81 degrees at Stonehenge

This post is the companion to the short film 81 degrees at Stonehenge. It sets out why two stones at the centre of the monument are turned off the solstice axis, how far, and how the angle can be laid out with a single straight line. The evidence, numbers and caveats follow.

The axis

Stonehenge's main axis runs from the midsummer sunrise in the north-east to the midwinter sunset in the south-west, through the entrance gap between Stones 30 and 1. The reference value used here is the geometrical axis of the trilithon horseshoe, 49.95° true (49.81° on the National Grid; Thom et al. 1974), which Ruggles takes as the best estimate (49.8° ± 0.2°). Most of the stones at the centre are set square to it. Two are not.

Plan of the standing stones with the solstice axis. Stone positions from T. Daw's 3D model; Stone 56 from the Rees 1989 survey.

The Altar Stone

Atkinson (1956) noted that the Altar Stone, the recumbent green sandstone slab at the centre, does not lie at right angles to the axis. Gordon and Phyllis Freeman (2001) observed that its twist lines it up with the midwinter sunrise. Simon Banton later ran the same line through a tooled notch in Stone 58 and along the edge of Stone 53, and found it ran along the centre line of the Altar Stone. Parker Pearson et al. (2024) describe its long sides as "aligned approximately on the midwinter sunrise".

Most of the Altar Stone lies under the fallen Stone 55 and lintel 156, so modern surveys show only small exposed patches. The two plans that draw its whole outline, Petrie's (1880) and Atkinson's plan of his cutting 53 (Cleal et al. 1995, Fig. 286), put its long axis at about 82–83° to the solstice axis, each to about ±1.5°. The film calls it "near 81°".

The Altar Stone against a square-set line. Outline schematic.

Stone 56 and the Great Trilithon

Stone 56, the tallest stone at Stonehenge and the surviving upright of the Great Trilithon, is turned the same way. The twist was first noted on sarsen.org in June 2012 and published in 2015 as "about 80°" to the axis, a skew of about 10° (Daw 2015). Stone 56 was leaning badly in 1901, and William Gowland excavated around it while it was straightened. His record shows it was reset in its original position, and his excavation of the socket of the fallen Stone 55 showed how its partner had stood:

"If set back in its place thus indicated the 'recumbent stone' would be exactly in line with the 'leaning stone.'" (Gowland 1901)

The recumbent stone is 55; the leaning stone is 56. The whole trilithon, not one stone, was set on the twisted line.

W. Gowland, "Plan of the excavations around the stone", Archaeologia 58 (1902), Fig. 7. Public domain.

Three surveys of Stone 56

Stone 56 is wedge-shaped at ground level. Its inner (north-east) face is rough and stands roughly square to the axis; its back (south-west) face is straight, and it is the back face that the midsummer sun sets along. The back face was measured on three independent surveys, each outline digitised and a straight line fitted to the middle 60–70% of the face:

• Gowland's 1901 excavation plan (1902, Fig. 7), oriented by its drawn north arrow: 80.0–80.7°.
• M. J. Rees & Co. for English Heritage, 1:200 on the National Grid, 1989: 82.0°.
• The English Heritage laser scan of 2011 (Abbott & Anderson-Whymark 2012, Fig. 1): 80.1°.

The mean of the three is 80.8°, each figure good to about ±1–1.5°. Two further plans, not independent of these, give 80.5° (Cleal et al. 1995, Plan 2) and 81.4° (Field et al. 2015, Fig. 2). A stone set square to the axis would read 90°.

The three independent outlines of Stone 56 and their back-face lines. Gowland's outline is placed nominally on the Rees centroid; its angle is unaffected.

Stone 56 as surveyed in 1989, its back face extended, at 81° to the axis

Not just two stones

Other features at the centre follow the same twisted line (Daw 2015). Two postholes north-east of the Altar Stone, 3362 and 3364, mark a pair of wooden posts set on it. At the south-western end of the inner bluestone horseshoe, the pair of bluestone pillars 66 and 68 (68 now pushed over, its original position known from Gowland's records) define the end of the horseshoe on the same alignment. The outer bluestone circle, badly damaged near the axis and largely unexcavated, appears to be twisted the same way. None of these on its own proves the twist was deliberate; together they show it was not confined to one stone.

