Cabochon Dimension Calculator – Volume, Weight And Dome Geometry
The Cabochon Dimension Calculator on MyTimeCalculator is designed for lapidaries, gem cutters and serious collectors who want more than just a simple carat estimate. It uses a geometric model based on ellipses and ellipsoids to estimate cabochon volume, carat weight, dome shape and symmetry from a small set of measurements.
Instead of guessing or relying only on standard size charts, you can enter length, width, total height, girdle thickness, dome profile and gemstone density. The calculator then reports approximate volume, carat weight, height-to-width ratio, symmetry score and material removal percentage for the stone.
Cabochon Geometry Model
The calculator breaks the cabochon into two main parts: an elliptical base and an ellipsoidal dome. This gives a more realistic approximation than treating the stone as a simple block.
- The base is modeled as an elliptical cylinder with thickness equal to the girdle thickness.
- The dome is modeled as a modified half-ellipsoid whose height is the dome height above the girdle.
Let L be length, W be width, H be total height and G be girdle thickness. Then the dome height D is:
The semi-axes of the ellipse are a = L ÷ 2 and b = W ÷ 2. These values are used in the volume formulas for the base and dome.
Base Volume Formula
The cabochon base is approximated as an elliptical cylinder. The footprint area of an ellipse is π × a × b, and multiplying by thickness G gives base volume:
This part of the stone corresponds to the straight or slightly bevelled girdle plus any flat back area.
Dome Volume Formula
The dome is treated as a half-ellipsoid. A full ellipsoid with semi-axes a, b and c has volume:
A perfect half-ellipsoid dome would therefore have ideal volume:
In the calculator, c is taken as the dome height D = H − G. To adapt this ideal geometry to low and high domes, a dome profile factor F is applied:
Low domes use F below 1.0, medium domes use F near 1.0 and very high domes use F greater than 1.0. A cupped or flatter back profile may reduce the effective dome volume further, which is reflected by subtracting volume when you select the corresponding profile.
Total Cabochon Volume
The total cabochon volume Vtotal is the sum of the base and dome volumes:
All calculations are carried out in cubic millimeters (mm³). This is convenient because cabochon dimensions are usually measured in millimeters.
From Volume To Carat Weight
To convert geometric volume into an estimated carat weight, the calculator uses the relationship between cubic centimeters, density and grams. One carat is 0.2 g, and 1 cm³ equals 1000 mm³. If ρ is density in g/cm³ and V is volume in mm³, then:
Dividing by 0.2 converts grams to carats:
The calculator uses this formula with preset densities for common cabochon materials and a custom density field when you need full control.
Height-To-Width Ratio And Dome Ratios
Beyond volume and weight, profile ratios are critical for wearability and aesthetics. Two important ratios are:
- Height-to-width ratio: H ÷ W
- Dome-to-width ratio: D ÷ W, where D = H − G
A high height-to-width ratio indicates a tall cabochon, which can look dramatic but may sit higher in jewelry settings. A lower ratio gives a flatter, more understated profile. The dome-to-width ratio shows how much of that height is in the curved dome above the girdle.
Symmetry Score
For many cabochon shapes, balanced proportions are a sign of good cutting. The calculator uses a simple symmetry score based on the relationship between length and width. If ratio R is defined as:
Then the farther R moves away from 1.0, the more stretched the cabochon becomes. The calculator converts this difference into a score between 0 and 100, where values near 100 indicate a more symmetrical outline for shapes that are expected to be balanced, such as ovals and cushions.
Material Removal Estimate
Lapidaries often want to know how much rough will be removed when cutting a cabochon. The calculator approximates this by comparing the final cabochon volume with a notional preform block that is thicker than the finished stone. If the preform thickness is taken as a multiple k of the final height H, then the block volume is:
The material removal fraction Rremoval is then:
Expressed as a percentage, this number gives a feel for how much rough is likely to be ground away during shaping and polishing. The calculator uses a moderate preform multiplier to represent a realistic starting thickness.
How To Use The Cabochon Dimension Calculator
- Measure or enter cabochon length, width and total height in millimeters.
- Enter girdle thickness to separate the base from the dome height.
- Select the approximate cabochon shape, such as oval, round, pear or freeform.
- Choose a dome profile that best describes the stone: low, medium, high, very high or cupped/flat back.
- Select the gemstone type to load an appropriate density, or use custom density when needed.
- Click calculate to see estimated volume, carat weight, geometry ratios, symmetry score and material removal percentage.
Practical Considerations And Tolerances
Real cabochons rarely match mathematical shapes exactly. Domes can be irregular, backs may be slightly hollowed, girdles can be bevelled and outlines may deviate from perfect ellipses. For that reason, the calculator should be viewed as a technical guide, not a guarantee of exact weight.
If you are cutting, you can use the tool to plan target sizes and expected finished weights from your rough. If you are buying or selling, you can compare dimensions and profiles across stones to understand why two cabochons with similar weights might look very different in height or spread.
Cabochon Dimension Calculator FAQs
Frequently Asked Questions About Cabochon Geometry
Key points about cabochon volume, weight and dome calculations in one place.
The calculator models the cabochon as an elliptical base plus an ellipsoidal dome. It uses length, width, total height and girdle thickness to compute base volume as π × a × b × G and dome volume as a modified half-ellipsoid before adding them together.
The more carefully you measure length, width, total height and girdle thickness, the more realistic the volume estimate will be. Dome profile and gemstone density refine the result by adjusting the dome shape and weight conversion.
You need at least an estimated height and girdle thickness to model the dome. If you only know length and width, consider measuring the height with a caliper or estimating it from similar stones before using the calculator.
Different gemstones have different densities. Two cabochons with identical dimensions can have significantly different carat weights if one is opal and the other is garnet. Density bridges the gap between geometric volume and weight in carats.
The model uses a simplified elliptical base, so fine details such as bevels or chamfers are not explicitly modeled. If a girdle is heavily bevelled, treating the effective girdle thickness as slightly lower can bring the estimate closer to reality.
A high symmetry score indicates that length and width are in good proportion for the chosen shape, which usually means the cabochon appears visually balanced. Lower scores suggest more elongated outlines or uneven proportions.
No. A calibrated scale is the only way to know the exact finished weight. The calculator is meant for planning, estimation and comparison rather than replacing precise measurement hardware.
Yes. Cutters can use it to plan yields from rough and set profile targets. Buyers can use it to understand why two stones with similar carat weights might have different spreads, heights and visual presence in jewelry.
Changing the dome profile while keeping length, width, height and girdle fixed lets you see how the assumed dome curvature changes volume, weight and material removal. This is useful for exploring the trade-off between height and weight retention.
MyTimeCalculator offers additional tools such as Ruby Price Calculator, Opal Price Calculator, Tourmaline Price Calculator and Spinel Price Calculator. Using them together with the Cabochon Dimension Calculator helps you plan both geometry and pricing for your gemstone projects.