Angkor Wat: how close are the simple ratios?

A proposed grid for a twelfth-century temple

Angkor Wat was built under Suryavarman II in twelfth-century Cambodia. Vacharee Svamivastu and Komsan Maleesee's 2025 study reads its galleries, raised base, wall and moat as seven enclosing layers organised with a square basic module of 2.75 metres. This is their architectural model, assembled from survey material and comparisons with Hindu technical treatises; the counts below belong to that model.¹

Start with the third enclosure, the outer gallery. Their Figure 26 represents it as 60 modules north-south by 72 east-west. Dividing both counts by 12 gives 5:6 exactly. At the proposed module length, those counts imply 165 by 198 metres. These metre values are our multiplication of the model, not a second survey confirming it.

Exact reduction and approximation need different labels

The same paper lists the middle gallery as 35:42, which also reduces exactly to 5:6. But its larger enclosures receive approximate comparisons: the raised base to 3:4, the wall and inner moat bank to 5:6, and the outer moat bank to 7:8. The word approximately now does substantial work. How close are those pairs?¹

We can compare them with one explicit rule. Divide each count pair's short side by its long side, divide that result by the proposed simple ratio, subtract one, and multiply by 100. The percentage is relative to the proposed ratio. A negative result means the model's short-to-long proportion is smaller; zero means exact equality of the two fractions.

This test compares numbers in the published model. It has no survey-error allowance or historical acceptance threshold. It cannot label a difference acceptable to the builders, or interpret it as an error in the surviving fabric.

Six count pairs give different degrees of fit

Population: the six non-square enclosure pairs listed on p. 22. Inputs: the paper's module counts and named simple comparisons. Results: our signed relative differences, rounded to two decimal places. Formula: 100 × [(count ratio ÷ comparison ratio) − 1]. These are differences between model proportions, not measured construction errors.

Take the enclosing wall. Its counts give 290 ÷ 365 ≈ 0.79452; the comparison gives 5 ÷ 6 ≈ 0.83333. Their relative difference is 100 × [(290/365)/(5/6) − 1] ≈ −4.66%. The outer gallery has the same 5:6 label but no such difference: 60/72 is exactly 5/6. A shared label therefore does not imply equally close fits.

The table also distinguishes simplification from approximation. The base's 91:117 reduces exactly to 7:9, while the outer moat's 450:525 reduces to 6:7. Calling them approximately 3:4 and 7:8 selects different, nearby proportions for interpretation. That can be a useful comparison, provided the distance from the actual count ratio remains visible.

The ratio cannot independently recover the module

The exact gallery ratios do not by themselves identify a 2.75 metre ruler. Multiply both sides by any common positive length and it cancels in the division: (60 × module)/(72 × module) = 5/6. Thus 165/198 is the same proportional information as 60/72. It does not supply independent support for the module used to produce the metre pair.

The paper's literature review also attributes a trial-based 0.43545 metre cubit to Eleanor Mannikka. That is a secondhand account of a different reconstruction, rather than another name for the 2.75 metre grid.¹ Neither candidate needs to be selected to reproduce this ratio test. Choosing a historical unit requires evidence beyond the dimensionless proportions.

What the comparison can establish

The published model contains two exactly matching gallery proportions and four looser comparisons for the surrounding rectangles. Reporting the differences makes that structure more precise without treating every rectangle as an exact expression of its assigned simple ratio. It neither confirms nor disproves the proposed religious interpretation: numerical resemblance and the historical reasons for choosing a plan remain separate questions.

A stronger historical test would compare independently specified measuring lines, survey uncertainties and construction phases with a module chosen before examining the test dimensions. Until then, this calculation establishes the relationships between the paper's stated numbers. Continue to the Khmer Hat dossier for the specific cubit candidate, False Precision for the limits of extra digits, or the Red Pyramid for a two-dimension test of scale and shape.