Catheter Shaft Calculator
Braid angle, coverage and wall stack for a catheter shaft, computed from published relations that are cited on screen.
10xand.com · Catheter Shaft Calculator · published relations, cited on screen
Shaft Construction Sheet
Layers are added from the lumen outward in the order shown: liner, hypotube, reinforcement, reflow tubing, heat shrink. A blank field is a layer this shaft does not have, not a zero. Enter inches; every result is shown in inches and millimetres. The reinforcement row is derived from the panel below it, because a braid contributes twice its wire thickness to the radius and typing that by hand is the single easiest mistake in this arithmetic.
OD = ID + 2 · Σ(layer radial thickness) — A6, public-domain tube geometry
As entered. Every layer builds outward from it — A6
wall = (OD − ID) / 2 — A6, public-domain tube geometry
A = π·ID² / 4 and A = π(OD² − ID²) / 4 — A6
| Layer | Atlas category | Radial (in) | Adds to OD (in) | OD after (in) | OD after (mm) |
|---|---|---|---|---|---|
| Layer contributions appear here once the fields above are filled. | |||||
Each layer adds twice its radial thickness to the diameter — OD_finished = ID_lumen + 2 · Σ(t) — A6
t is the thickness, w is the width. For round wire the two are the same number and the width field is switched off. For ribbon they are not, and swapping them changes coverage without changing anything that looks wrong.
Braid mandrel OD, derived — the stack's outside diameter where the reinforcement is applied: —. D_mandrel = ID_lumen + 2 · Σ(thickness of every layer beneath the reinforcement) — A6
This marks one of the two cells below. It never hides the other one: both conventions are printed on screen and on the sheet, always.
tan α = π · D_m / h — A-A-59569A §2.2.3; Interference Technology; Lababidi 2013 §5.0
β = 90° − α — A1. Patents state braid angle in both conventions; neither is wrong
h = C / (2P) — A2, from P · h = C / 2; A-A-59569A §2.2.3 for the pick definition
D_m = D_mandrel + 2t, never the mandrel OD — A1; two interlaced layers occupy 2t
F = N · w / (2π · D_m · cos α) — A3, A-A-59569A §2.2.3. Denominator is 2π·D_m, i.e. 4π·R
CF = 2F − F², F clamped at 1 — A3, A-A-59569A §2.2.3; corroborated by Carol/General Cable
PIC₄₅ = C / (2π · D_m) — A2, the inverse of tan α = 2π · D_m · P / C
α_max = arccos( N · w / (2π · D_m) ) — A5, ribbon only. Round wire jams well before closure
— Picks per inch to reach that angle P = C · tan α / (2π · D_m) — A2, inverted. Undefined at 0° and at 90°
N = C × ends per carrier. w is the width of one end perpendicular to its own axis — A3
A coil is one layer of wire where a braid is two interlaced ones, so it adds one wire thickness to the radius and not two. There are no default values in this panel: nothing published gives a coil pitch for a shaft in general, and a number here that came from nowhere would read as a starting point.
coil OD = D_mean + wire, coil ID = D_mean − wire, D_mean = D_mandrel + t — A7
turns per inch = 1 / pitch — A7
gap = pitch − turn width; axial fill = turn width / pitch — A7. Zero gap is closed wound
one turn = √((π·D_mean)² + pitch²), × turns per inch — A7, a helix rather than a ring
OD_mm = Fr / 3, nominal rounded UP to the next 0.1 mm — A8, ISO 20697:2018
1 in = 25.4 mm exactly; tolerance ±1 Fr = ±0.333 mm — A8, ISO 20697:2018
Fr = 3 × mm, snapped to the nearest whole label size — A8. The label leads; the arithmetic follows
Signed, in French. 1.98, 2.00, 2.05 and 2.10 mm are all one labelled 6 Fr device — A8
No gauge conversion, deliberately. The authoritative gauge-to-dimension mapping is ISO 9626:2016, Table 1, which is copyright ISO and carries a notice barring internet posting — so it is linked here and never reproduced. The free substitute is worse than nothing: the public-domain Birmingham Wire Gauge table is the ancestor of the medical gauge rather than the medical gauge itself, and it is out by as much as 5.8% at 23 G against the ISO designated metric size. Enter the OD and ID from your own drawing or supplier certificate and this page will do the arithmetic on those.
The pitch triangle: π · D_m circumferential against h axial, drawn to scale — A1
Radii to scale from the entered dimensions — A6
The unrolled braid panel is on screen only. At sheet scale its angle labels stop being legible, and a drawing that cannot be read is worse than a stated omission — the braid angle, the axial pitch and the mean braid diameter it draws are all printed as figures above.
What a braid angle is, and why this page prints two of them
Unroll one turn of a braided shaft onto a flat sheet and the wire becomes the hypotenuse of a right triangle. The base is the circumference the wire travelled around, π · D_m, and the height is the distance it advanced along the shaft in that turn — the axial pitch h. Everything else follows: tan α = π · D_m / h.
D_m is the mean braid diameter, the mandrel outside diameter plus twice the wire thickness, because two interlaced layers of wire sit on the mandrel and the helix runs through the middle of them. Using the mandrel OD instead is a 7.7% diameter error on a 0.0005″ ribbon over a 0.013″ mandrel, and that error compounds into the angle and then into coverage.