The sky in 2500 BC

The direction of sunrise at a solstice depends on the latitude and on the tilt of the earth's axis, which changes slowly. For Stonehenge (51.18° N) in 2500 BC, with the obliquity of the ecliptic at 23.973° (Vondrák et al. 2011), the midsummer sun rose at 49.6° and the midwinter sun at 130.4°, on a level horizon. The two sunrises were 80.8° apart. The same angle separates the two sunsets, and so the main axis (midsummer sunrise to midwinter sunset) and the second solstice line (midwinter sunrise to midsummer sunset) cross at 80.8°. A horizon altitude of 0.6° changes this by only 0.02°. The angle depends mainly on the date: it was 80.6° in 2000 BC and is 78.8° today. Simon Banton's figure for 2500 BC is 80° 49′ 25″.

The Altar Stone and Stone 56 lie along the second line. Seen from inside the circle, the midsummer sunset runs down the back face of Stone 56; it was photographed there in 2014, 2015 and 2022. The midwinter sunrise no longer reaches that direction, so Banton (2026) photographed the major-standstill moonrise of 2024–25 in its place, through the notch in Stone 58 and along the Altar Stone.

The four solstice directions at Stonehenge, 2500 BC. Diagram, level horizon.

 

Midsummer sunset beside Stone 56. Photo: T. Daw, 2015.

The clock face

The outer sarsen circle had 30 uprights and 30 gaps. Taking the centres of both gives sixty equally spaced marks round the circle, like the minutes on a watch (Daw 2024). Set the main axis from 12 (midsummer sunrise) to 6 (midwinter sunset). The entrance gap is at 12, so the stones fall on the odd minutes and the gaps on the even ones.

A straight line from the 15-minute mark to the 42-minute mark crosses the axis at exactly 81°. The geometry is simple: a chord between marks a and b is perpendicular to the radius through their midpoint, so it lies at 3(a + b) + 90 degrees to the axis, modulo 180. For 15 + 42 = 57, that is 81°. Any chord whose ends add to 57 is parallel to it.

The sixty-mark circle, the axis from 12 to 6, and the 15–42 line at 81°. The Altar Stone and Stone 56 are drawn parallel to the line: schematic.

The gaps matter. Chords between stone centres alone come out in steps of 6°, so the nearest to 81° are 78° (15 to 41) and 84° (15 to 43). Only with the gaps counted does 81° fall out. A sixty-mark circle can make any multiple of 3° with one chord, so 81° is easy to set out rather than forced by the circle; the case is that it is easy and it matches the sky.

Stones only: 78° and 84°. Stones and gaps: 81°.

The Bush Barrow lozenge

The gold lozenge from Bush Barrow (Wilsford G5), on Normanton Down about a kilometre south-west of Stonehenge, was dug by William Cunnington for Richard Colt Hoare in 1808 and is now in the Wiltshire Museum, Devizes. It is a sheet of gold 184 × 156 mm, from a burial of about 1950 BC, some five centuries after the sarsens went up. Thom, Ker and Burrows (1988) measured the acute angles of its diamond at 81° and noted that this was the angle between the midsummer and midwinter sunrises at the latitude of Stonehenge (MacKie 2009). The Wiltshire Museum's own page gives 80°.

The Bush Barrow gold lozenge, Wiltshire Museum, with its acute angle marked "about 81°" (the published figure; the photo is taken at an angle through display glass and is not a measurement). Photo: Pasicles, CC0, via Wikimedia Commons.

Caveats

• The Altar Stone may once have stood. Atkinson (1956) and Cleal et al. (1995) left open that it was a fallen upright. Burl (2006) and Parker Pearson et al. (2024) favour a deliberate recumbent; Burl put the chance of a fallen upright landing on the solstice line at about 1 in 165. It is not settled by excavation.
• Precision. Ruggles (1997) warns that Stonehenge's near horizon does not justify alignment claims finer than about 1°. The angle here is a ground layout, not a horizon sighting, and Stone 56's back face is measured to about ±1–1.5° on each survey. The Altar Stone is near 81°, not measured to a degree.
• The lozenge is later. A shared angle on a craft object of c. 1950 BC is suggestive, not proof of shared knowledge.
• Sixty marks is a circle, not a number system. There is no evidence of base-60 counting in Neolithic Britain. That the builders used the 15–42 chord is a hypothesis; the geometry and the sky angle are not.
• Not the same as the calendar theory. Darvill (2022) proposed that the sarsens encode a solar calendar; Magli and Belmonte (2023) rejected it. The clock-face reading here is about angles, not days.

