The two formulas on this page
Both are the bench's own tools (the same arithmetic the app's Whip page runs): the wrap estimates the cord's length, the bracelet estimates the buckle-to-buckle size. No invented numbers; these two decide everything else here.
| the piece | the formula | reads as |
|---|---|---|
| a handle wrap | cord = length ร ฯ ร (diameter + cord ร) รท cord ร | each pass travels the cylinder at the wrap's own pitch; a fatter cord wraps fewer, wider passes that each take more length โ the tool calls its answer generous, on purpose |
| a cobra bracelet | buckle-to-buckle = wrist + ฯ ร thickness + fit | the bend adds ฯ ร thickness of cord on its own โ the term every straight-chord estimate forgets |
The sizes: paracord by the millimetre
The cord sizes used across the bench's pages: 550 cord โ 4 mm, 325 โ 3 mm, 95 โ 2 mm โ the estimates, and the field is editable: measure yours, the tool takes the real number.
One worked wrap
The tool's own defaults make the example: a handle 10 in long, 18 mm (0.709 in) across, wrapped in 4 mm (0.15625 in) 550 cord:
- cord = 10 ร ฯ ร (0.709 + 0.15625) รท 0.15625 = 10 ร ฯ ร 5.5368 โ 173.9 in โ 14.5 ft. The tool prints exactly this and rounds: about 14.5 feet, generous.
- Halve the cord to 2 mm (95) and the same handle wants โ 25.7 ft โ thinner cord, more passes, each pass shorter: the diameter term in the formula is the whole story.
One worked bracelet
A wrist that measures 7 in, 550 cord as the core (5/16 in thick, the tool's default), and a fit allowance of 3/4 in for the buckle hardware:
- L = 7 + ฯ ร 0.3125 + 0.75 = 7 + 0.98 + 0.75 โ 8.73 in buckle end to buckle end.
- Measure again with the watch on if the bracelet shares a wrist โ the fit term is the honest place to add it, not memory.
Mistakes worth avoiding
| the mistake | what it costs |
|---|---|
| wrist + fit, no ฯ term | the bracelet arrives short by ฯ ร thickness โ about an inch on 550 cord; the tool never skips it |
| the wrap length trusted on a fat cord | fat cord raises each pass's length but cuts their count โ measure the cord, not the label |
| pulling the last passes tight and the first loose | the wrap drifts down the handle; snug each pass as you go, then re-snug the first three once the end is set |
| ends melted before the last pass is snugged | nothing left to adjust; finish the ends last |
The app helps
The Wrap page runs the cord formula with its generous margin, and the Bracelet page runs the buckle math with the thickness and the fit as inputs. The bench's Knot TV carries the weave rows that show the cobra and the cross-wraps in motion; the build sheets keep the wrap on the shopping list with its measured cord.
Sources: both formulas are the app's own tool arithmetic (the same numbers the tools page answers with); the paracord sizes are the estimates in the whip-plaiting guide's table, measured against real 550 and 95.