Measurement & Calculation
The primary quantitative tests for coloured-gemstone identification: specific gravity, refractive index, and the calculations that flow from them.
Specific Gravity
Calculate SG from hydrostatic weighing
Enter the weight of your stone in air and water to calculate its specific gravity.
Formula: SG = Wair ÷ ((Wair − Wwater) ÷ ρwater(T))
Example (Diamond): 3.52g in air, 2.52g in water at 20 °C = SG 3.52
Tip: Ensure the stone is fully submerged and free of air bubbles. Temperature correction matters most for low-SG materials (opal, amber, beryl).
RI Lookup
Find gems by refractive index range
Enter an RI reading to find matching gemstones. Toggle Double reading to enter both shadow-edge readings (ω/ε or α/γ) and infer birefringence + optic character automatically.
Common Gem RI Reference
| Gem | RI | SG |
|---|---|---|
| Diamond | 2.417 | 3.52 |
| Ruby/Sapphire | 1.762-1.770 | 3.99-4.00 |
| Emerald | 1.570-1.590 | 2.67-2.78 |
| Spinel | 1.712-1.736 | 3.58-3.61 |
| Topaz | 1.609-1.617 | 3.49-3.57 |
| Tourmaline | 1.624-1.644 | 3.00-3.25 |
| Quartz | 1.544-1.553 | 2.65 |
| Zircon | 1.925-1.984 | 4.00-4.70 |
| Garnet (Pyrope) | 1.730-1.760 | 3.65-3.87 |
| Garnet (Almandine) | 1.760-1.830 | 3.95-4.30 |
| Peridot | 1.654-1.690 | 3.28-3.48 |
| Aquamarine | 1.570-1.590 | 2.68-2.74 |
| Tanzanite | 1.691-1.700 | 3.10-3.38 |
| Alexandrite | 1.745-1.755 | 3.70-3.73 |
| Opal | 1.370-1.470 | 1.98-2.25 |
Birefringence
Calculate birefringence from RI readings
Enter the maximum and minimum refractive index values to calculate birefringence.
Formula: Birefringence = RI(max) − RI(min)
Example (Quartz): 1.553 − 1.544 = 0.009 (Low)
Example (Zircon): 1.984 − 1.925 = 0.059 (Very High)
Note: Isotropic gems (cubic system) have no birefringence.
Critical Angle
Total internal reflection angle from RI
Enter the refractive index to calculate the critical angle for total internal reflection.
Formula: θc = arcsin(1 ÷ RI)
Why This Matters
Light entering a gem at angles greater than the critical angle will be totally internally reflected back into the stone. A smaller critical angle means more light is reflected, creating more brilliance. This is why diamond (θc = 24.4°) appears more brilliant than quartz (θc = 40.5°).
Diamond (RI 2.417): θc = 24.4° (excellent light return)
Corundum (RI 1.77): θc = 34.4° (good light return)
Quartz (RI 1.55): θc = 40.2° (moderate light return)
Dispersion Calculator
Calculate fire and brilliance from RI at different wavelengths
Enter the refractive index at red (C-line, 656nm) and violet (F-line, 486nm) wavelengths to calculate dispersion.
Formula: Dispersion = RI(violet) − RI(red)
Gem Dispersion Reference
Why Dispersion Matters
Dispersion measures how much a gem splits white light into spectral colours. Higher dispersion creates more "fire" (the rainbow flashes seen in a well-cut stone). Diamond's high dispersion (0.044) is why it shows exceptional fire, while quartz's low dispersion (0.013) produces minimal colour flashes.
Carat Estimator
Estimate weight from dimensions and specific gravity
Enter stone dimensions to estimate carat weight.
Formula: Weight = L × W × D × SG × Shape Factor
Note: These are estimates. Actual weight varies with exact proportions, symmetry, and cut quality. The girdle factor accounts for material carried in a thicker-than-medium girdle.
Example (1ct diamond): 6.5 × 6.5 × 4.0 mm, SG 3.52, Round, medium girdle = ~1.0 ct
Density Estimator
Alternative SG calculation for irregular shapes
Calculate density (SG) for irregular or fragile stones using volume estimation methods.
Formula: Density = Weight ÷ Volume
Volume from water displacement
Submerge stone in graduated cylinder and measure volume change
When to Use This Tool
- • Fragile or porous stones that can't be submerged
- • Irregular rough specimens without standard shapes
- • Quick field estimates when lab equipment isn't available
- • Large specimens too big for standard SG equipment
Hanneman / Hodgkinson Short-cut RI
Bracket RI with contact-liquid relief for over-the-limit and rough stones
For stones above the refractometer scale (RI > 1.81) or rough material with no polished facet. Place the stone in a drop of each liquid and compare relief, then report what you see.
About these calculators & methodology
Specific gravity and refractive index are the two primary quantitative tests in coloured-gemstone identification. SG is determined hydrostatically using Archimedes' principle: the gem is weighed in air and in water, and the ratio reveals density to two decimal places, enough to separate spinel (3.60) from synthetic spinel (3.52) or glass fills. RI is read directly from a critical-angle refractometer and narrows identification to a handful of species within seconds. Together they form a measurement pair that, for most coloured stones, is sufficient to establish a confident working identification before any other test is applied.
Birefringence (the difference between the maximum and minimum refractive indices) is a direct optical constant of the crystal structure. High birefringence causes visible doubling of back facet edges, a feature diagnostic for zircon (BR up to 0.059), sphene (up to 0.051), and peridot (up to 0.038). The birefringence calculator on this page takes two RI readings and returns the value alongside a qualitative interpretation. The critical angle calculator converts an RI reading into the total-internal-reflection angle, useful when working with a polarimeter or verifying refractometer calibration against a known standard.
The carat estimator uses the formula ct = L × W × D × SG × shape_factor × girdle_factor to give a weight estimate from dimensional measurements when a scale is unavailable. Nine shape-correction factors are built in covering round brilliant, oval, pear, marquise, cushion, emerald cut, heart, trillion, and cabochon, and the girdle-thickness multiplier runs from 1.00 (thin) to 1.12 (very thick) to account for the mass contribution of deep girdles. This is particularly useful when assessing parcels where individual weighing is impractical.
For stones with RI above the refractometer range (commonly 1.81 for contact liquids), the Hanneman/Hodgkinson shortcut provides an indirect RI estimate. The technique infers RI from the position of the liquid-relief shadow band when a known liquid is used as the contact medium. The tool covers five standard liquid values: water (1.33), methylene iodide variants, and monobromonaphthalene (1.66); it maps each relief position to the corresponding RI range for demantoid, sphene, zircon, and high-index synthetics including strontium titanate and rutile. Correct application of this shortcut requires understanding that it yields a range, not a single value, and should always be combined with SG and spectroscope data.
All calculators on this page reference the same mineral database used throughout gemmology.dev: 96 families covering natural species, synthetics, simulants, and composite stones. Matching results are shown with origin badges (natural / synthetic / simulant / composite) so that the distinction between, for example, natural alexandrite (Cr-bearing chrysoberyl) and its synthetic counterpart is immediately visible in the output.