diff --git a/python/core/geometry/qgscurve.sip.in b/python/core/geometry/qgscurve.sip.in
index 8e0d1a4e800..00b6516bd43 100644
--- a/python/core/geometry/qgscurve.sip.in
+++ b/python/core/geometry/qgscurve.sip.in
@@ -186,6 +186,26 @@ Returns the y-coordinate of the specified node in the line string.
 Returns a QPolygonF representing the points.
 %End
 
+    double straightDistance2d() const;
+%Docstring
+Returns the straight distance of the curve, i.e. the direct/euclidean distance
+between the first and last vertex of the curve. (Also known as
+"as the crow flies" distance).
+
+.. versionadded:: 3.2
+%End
+
+    double sinuosity() const;
+%Docstring
+Returns the curve sinuosity, which is the ratio of the curve length() to curve
+straightDistance2d(). Larger numbers indicate a more "sinuous" curve (i.e. more
+"bendy"). The minimum value returned of 1.0 indicates a perfectly straight curve.
+
+If a curve isClosed(), it has infinite sinuosity and will return NaN.
+
+.. versionadded:: 3.2
+%End
+
 
 
   protected:
diff --git a/src/core/geometry/qgscurve.cpp b/src/core/geometry/qgscurve.cpp
index 0ff86f01918..dd90a760e17 100644
--- a/src/core/geometry/qgscurve.cpp
+++ b/src/core/geometry/qgscurve.cpp
@@ -200,6 +200,20 @@ QPolygonF QgsCurve::asQPolygonF() const
   return points;
 }
 
+double QgsCurve::straightDistance2d() const
+{
+  return startPoint().distance( endPoint() );
+}
+
+double QgsCurve::sinuosity() const
+{
+  double d = straightDistance2d();
+  if ( qgsDoubleNear( d, 0.0 ) )
+    return std::numeric_limits<double>::quiet_NaN();
+
+  return length() / d;
+}
+
 void QgsCurve::clearCache() const
 {
   mBoundingBox = QgsRectangle();
diff --git a/src/core/geometry/qgscurve.h b/src/core/geometry/qgscurve.h
index ff84cfec680..e331c94b61c 100644
--- a/src/core/geometry/qgscurve.h
+++ b/src/core/geometry/qgscurve.h
@@ -168,6 +168,26 @@ class CORE_EXPORT QgsCurve: public QgsAbstractGeometry
      */
     QPolygonF asQPolygonF() const;
 
+    /**
+     * Returns the straight distance of the curve, i.e. the direct/euclidean distance
+     * between the first and last vertex of the curve. (Also known as
+     * "as the crow flies" distance).
+     *
+     * \since QGIS 3.2
+     */
+    double straightDistance2d() const;
+
+    /**
+     * Returns the curve sinuosity, which is the ratio of the curve length() to curve
+     * straightDistance2d(). Larger numbers indicate a more "sinuous" curve (i.e. more
+     * "bendy"). The minimum value returned of 1.0 indicates a perfectly straight curve.
+     *
+     * If a curve isClosed(), it has infinite sinuosity and will return NaN.
+     *
+     * \since QGIS 3.2
+     */
+    double sinuosity() const;
+
 #ifndef SIP_RUN
 
     /**