Diamond Pavilion Angle: Complete Guide and Calculation

Diamond Pavilion Angle: Complete Guide and Calculation

Diamond Pavilion Angle: Complete Guide and Calculation

Posted by Sharif Khan on 26th Dec 2020

Have you ever bought a diamond as a present for that special person in your life? Whilst doing so, you most probably took your time going through websites and resources online that elaborate on the best kind of diamond. But, if you’re still a rookie in the world of diamonds, the jargon and calculations that mark it can make you want to throw in the towel. The good news, however, is that we have your back.

In this article, we will walk you through the meaning of the diamond pavilion angle, ways to calculate it using simple mathematics, and the requisite techniques to help you determine an ideal cut diamond.

Key takeaways:

An ideal pavilion angle is immensely responsible for the exquisite, eye-catching appearance we see in polished diamonds. The angle refracts light from one facet to another and then reflects it to you through the table. Your diamond can never have the ideal, stunning look if it lacks a perfect pavilion.

Whilst shopping, be careful not to fall for poorly cut diamonds. Do the diamond’s pavilion depth, pavilion angle, and other dimensions fall within the perfect ranges? The news worth cherishing is that you now know how to calculate these dimensions. Also, kindly note that these seemingly minute details can prove decisive in differentiating between ideal and poorly cut diamonds.

So, now that you are cognizant of all the prerequisites, go ahead and shop with confidence.

What is a diamond pavilion angle?

Before light is shed upon this question, we ought to first understand as to what does diamond pavilion actually connote. As per the simplest of all definitions to date put forth, a pavilion is a diamond’s bottom half hidden under a ring arrangement that plays a very crucial part in the metal’s general appearance. Why is it so? Because it has facets that assist in light reflection, penetration, and bouncing. The result is fire and brilliance.

The pavilion consists of three parts; namely the culet, the girdle, and the pavilion facets.

  • Girdle - the outermost edge of the metal
  • Pavilion facets - the part that slopes between the culet and the girdle
  • Culet - the meeting point of the sloping pavilion facets

Therefore, the pavilion angle is the pavilion facets’ angle in relationship to the plane of the girdle.

James Allen

The effects of the Pavilion on the diamond’s sparkle:

The shining and sparkling nature of the metal relies heavily on the pavilion. When you shine light through a diamond, it passes through the table and crown, and once it reaches the pavilion, it bounces and sparkles through the metal. The pavilion angle will determine how the refraction and sparkling occur.

Too shallow pavilions will give a “fisheye” effect because of the girdle’s reflection in the table, ensuing in unsatisfactory results. The light going perpendicularly through the crown will bend too much and will not refract across the opposite pavilion facet. Instead, it will jump off the crown facet at the opposite and exit the stone through the second pavilion facet. In simpler terms, it will go through the gem and leak out through the bottom.

On the other hand, if your diamond has a pavilion that is too deep, the table surface will look darker and create the impression of a “nail head”—and, at the end of the day, this is not what one wants in a diamond.

The exact process that takes place while light is being shone through a diamond is as follows:

The light will bounce at a shallow point and will then again leak out from the bottom near the culet: this is so because the perpendicular light going through the table and crown facet will not be steep enough to bounce well at the first pavilion facet. Consequently, the opposite pavilion facet will not correctly reflect the light.

For an ideal angle, the light goes through the crown facet and bounces off the first pavilion facet. It will then proceed to the opposite pavilion facet and bounce again, eventually leaking off through either the second crown facet or table facet and return to the observer. A perfect combination of pavilion and crown facets will give an excellent equilibrium between fire and brightness while cutting down unwanted leakage of light.

Ideal Pavilion angles:

According to Marcel Tolkowsky’s calculations, 40.75 degrees is the perfect pavilion angle of a diamond. Surprisingly, long before scientists determined this angle mathematically, cutters, who have for centuries on end been believing that an angle of more than 41 degrees would be too deep, were able to achieve the same results.

Sellers of poorly cut stones, on the contrary, will argue that it is laughable to have a diamond with a 41-degree slope. Be that as it may, it cannot be denied that light leaks beyond a particular critical angle. In reality, what occurs is not too much cliff but a seamless change from stronger to weaker reflections as leakage increments. The point that needs to be paid heed to is that this transition happens at around 41 degrees, and so something nearer to 40.75 degrees is satisfying unless you want an ideal stone with 40.9 degrees.

Most studies have concluded that angles below 40.5 degrees are too shallow and will result in light leakages and obstructions. The Gemological Institute of America (GIA) always round off the 40.5 degrees angle to 40.6 in their reports. Resultantly, we arrive at an acceptable pavilion angle range of 40.6- 41 degrees.


Calculate the Pavilion angle:

The mathematics behind the said calculation, otherwise extremely important, is not as hard as it appears. To enable yourself to do so better, you must know the following first:

  • Crown depth
  • Pavilion depth
  • Table

All of these dimensions are usually in % of the average diameter.

Now that you are aware of the aforementioned aspects, follow the following steps:

  • Take out your calculator and enter the pavilion depth
  • Then divide the pavilion depth by 50
  • Last, calculate the Tan Inverse (Tan-1). (You need not worry. Simply hit the Tan-1 button on your calculator.)

If you don’t have the Tan-1 button in your calculator, do the following instead:

  • Locate the symbol Tan-1 written above the Tan button, and then press the shift button followed by hitting the Tan button.

Voila! You’ve found the pavilion angle.

This example should do:

Pavilion depth = 42.9 %

Therefore, 42.9÷ 50 = 0.858

The Tan-1 of 0.858 = 40.63 degrees

As seen above, apart from the pavilion angle, there are other dimensions that carry similar importance. An experienced diamond cutter will know how to relate them proportionately so as to come up with a stunning gem.

A super excellent round cut diamond will have the following ranges:

  • Depth = 61%- 62.5%
  • Pavilion angle = 40.6%- 41%
  • Table size = 54%- 57%
  • Crown angle = 34%- 35%
  • Girdle thickness = Thin-medium
  • Culet = None