As of Version 9.0, vector analysis functionality is built into the Wolfram Language »


gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f1,f2,f3} with respect to the parameter t in the default coordinate system.


gives the derivative of the arc length of a curve in the coordinate system coordsys.


  • To use ArcLengthFactor, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • The parametrized curve coordinates {f1,f2,f3} should be given in coordsys, if specified, or the default coordinate system otherwise.
  • If the parametrized curve coordinates {f1,f2,f3} are not given, the default coordinate variables for coordsys are used.
  • Integrate[ArcLengthFactor[{f1,f2,f3},t],{t,t1,t2}] gives the length of the arc described by {f1,f2,f3} from t1 to t2.


Basic Examples  (1)

Find the arc length factor of a helix:

Compute the arc length of the helix from t=0 to t=20: