Jewelry necklace multi-strand layout calculator

Calculate semicircle strand lengths and whole bead counts with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use semicircle strand lengths and whole bead counts to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

JSON Strands [ID,desired semicircular drop mm,bead pitch mm]
[["A",70,6],["B",80,6],["C",90,8]]
Supplied clasp take-up per strand (mm)
20
Semicircle strand lengths (mm)
[["A",239.911485751],["B",271.327412287],["C",302.743338823]]
Whole bead counts
[["A",37],["B",42],["C",36]]
Rounded beaded lengths (mm)
[["A",242],["B",272],["C",308]]

Try another scenario

JSON Strands [ID,desired semicircular drop mm,bead pitch mm]
[["A",70,6],["B",80,6],["C",90,8]]
Supplied clasp take-up per strand (mm)
25
Semicircle strand lengths (mm)
[["A",244.911485751],["B",276.327412287],["C",307.743338823]]
Whole bead counts
[["A",37],["B",42],["C",36]]
Rounded beaded lengths (mm)
[["A",247],["B",277],["C",313]]
Calculation method

Calculation method

Semicircle strand lengths (mm)

J([[r[0],math.pi*r[1]+b] for r in a])

Whole bead counts

J([[r[0],ceil(math.pi*r[1]/r[2])] for r in a])

Rounded beaded lengths (mm)

J([[r[0],ceil(math.pi*r[1]/r[2])*r[2]+b] for r in a])

Symbols and units
a
JSON Strands [ID,desired semicircular drop mm,bead pitch mm]
b
Supplied clasp take-up per strand (mm)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Each strand is a semicircle with radius equal supplied drop, independent clasp take-up. Positive bead pitch. This is an explicit supported idealized layout, not catenary drape or arbitrary clasp-width geometry. Supported limits: All numeric inputs must be finite. Only the explicitly described mathematical scenario is supported.
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