Chapter 3.1 Distances, angles, and their standard uncertainties

Reciprocal space

First Online Edition (2006)

Part 3. Dual bases in crystallographic computing

  1. D. E. Sands

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000559

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Sands, D. E. 2006. Distances, angles, and their standard uncertainties. International Tables for Crystallography. B:3:3.1:348–352.

Author Information

  1. Department of Chemistry, University of Kentucky, Chemistry–Physics Building, Lexington, Kentucky 40506-0055, USA

Publication History

  1. Published Online: 1 JAN 2006


Methods for calculating distances and angles and the standard uncertainties in these quantities using the techniques of tensor analysis are described. A Fortran program showing how this tensor formulation can be adapted to computer languages is also given.


  • standard uncertainties;
  • bond lengths;
  • bond angles;
  • scalar products;
  • vectors;
  • vector product;
  • vector length;
  • permutation tensors;
  • components of vector products;
  • vector relationships;
  • planes;
  • variance–covariance matrices;
  • mean values