Measurement & Calculation
Essential measurement and calculation tools for gem identification, including SG, RI, birefringence, dispersion, and carat estimation.
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.