Diamond Pavilion Angle Calculator

Diamond Pavilion Angle Calculator – Depth %, Geometry And Reverse Mode

The pavilion is the lower part of a diamond, below the girdle. In a round brilliant, the pavilion main facets meet at the culet and are tilted at a specific angle relative to the girdle plane. That angle is called the pavilion angle, and it is a critical parameter in cut grading. This Diamond Pavilion Angle Calculator helps you move easily between pavilion depth percentage, pavilion angle in degrees and simple geometric measurements.

The depth-based method is convenient when you are working from grading reports or charts that express pavilion size as a percentage of the average girdle diameter. The geometric method is ideal when you are modeling a stone in CAD or working directly from millimeter measurements. The reverse mode lets you start from a chosen pavilion angle and see the equivalent pavilion depth percentage and millimeter depth.

Method 1: Pavilion Angle From Pavilion Depth Percentage

Grading systems often express pavilion size as a pavilion depth percentage. This is defined as pavilion depth divided by the average girdle diameter, multiplied by 100. For a round brilliant, a widely used approximation relates this depth percentage to pavilion angle using basic trigonometry.

If we treat the pavilion as a triangle and measure the angle between the pavilion main facet and the girdle plane, then in a simplified model:

Substituting the definitions for depth and radius in terms of diameter and simplifying gives a useful approximation:

To solve for pavilion angle, we take the inverse tangent (arctan):

In the calculator, the denominator 50 is exposed as a configurable constant. Leaving it at 50 matches the standard round brilliant approximation. Adjusting it slightly lets advanced users experiment with different reference conventions or special-case proportion systems.

Method 2: Pavilion Angle From Geometric Measurements

When you know physical measurements in millimeters, you can compute pavilion angle directly from pavilion depth and average girdle diameter. The model is again a simple right triangle, with pavilion depth as the vertical leg and pavilion radius as the horizontal leg.

Solving for pavilion angle gives:

This method does not require percentages. It works directly with millimeters, making it practical when working with CAD drawings, microscope measurements or proportion gauges. The calculator also converts the resulting angle back into an implied pavilion depth percentage so you can compare it with grading charts and ideal ranges.

Reverse Mode: Pavilion Depth Percentage From Pavilion Angle

Sometimes you start with a target pavilion angle, such as a value inside a recommended cut range, and want to see what pavilion depth percentage this corresponds to in the simplified round brilliant model. Rearranging the depth formula from Method 1 provides a direct answer.

Solving for pavilion depth percentage:

In the calculator, the denominator constant is again exposed so that you can choose the same value used in your preferred grading tables. When you also enter an average girdle diameter, the tool converts pavilion depth percentage into pavilion depth in millimeters as well:

This reverse mode is handy when designing a diamond in software or studying how small changes in pavilion angle affect pavilion depth and overall proportions.

Typical Ideal Ranges For Round Brilliant Pavilion Angle

Different labs and cut systems use slightly different ideal ranges, but many high-performance round brilliant designs place pavilion angles roughly around the low 40-degree range. As a rough guideline, one often sees pavilion angles near about 40.6° to 41.0° paired with crown angles and tables that support strong light return.

When pavilion angle becomes too shallow, the pavilion depth percentage drops and light rays may leak out of the bottom of the diamond instead of reflecting back toward the viewer. When pavilion angle becomes too steep, pavilion depth percentage rises and light can reflect at unhelpful angles, darkening portions of the stone.

How Pavilion Depth Percentage Relates To Pavilion Angle

The depth percentage and angle are tied together by tangent functions. In the simplified model with a constant denominator of 50, a small change in pavilion angle translates into a measurable change in pavilion depth percentage.

For example, if PavilionAngle is around 40.8°, then tan(40.8°) is roughly 0.86. Multiplying by 50 yields an approximate pavilion depth percentage near the low 43% range. You can verify this numerically by entering the angle into the reverse tab of the calculator.

Interpreting The Calculator’s Cut Comments

The calculator provides short interpretation notes when you compute pavilion angle or depth. These notes are based on broad categories, not strict grading rules.

• If pavilion angle and pavilion depth percentage fall near a common ideal range, the note will mention that the pavilion is within a balanced zone for many round brilliant designs.
• If pavilion angle is noticeably shallower than typical ideal values, the note warns that this geometry may lean toward light leakage through the pavilion.
• If pavilion angle is noticeably steeper than typical ideal values, the note warns that the pavilion may be on the deep side, potentially darkening the stone or shifting brightness patterns.

These comments are intentionally general because real cut performance depends on many other parameters beyond pavilion alone, including crown angle, table size, total depth, facet indexing and symmetry.

When To Use Depth % Versus Geometric Mode

Both forward modes in the Diamond Pavilion Angle Calculator are valid. Choosing between them is mostly about which data you have available.

• Use the depth percentage method when your starting point is a grading report, proportion chart or reference that lists pavilion depth %.
• Use the geometric method when you have millimeter measurements from a scanner, microscope or CAD model and want a direct angle from geometry.
• Use the reverse mode when you know the pavilion angle you want and need to see the equivalent pavilion depth percentage or depth in millimeters.

Step-By-Step: Using The Diamond Pavilion Angle Calculator

• Select the Pavilion Angle From Depth % tab if you have pavilion depth percentage from a report. Enter the depth %, keep the denominator at 50 for round brilliants and choose your desired decimal places, then calculate the pavilion angle.
• Select the Pavilion Angle From Geometry tab if you know pavilion depth and average girdle diameter in millimeters. Enter both values, choose decimals and calculate the angle and implied pavilion depth percentage.
• Select the Pavilion Depth % From Angle tab if you start from a pavilion angle. Enter the angle in degrees, keep the denominator at 50 (or adjust to match your system) and optionally provide a girdle diameter to see pavilion depth in millimeters.
• Review the interpretation notes to see whether the results sit in a broadly shallow, ideal or deep zone relative to typical round brilliant guidelines.