Calculate millimeter-to-carat weights across 50+ gemstone species and lapidary cuts, raytrace 3D brilliance and dispersion fire, inspect CVD/HPHT vs. natural diamonds, verify ruby rutile silk and emerald authenticity, and evaluate Mohs wear durability—instantly in your browser with calm, eye-comfortable jewel optics.
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Table %, Depth % & Crown/Pavilion Estimator
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12-Point Gemological Authenticity Diagnostic
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Single-Refraction Fire vs. Ruby
Milk-and-Honey Sharpness Grader
Millimeter to Carat Size Chart
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100+ Refractive Index, SG & Birefringence
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Standardized refractive indices, birefringence (DR), hydrostatic specific gravity (SG), optical dispersion, and forensic treatment markers across major precious and collector gem species.
| Gem Species & Formula | Crystal System & Optic Sign | Refractive Index (RI) & Birefringence | Specific Gravity & Mohs | Forensic Inclusion & Treatment Benchmark |
|---|---|---|---|---|
| Diamond (Natural / CVD / HPHT — C) | Cubic (Isometric) • Singly Refractive (SR) | RI 2.417–2.419 • Dispersion 0.044 | SG 3.52 • Mohs 10.0 | Natural Ia shows N3 cape lines; CVD displays cross-polarized tatami strain & SiV- 737 nm doublet; HPHT may show metallic flux & phosphorescence |
| Ruby & Sapphire (Corundum — Al₂O₃) | Trigonal • Uniaxial Negative (U−) | RI 1.762–1.770 • DR 0.008–0.009 | SG 3.99–4.05 • Mohs 9.0 | Intact 60°/120° intersecting rutile silk confirms <1,300°C unheated origin; snowball/discoid tension halos indicate high-heat or Be-diffusion treatment |
| Emerald (Cr/V Beryl — Be₃Al₂Si₆O₁₈) | Hexagonal • Uniaxial Negative (U−) | RI 1.577–1.583 • DR 0.005–0.009 | SG 2.71–2.78 • Mohs 7.5–8.0 | Colombian 3-phase jagged fluid inclusions (SG ~2.76) vs. flux-grown synthetic wispy veil feathers (lower RI ~1.561, SG ~2.66) |
| Alexandrite (Chrysoberyl — BeAl₂O₄:Cr³⁺) | Orthorhombic • Biaxial Positive (B+) | RI 1.746–1.755 • DR 0.008–0.010 | SG 3.70–3.78 • Mohs 8.5 | Strong trichroism (green / orange-yellow / purple-red); 580 nm Cr³⁺ absorption band drives 6500K daylight green to 2700K incandescent red shift |
| Red, Mahenge & Cobalt Spinel (MgAl₂O₄) | Cubic (Isometric) • Singly Refractive (SR) | RI 1.712–1.718 (Synth ~1.727) • Disp 0.020 | SG 3.58–3.64 • Mohs 8.0 | Octahedral negative crystals & zero pleochroism separate natural spinel from doubly refractive ruby; Verneuil synthetic shows snake-like anomalous strain |
| Precious Opal (SiO₂·nH₂O Silica Lattice) | Amorphous • Isotropic Photonic Array | RI 1.44–1.46 (Hydrophane 1.37–1.45) | SG 1.98–2.20 • Mohs 5.5–6.5 | 150–300 nm silica spheres diffract Bragg spectral play-of-color; synthetic Gilson opal exhibits lizard-skin / chicken-wire columnar mosaic under 10× loupe |
| Paraiba & Chrome Tourmaline (Elbaite) | Trigonal • Uniaxial Negative (U−) | RI 1.624–1.644 • Strong DR 0.018–0.022 | SG 3.02–3.12 • Mohs 7.0–7.5 | Cu²⁺ and Mn³⁺ absorption bands at 700 nm & 515 nm create neon Paraiba glow; strong 0.020 birefringence visibly doubles back-facet junctions |
| Tanzanite (Vanadium Zoisite — Ca₂Al₃(SiO₄)₃(OH)) | Orthorhombic • Biaxial Positive (B+) | RI 1.691–1.700 • DR 0.009 | SG 3.35 • Mohs 6.5–7.0 (1 Perfect Cleavage) | Unheated crystals show strong trichroism (blue / violet-purple / bronze-brown); gentle 550°C heat removes brown axis to yield dichroitic royal violet-blue |
Every gem toolkit on GemsMakers applies peer-reviewed crystallography, volumetric specific-gravity equations, and Fresnel–Snell ray optics directly in your browser—delivering laboratory-grade estimates without server uploads.
