespace gtsam {
      *        allocateVectorValues */
     VectorValues gradientAtZero() const;
 
-    /** Mahalanobis norm error. */
+    /** 0.5 * sum of squared Mahalanobis distances. */
     double error(const VectorValues& x) const;
 
     /**
diff --git a/gtsam/linear/GaussianBayesTree.h b/gtsam/linear/GaussianBayesTree.h
index fcc73f80e..b6f5acd52 100644
--- a/gtsam/linear/GaussianBayesTree.h
+++ b/gtsam/linear/GaussianBayesTree.h
@@ -106,7 +106,7 @@ namespace gtsam {
      * @return A VectorValues storing the gradient. */
     VectorValues gradientAtZero() const;
 
-    /** Mahalanobis norm error. */
+    /** 0.5 * sum of squared Mahalanobis distances. */
     double error(const VectorValues& x) const;
 
     /** Computes the determinant of a GassianBayesTree, as if the Bayes tree is reorganized into a
diff --git a/gtsam/linear/NoiseModel.cpp b/gtsam/linear/NoiseModel.cpp
index a6ebea394..b324ea784 100644
--- a/gtsam/linear/NoiseModel.cpp
+++ b/gtsam/linear/NoiseModel.cpp
@@ -157,7 +157,7 @@ Vector Gaussian::unwhiten(const Vector& v) const {
 }
 
 /* ************************************************************************* */
-double Gaussian::Mahalanobis(const Vector& v) const {
+double Gaussian::squaredMahalanobisDistance(const Vector& v) const {
   // Note: for Diagonal, which does ediv_, will be correct for constraints
   Vector w = whiten(v);
   return w.dot(w);
@@ -573,7 +573,7 @@ void Isotropic::print(const string& name) const {
 }
 
 /* ************************************************************************* */
-double Isotropic::Mahalanobis(const Vector& v) const {
+double Isotropic::squaredMahalanobisDistance(const Vector& v) const {
   return v.dot(v) * invsigma_ * invsigma_;
 }
 
diff --git a/gtsam/linear/NoiseModel.h b/gtsam/linear/NoiseModel.h
index 6c42fc7ba..4d86e77da 100644
--- a/gtsam/linear/NoiseModel.h
+++ b/gtsam/linear/NoiseModel.h
@@ -207,12 +207,25 @@ namespace gtsam {
       virtual Vector unwhiten(const Vector& v) const;
 
       /**
-       * Mahalanobis distance v'*R'*R*v = <R*v,R*v>
+       * Squared Mahalanobis distance v'*R'*R*v = <R*v,R*v>
        */
-      virtual double Mahalanobis(const Vector& v) const;
+      virtual double squaredMahalanobisDistance(const Vector& v) const;
+
+      /**
+       * Mahalanobis distance
+       */
+      virtual double mahalanobisDistance(const Vector& v) const {
+        return std::sqrt(squaredMahalanobisDistance(v));
+      }
+
+#ifdef GTSAM_ALLOW_DEPRECATED_SINCE_V4
+      virtual double Mahalanobis(const Vector& v) const {
+        return squaredMahalanobisDistance(v);
+      }
+#endif
 
       inline virtual double distance(const Vector& v) const {
-        return Mahalanobis(v);
+        return squaredMahalanobisDistance(v);
       }
 
       /**
@@ -564,7 +577,7 @@ namespace gtsam {
       }
 
       virtual void print(const std::string& name) const;
-      virtual double Mahalanobis(const Vector& v) const;
+      virtual double squaredMahalanobisDistance(const Vector& v) const;
       virtual Vector whiten(const Vector& v) const;
       virtual Vector unwhiten(const Vector& v) const;
       virtual Matrix Whiten(const Matrix& H) const;
@@ -616,7 +629,7 @@ namespace gtsam {
       virtual bool isUnit() const { return true; }
 
       virtual void print(const std::string& name) const;
-      virtual double Mahalanobis(const Vector& v) const {return v.dot(v); }
+      virtual double squaredMahalanobisDistance(const Vector& v) const {return v.dot(v); }
       virtual Vector whiten(const Vector& v) const { return v; }
       virtual Vector unwhiten(const Vector& v) const { return v; }
       virtual Matrix Whiten(const Matrix& H) const { return H; }
diff --git a/gtsam/linear/tests/testNoiseModel.cpp b/gtsam/linear/tests/testNoiseModel.cpp
index 10578627f..3f6550b9f 100644
--- a/gtsam/linear/tests/testNoiseModel.cpp
+++ b/gtsam/linear/tests/testNoiseModel.cpp
@@ -68,10 +68,10 @@ TEST(NoiseModel, constructors)
   for(Gaussian::shared_ptr mi: m)
     EXPECT(assert_equal(unwhitened,mi->unwhiten(whitened)));
 
-  // test Mahalanobis distance
+  // test squared Mahalanobis distance
   double distance = 5*5+10*10+15*15;
   for(Gaussian::shared_ptr mi: m)
-    DOUBLES_EQUAL(distance,mi->Mahalanobis(unwhitened),1e-9);
+    DOUBLES_EQUAL(distance,mi->squaredMahalanobisDistance(unwhitened),1e-9);
 
   // test R matrix
   for(Gaussian::shared_ptr mi: m)