Faceting Angle Calculator

The pavilion angle needs to exceed the stone's critical angle -- the angle of incidence, measured as arcsine of 1 divided by refractive index (RI), beyond which light hitting the facet from inside reflects rather than escapes. Critical angle shrinks as RI climbs, so a high-RI material like diamond needs a much smaller pavilion angle to clear that threshold than a low-RI material like quartz, which is exactly the inverse relationship this calculator returns as refractive index increases.

Quartz, with a refractive index around 1.544, gets an optimal pavilion angle in the mid-40s of degrees. Plugging diamond's refractive index (2.417) into this same critical-angle-plus-margin formula returns roughly 27.4 degrees, but that number shouldn't be taken as diamond's real cutting angle -- this simplified model underestimates badly at very high RI, and diamond is conventionally faceted with a pavilion-main angle around 40-41 degrees using empirical, brilliance-optimized angle tables rather than a bare total-internal-reflection margin. The formula is intended for -- and most accurate on -- lower-RI colored stones like quartz, not diamond.

No -- the minimum pavilion angle this calculator returns is always set two degrees above the critical angle, which is the smallest margin considered safe for reliable total internal reflection. Cutting closer to the critical angle itself risks light leakage at the pavilion, producing a stone with a visible dark or washed-out area (sometimes called a fish-eye or window) rather than full brilliance.

No -- crown angle steps down at different refractive-index breakpoints depending on the cut style selected, and step cuts and Portuguese cuts get noticeably lower crown angles than a standard brilliant at the same refractive index. A standard brilliant on a typical RI-1.5 material gets a 42-degree crown, while a step cut on the same material comes in around 38 degrees, reflecting the different light-return goals of each faceting style.