Notes on the film

• The plan of the standing stones comes from T. Daw's 3D model of Stonehenge. The orientations of Stone 56 and the Altar Stone in that model were set from the Twisted Trilithon paper, so they are not used as evidence: Stone 56 is drawn from the Rees 1989 survey outline, and the Altar Stone is marked as schematic.
• On the clock-face diagrams the Altar Stone and Stone 56 are placed at their plan positions and drawn parallel to the 81° line, as an illustration.
• Sun positions are for 2500 BC on a level horizon, for the centre of the disc.

Sources

• Abbott, M. and Anderson-Whymark, H. 2012. Stonehenge Laser Scan: Archaeological Analysis Report. English Heritage Research Report Series 32-2012.
• Atkinson, R. J. C. 1956. Stonehenge. London: Hamish Hamilton.
• Banton, S. 2026. The secondary solstice axis at Stonehenge: using the Moon as a proxy for the ancient Sun. Journal of Skyscape Archaeology, 133–141. doi:10.1558/jsa.33686
• Burl, A. 2006. Stonehenge: A New History of the World's Greatest Stone Circle. London: Constable.
• Cleal, R. M. J., Walker, K. E. and Montague, R. 1995. Stonehenge in its Landscape: Twentieth-century Excavations. English Heritage Archaeological Report 10.
• Darvill, T. 2022. Keeping time at Stonehenge. Antiquity 96: 319–335. doi:10.15184/aqy.2022.5
• Daw, T. 2015. The Twisted Trilithon of Stonehenge. Wiltshire Archaeological and Natural History Magazine 108: 15–24.
• Daw, T. 2024. Sexagesimal Stonehenge: the geometry of the Stonehenge sarsen trilithons. doi:10.13140/RG.2.2.16275.86560
• Daw, T. 2025. The geometry of the horseshoe stones at Stonehenge. doi:10.13140/RG.2.2.23505.65127
• Field, D. et al. 2015. Analytical surveys of Stonehenge and its environs, 2009–2013: Part 2, the stones. Proceedings of the Prehistoric Society 81: 125–148. doi:10.1017/ppr.2015.2
• Freeman, G. R. and Freeman, P. J. 2001. Observational archaeoastronomy at Stonehenge: winter solstice sun rise and set lines accurate to 0.2° in 4000 BP. In J.-L. Pilon, M. W. Kirby and C. Thériault (eds), A Collection of Papers Presented at the 33rd Annual Meeting of the Canadian Archaeological Association, 200–219.
• Gowland, W. 1901. The recent excavations at Stonehenge, with inferences as to the origin, construction, and purpose of that monument. Abstract of a report presented to the Society of Antiquaries, 19 December 1901. Man.
• Gowland, W. 1902. Recent excavations at Stonehenge. Archaeologia 58: 37–118. doi:10.1017/S0261340900008882
• MacKie, E. W. 2009. The prehistoric solar calendar: an out-of-fashion idea revisited with new evidence. Time and Mind 2: 9–46. doi:10.2752/175169709X374263
• Magli, G. and Belmonte, J. A. 2023. Archaeoastronomy and the alleged "Stonehenge calendar". Antiquity. doi:10.15184/aqy.2023.33
• M. J. Rees & Co. 1989. Stonehenge survey, 1:200, drawing AS16/1, for English Heritage. Historic England Archive MP/STO0861.
• Parker Pearson, M. et al. 2024. Stonehenge and its Altar Stone: the significance of distant stone sources. Archaeology International 27: 113–137. doi:10.14324/AI.27.1.13
• Petrie, W. M. F. 1880. Stonehenge: Plans, Description, and Theories. London: Stanford.
• Ruggles, C. 1997. Astronomy and Stonehenge. In B. Cunliffe and C. Renfrew (eds), Science and Stonehenge. Proceedings of the British Academy 92.
• Thom, A. et al. 1974. Stonehenge. Journal for the History of Astronomy 5: 71–90.
• Thom, A. S., Ker, J. M. D. and Burrows, T. R. 1988. The Bush Barrow gold lozenge: is it a solar and lunar calendar for Stonehenge? Antiquity 62: 492–502. doi:10.1017/S0003598X00074597
• Vondrák, J., Capitaine, N. and Wallace, P. 2011. New precession expressions, valid for long time intervals. Astronomy & Astrophysics 534: A22.

Earlier posts on sarsen.org: Twisted Stone 56 (2012); The Twisted Trilithon of Stonehenge (2015); Sexagesimal Stonehenge (2024); Stonehenge clockface solstitial alignments (2025); Visualising the secondary solstice axis (2026).