Some sources measure the angle from the longitudinal axis. Others measure it from the transverse plane. The same braid is 33° in one and 57° in the other.
This is the part no free page answers honestly, so here it is plainly. The cable-shielding literature — A-A-59569A §2.2.3, Interference Technology's review of shielded cables, and Carol/General Cable's braid-shield equations — measures the angle from the axis and writes it α. Several catheter patents state braid angles from the transverse plane, which is the complement β = 90° − α. Neither is wrong and neither document usually says which one it is using. A supplier who quotes "a 55° braid" may mean a shallow braid or a steep one, and the only way to know is to ask which reference the number is against. This tool computes in α, prints both, and marks whichever one you told it your supplier uses.
What a pick counts
A pick is one carrier crossing, counted in one direction only. There are C / 2 of them per full helical revolution, so P · h = C / 2 and h = C / (2P). That is the definition in A-A-59569A §2.2.3, it is what every source that supplies an equation implements, and it falls out of the machine as well: a maypole braider has C / 2 horn gears and a carrier makes C / 2 transfers per orbit.
Two vendor pages describe a pick as crossings of one wire counted both ways, which is a factor of two out, and neither supplies an equation. Rather than argue with them, this page exposes h as a visible number: measure the axial advance of one wire on a real part and you can settle it in thirty seconds.
Why coverage is shown with its fill fraction beside it
Coverage is CF = 2F − F², where F = N · w / (2π · D_m · cos α) is the fraction of the surface one layer of ends would occupy. The trap is that CF turns back downward past F = 1. Double the fill by dividing by 2π·R instead of 4π·R — the most common error in this arithmetic — and a fill of 1.31, which is physically impossible, still returns a coverage around 91%. The percentage looks fine. That is why F is on this page as a number of its own, and why coverage above F = 1 is labelled as outside the model rather than quietly clamped.
One more thing worth knowing before you check this against a textbook: over a mandrel, where D_m is fixed, coverage rises with braid angle. In a free braid, where the helical length is fixed instead, coverage is at a minimum near 45°. The trend reverses between the two cases, and much published coverage data is the second case. A catheter braided over a mandrel is the first.
Why we are giving it away
Because the relations are public, the arithmetic is tedious, and engineers currently do this in spreadsheets they cannot cite. Handing you something that works — with the equation and its source printed under every number — is a better argument about how we work than any page describing how we work.
The same discipline shows up in the paid lines: the design and development work carries its provenance the same way, and the Component Atlas this tool serves draws every part from the same numbers the tables state. Nothing on this page is a lookup against a dataset we control, which is why it keeps working with the network switched off.
Questions
Is a braid angle measured from the axis or from the transverse plane?
Both, depending on who wrote the document in front of you. The cable-shielding literature — A-A-59569A, Interference Technology, Carol/General Cable — measures from the longitudinal axis and calls it alpha. Several catheter patents state their numbers from the transverse plane, which is the complement, beta = 90 degrees minus alpha. A 30 degree braid in one convention is a 60 degree braid in the other, and neither document usually says which it is using. This tool computes in alpha and prints both, always, so a figure can be matched to whichever convention your supplier quotes.
Does one pick count crossings in one direction or both?
One. A-A-59569A defines a pick as crossings in the same direction, and every source that supplies an equation gives picks times axial pitch equal to half the carrier count. Two vendor pages describe a pick as crossings counted both ways, which is a factor of two out, and neither supplies an equation. This tool implements the half-carrier form and prints the axial pitch as a visible intermediate so you can check it against a measured part with a loupe and a rule.
Why does this page show a fill fraction as well as a coverage percentage?
Because coverage alone hides the most common error in this arithmetic. Coverage is 2F minus F squared, which turns back downward past F = 1: a fill fraction of 1.31, which is physically impossible, returns a coverage of about 91 per cent, and a percentage in the nineties looks like a good answer. Printing F beside it makes a doubled fill visible as 1.31 instead of hidden inside a believable percentage.
Why is there no wire gauge conversion here?
ISO 9626:2016 Table 1 maps needle gauge to tubing dimensions, and it is copyright ISO with a notice that bars internet posting. The free alternative is a trap: the public-domain Birmingham Wire Gauge table is the ancestor of the medical gauge, not the medical gauge, and it is out by as much as 5.8 per cent at 23 G against the ISO designated metric size. So this tool asks for the OD and ID from your own drawing or supplier certificate, does the arithmetic on those, and links ISO 9626 for the mapping.
Why will this tool not give me the outer diameter of a sheath from its French size?
Because a sheath is labelled by its inner diameter — the largest catheter it will pass — while a catheter and a dilator are labelled by their outer diameter. The difference between a sheath inner and outer diameter is set by its wall and runs roughly one to two French depending on manufacturer and material, so it is not computable from the label. The tool asks the device class and refuses that direction rather than returning a confident wrong number.
Does this tell me anything about how a shaft will behave?
No, and that is a scope decision rather than a wording one. Geometry is a fact about a shape; how a shaft pushes, tracks, kinks or fails under pressure is a fact about a device, and this page makes no claims about devices. Nothing here evaluates a material, a durometer or a construction, and no figure on it is a rating of any kind.
The brief
Tell us what you are working on
What are you trying to clear, and what is in the way? A person reads these and replies.