Mounted gemstones cannot be placed on a carat scale. Our calculators multiply Length × Width × Depth (mm) by species Specific Gravity (relative to diamond 3.52) and cut-specific bulge/pavilion shape factors (0.0061 round brilliant to 0.0082 emerald step-cut).
A gem's critical angle θc = arcsin(1 / n) governs whether light reflects back through the crown as brilliance or leaks out the pavilion as a dull window (24.4° in diamond vs. 34.5° in corundum and 39.3° in emerald).
Combine optical birefringence, pleochroism lighting shifts, rutile silk microscopy, cleavage plane vulnerability, and ultrasonic/steam thermal shock thresholds before buying, setting, or cleaning fine gemstones.
Gemologists use the standard volumetric formula: Carat Weight = Length (mm) × Width (mm) × Depth (mm) × Specific Gravity Ratio × Shape Factor (+ girdle/pavilion bulge correction). Because 1 metric carat equals exactly 200 milligrams (0.200 g), a 6.5 mm round ruby (SG 4.00) weighs ~14% more than an identically sized 6.5 mm round diamond (SG 3.52), while a 6.5 mm emerald (SG 2.72) weighs ~23% less.
Start with optical character and magnification: glass imitations are singly refractive with spherical gas bubbles, swirled striae, and warm-to-the-touch thermal conductivity. Natural emeralds show 3-phase jagged inclusions and RI 1.577–1.583 (vs. ~1.561 in flux synthetics); natural unheated rubies retain 60°/120° boehmite or rutile silk needles (vs. curved striae in flame-fusion synthetics); and genuine precious opals show natural sand/potch transitions rather than the lizard-skin columnar pattern of synthetic opal or glue seams of doublets/triplets.
All three are real crystalline carbon (Mohs 10, RI 2.417, SG 3.52) and pass standard thermal diamond pens. However, ~98% of natural diamonds are Type Ia containing aggregated nitrogen (cape 415 nm line), whereas CVD and HPHT lab-grown diamonds are predominantly Type IIa/IIb (nitrogen-free). Under cross-polarized filters, CVD diamonds reveal characteristic banded "tatami" strain, while HPHT diamonds often display cuboctahedral growth sectors, trace Fe/Ni/Co flux inclusions, or short-wave UV greenish-blue phosphorescence.
Every gemstone has a mathematical critical angle θc = arcsin(1/RI). If a pavilion is cut too shallow, light hits below the critical angle and leaks straight through the bottom ("windowing" or fish-eye effect); if cut too deep, light exits out the opposite pavilion ("extinction" darkness). Proper crown angle and table percentage balance white-light return (brilliance) against spectral rainbow splitting (dispersion/fire).
Fine red, Mahenge pink-neon, and cobalt-blue spinels (Mohs 8.0, singly refractive) are never routinely heat-treated and occur in far smaller geological quantities than corundum. Natural alexandrite (chromium chrysoberyl, Mohs 8.5) requires rare geochemical contact between beryllium-rich pegmatites and chromium-rich ultramafic rock, producing the iconic 6500K daylight emerald-green to 2700K incandescent ruby-red color change.
Unlike faceted stones with conical or step-cut pavilions, cabochons have a flat or slightly convex base and an ellipsoidal dome. Their weight is calculated as Length (mm) × Width (mm) × Dome Height (mm) × Specific Gravity × Cabochon Profile Factor (typically 0.0026 to 0.0029 depending on low, medium, or high dome curvature plus girdle bevel).
No. Gemological durability combines three distinct properties: Hardness (resistance to surface scratching), Toughness (resistance to chipping/fracture, Measured by crystal cleavage planes), and Stability (resistance to heat, light, and chemicals). For example, diamond is Mohs 10 yet has 4 perfect octahedral cleavage directions that can chip on a sharp blow, whereas nephrite jade is only Mohs 6.0–6.5 but possesses interlocking fibrous toughness tougher than steel.
Yes. Every gemology calculator, 3D raytracer, authenticity checker, and valuation studio on GemsMakers runs 100% free in your browser with no account login and zero server storage of your private stone measurements or portfolio values.