Bonsai wire is sold in even half millimetre steps. 1.0, 1.5, 2.0, 2.5, and on up to 6.5. That ladder looks linear, so "go up one size" sounds like it should mean roughly the same thing wherever you are standing on it.
It doesn't. What a wire contributes is its resistance to being bent further, and that is a section property: the section modulus of a round wire goes as the cube of its diameter. Elastic or plastic, both do, so the ratio between two gauges is the same either way. The diameter climbs in even steps and the strength climbs as the cube.
| step |
diameter |
holding power |
| 1.0 to 1.5 mm |
+50% |
3.38x |
| 1.5 to 2.0 mm |
+33% |
2.37x |
| 2.0 to 2.5 mm |
+25% |
1.95x |
| 2.5 to 3.0 mm |
+20% |
1.73x |
| 3.0 to 3.5 mm |
+17% |
1.59x |
| 3.5 to 4.0 mm |
+14% |
1.49x |
| 4.0 to 4.5 mm |
+12% |
1.42x |
| 4.5 to 5.0 mm |
+11% |
1.37x |
| 5.0 to 5.5 mm |
+10% |
1.33x |
| 5.5 to 6.0 mm |
+9% |
1.30x |
| 6.0 to 6.5 mm |
+8% |
1.27x |
One step at the bottom of the ladder is worth about two and a half steps at the top.
Two practical things fall out of that, and both of them match advice I have seen repeated here.
The first is doubling up. Two wires side by side carry twice the moment of one, and twice the cube of the diameter means multiplying the diameter by 1.26, because 1.26 cubed is 2. At 1.5 mm that lands on 1.89, so two 1.5s are a shade under a single 2.0 and buy you exactly one step. At 4.0 mm it lands on 5.04, so two 4s genuinely stand in for a 5.0, which is two steps up. Using two thinner wires because you don't have the thick stuff is therefore a decent trade on a trunk and close to pointless on a shoot, where a single wire of the next size would have got you almost the same place.
The second is rounding. If a rule of thumb hands you 1.1 mm and the shelf goes 1.0, 1.5, then taking the 1.5 gives you two and a half times the wire you calculated. If it hands you 4.4 mm and you take the 4.5, you are 7% over. Same rounding rule, completely different consequence, and I suspect that is part of why wire on fine shoots so often looks heavier in photos than the person intended.
Where I get stuck is the 1/3 rule itself.
A fixed ratio means the wire's capacity scales as the cube of the branch diameter. The branch's own elastic resistance to being bent to a given radius scales as the fourth power of its diameter. Those two only stay in balance if the radius you are asking for grows in proportion to the branch, which is roughly what happens when you style to scale and not what happens when you want one specific piece of movement in one specific place. On that reading the 1/3 rule should quietly get thin on you as the branch gets thicker.
The honest caveat is that this argument treats the branch as elastic and it is not. Most of what stops a wired branch springing back is the wood taking a permanent set and creeping over the following weeks, not the wire holding it. Comparing gauges to each other needs no assumptions at all, which is why I trust the table. Working out how much wire a given branch actually needs does need assumptions I can't defend, so I am not going to pretend the second half is settled.
Worth disclosing since it is where this came from: I build a bonsai app called Kodama, and its wire calculator does exactly the rounding described above. Until I ran the numbers I had not noticed that the rounding is nearly free at the top of the range and costs a factor of three at the bottom. https://BigBalli.com/Kodama/
So, for people who wire a great deal more than I do. Does a third hold at both ends in practice, or do you find yourself going heavier than a third once a branch is past finger thickness? And does anyone deliberately go under a third on very fine work precisely because the next size up is such a big jump?
