Wednesday 10 January 2024

Sexagesimal Stonehenge – The Geometry of the Stonehenge Sarsen Trilithons

Sexagesimal Stonehenge – The Geometry of the Stonehenge Sarsen Trilithons.

(Updated draft)

Tim Daw*


Sexagesimal Stonehenge and the Bush Barrow Lozenge - Tim Daw

      Stonehenge is a mystery that attracts explanations which range from the banal to the fantastic. To claim a new theory is original, interesting, and credible is to set a high hurdle. This brief note presents what is believed to be a new geometric design that is simple, elegant, and intriguing.

      The positions of the five sarsen trilithons of the inner horseshoe at Stonehenge can be explained by a simple plan of chords based on the sixty points of the outer sarsen circle. This layout provides an accurate geometry for aligning to all the solstitial sunrises and sunsets.

      The same geometry is exhibited by the Bush Barrow Lozenge.


Key Words: Stonehenge, Bush Barrow Lozenge, Trilithons, Geometry, Sexagesimal.

* January 2024 Preprint DOI: 10.13140/RG.2.2.16275.86560 License  CC BY-SA 4.0

* January 2024 Revised Draft License  CC BY-SA 4.0

* *Cannings Cross Farm, All Cannings, Devizes Wiltshire SN10 3NP

* 750 Words


      From the earliest surveys of Stonehenge, the plans of the stone setting have attracted geometric speculation. From Inigo Jones (1655), Stukeley (1740) John Wood (1747) and John Smith(1771) to the innumerable modern speculators the arrangement of the stones has been attempted to be explained by many different diagrams.  Figure 1 is believed to be most accurate plan of the present positions of the stones.


Figure 1 Stonehenge Plan by Anthony Johnson, licensed under the Creative Commons Attribution 3.0 Unported license.

      For ease of explanation, I have taken the plan and turned it so the solstical axis is vertical. This is the alignment of the Midsummer Sunrise and Midwinter Sunset that passes through the monument. 


Figure 2 Modified Stonehenge Plan by Tim Daw based on Stonehenge Plan by Anthony Johnson, licensed under the Creative Commons Attribution 3.0 Unported license.


      In “The Twisted Trilithon – Stone 56 and its Skew”, Daw T 2015, it was argued that the central trilithon, Stones 55. 56 and 156, and the Altar Stone, 80 were originally positioned at an angle to the perpendicular of the solstical axis described, and that this angle of about 80 degrees to the axis aligned them to the other solstical sunrise and sunset, the midwinter sunrise and midsummer sunset. The calculated angle for this alignment is ”80° 49' 25" in 2500BCE, very close to 81° “ (Banton S, Pers Comm 2024).

      The outer circle of Sarsens can be considered to have had thirty standing stones and thirty gaps.  There appear to be parchmarks where missing stones are expected, Banton et al 2014, and so it is justifiable to use a completed circle as the template. Taking the centres of these we can generate a familiar pattern of sixty marks in a circle.

Figure 3 Clockface image generated by Tim Daw

      The diagram has every fifth mark enlarged; this is purely for ease of understanding as it echoes the familiar clockface.  Also added are a central marker and a central circle at half the diameter of the outer circle.

      A geometric property of such a circle is that a chord, a line across a circle that doesn’t necessarily pass through the centre, can be easily drawn at 81 degrees to a diameter line. To use the familiar clock idiom a line drawn from 42 minutes to 15 minutes is at 81 degrees to the vertical line. The same angle as the claimed additional solstical lines of the stones 55-56 and the Altar Stone.

       The Bush Barrow Gold lozenge found close to Stonehenge in Bowl Barrow Wilsford G5 as part of a rich assemblage of grave goods, now in the Wiltshire Museum, is based on the 81-degree angle. It dates from a more recent period than the construction of Stonehenge, but its use of the same angle suggests that the knowledge of its significance and method of recording it had continued.     


      Figure 4 The Bush Barrow Lozenge, Wiltshire Museum Photograph, overlain with angled lines and clockface by Tim Daw


      The other four trilithons of the inner horseshoe are also positioned on regular chords across the circle, to within an acceptable accuracy of the plan and their present positions which have been subject to movement and even re-erection.

      They appear to be positioned so that the centre of the flat inner surface of each trilithon is halfway from the outer circle to the centre of the monument.

      The proposed chords and as an overlay on the plan: 

 Figure 5 Clockface plan with chords generated by Tim Daw


Figure 6 Stonehenge Plan with chords. Based on figures 2 and 5

      This simple diagram with the suggestion that the architects of Stonehenge used the geometry of a sexagesimal circle may form the basis of further speculation and insights.


Acknowledgement: The invaluable help from Simon Banton in sharing his knowledge, skills, and enthusiasm. This paper is self-funded.


BANTON, S, et al. 2014 Parchmarks at Stonehenge, July 2013. Antiquity. 2014;88(341):733-739.

Banton S, 2024. WhatsApp message 3 January 2024

DAW, T 2015 The Twisted Trilithon – Stone 56 and its Skew,   WANHM vol. 108 (2015 pp15-24)

JONES I, 1655. The most notable antiquity of Great Britain, vulgarly called Stone-Heng on Salisbury plain, London

SMITH, J. 1771. Choir Gaur: The Grand Orrery of the Ancient Druids, Commonly Called Stonehenge on Salisbury Plain, Astronomically Explained and Mathematically Proved to be a Temple Erected in the Earliest Ages ... United Kingdom

STUKELEY W, 1740. Stonehenge, a Temple Restor'd to the British Druids, London : Printed for W. Innys and R. Manby, London

WOOD, John. 1747 Choir Gaure, Vulgarly called Stonehenge, on Salisbury Plain, Oxford




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