Graduated Strand Weight

Account heterogeneous graduated spherical bead density/count inventory using exact centered-bore napkin-ring volume, not subtracting a full-length cylinder through curved sphere; excludes cord/clasp and non-spherical pearls.

Description

A drilled spherical bead retains the exact napkin-ring volume around a centered cylindrical bore.

A drilled spherical bead retains the exact napkin-ring volume around a centered cylindrical bore. Subtracting a full-length cylinder would misrepresent the curved removed ends.^[1]

When to use Graduated Strand Weight

Use this tool to account heterogeneous graduated spherical bead density/count inventory using exact centered-bore napkin-ring volume, not subtracting a full-length cylinder through curved sphere; excludes cord/clasp and non-spherical pearls.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Graduated Strand Weight and understand its results

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
Enter beadOuterDiametersMm, beadDrillDiametersMm, beadCounts, beadDensitiesGramsPerCm3 using the field table and calculation rules, then run the tool.
Read modeledStrandBeadMassGrams, modeledNetBeadVolumesMm3. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
beadOuterDiametersMm	Bead outer diameters mm	list of number	Required
beadDrillDiametersMm	Bead drill diameters mm	list of number	Required
beadCounts	Bead counts	list of number	Required
beadDensitiesGramsPerCm3	Bead densities grams per cm3	list of number	Required

Pair positive bead diameters/densities with nonnegative drill diameters no greater than outer diameter and nonnegative integer counts. Compute class net mm³, divide by 1000 for cm³ and multiply by density/count; return net volumes and total grams.

Paired lists must be nonempty and have equal lengths.

net bead volume=π/6 × (outer diameter²−drill diameter²)^(3/2)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
modeledStrandBeadMassGrams	Modeled strand bead mass grams	number
modeledNetBeadVolumesMm3	Modeled net bead volumes mm3	list of number

json

{
  "input": {
    "beadOuterDiametersMm": [
      2,
      4
    ],
    "beadDrillDiametersMm": [
      0,
      0
    ],
    "beadCounts": [
      10,
      1
    ],
    "beadDensitiesGramsPerCm3": [
      2,
      2
    ]
  },
  "output": {
    "modeledStrandBeadMassGrams": 0.15079644737231007,
    "modeledNetBeadVolumesMm3": [
      4.1887902047863905,
      33.510321638291124
    ]
  }
}

Limitations and assumptions

Cord and clasp mass, eccentric holes and non-spherical beads are excluded.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Strand Length Bead Count: Fit a complete prefix of explicitly ordered variable-diameter beads and gaps around caller clasp length, retaining remainder; not a fixed bead-size lookup or permission to reorder a graduated strand. For a complementary task, use Jade Bangle ID-to-Weight Estimator: Estimate measured smooth bangle as elliptical-section torus under supplied density; no jade identity, rectangular section substitution or assumption of hidden cracks/voids.

References

Graduated Strand Weight — tool.io

Similar or alternative tools

Strand Length Bead Count
Fit a complete prefix of explicitly ordered variable-diameter beads and gaps around caller clasp length, retaining remainder; not a fixed bead-size lookup or permission to reorder a graduated strand.
Jade Bangle ID-to-Weight Estimator
Estimate measured smooth bangle as elliptical-section torus under supplied density; no jade identity, rectangular section substitution or assumption of hidden cracks/voids.