A 4 m x 4 m toroidal heliostat with receiver oriented dual-axis tracking, also called spinning-elevation tracking, was developed as an auxiliary heat source for a hydrogen production system. A series of spinning-elevation tracking formulas have been derived for this heliostat. This included basic tracking formulas, a formula for the elevation angle for heliostat with a mirror-pivot offset, and a more general formula for the biased elevation angle. This paper presents the new tracking formulas in detail and analyzes the accuracy of applying a simplifying approximation. The numerical results show these receiver oriented dual-axis tracking formula approximations are accurate to within 2.5 x 10(-6) m in image plane. Some practical tracking strategies are discussed briefly. Solar images from the toroidal heliostat at selected times are also presented. (C) 2010 Elsevier Ltd. All rights reserved.