Predicting bonsai trunk taper

Trunk cutback for bonsai
Trunk cutback for bonsai

Naturally, growing bonsai is not done by formulas and ratios. The best bonsai break all the ratios mentioned in this article. However, these are ratios that in general produce realistic trees. As such, these can be used as an assistant for people growing their own trees and looking for guidance in how to go ahead.

Planning your bonsai

Growing bonsai is loads of fun. It does however take a lot of time and imagination if you decide to grow from seed! (Do see our posts on growing Nebari with seedlings!). Just to imagine.. You have this tiny seed, a few mm across, that you are going to grow into a 80cm tall bonsai with a trunk of 10cm thick. A process taking half a lifetime. How do you even project which steps to take and when!?

Chopping trunk segments
Chopping trunk segments

Many bonsai are grown by growing a tree out to a large size, cutting back, letting it grow and then cut it back again, as generally described in the {cut and grow and cut method}. This is a good process to develop bonsai for species that easily back bud. In general this is the case for deciduous trees. For conifers this is sometimes a little more difficult process. The big question is of course.. If I cut my tree down, what size will my tree become? And how thick can I expect the final tree to become!?

As explained in why bonsai lose their taper, it is possible to make some general assumptions on how trunks grow and how the taper develops. If you have not read that article, it would help to read that first. That explains the calculations behind the table below.  What I have done is take the calculations for segment thickening and applied them to 4 consecutive segments. In this example, I simulated that each segment is cut back when it is 0.618 times the thickened of the previous segment. The 0.618 is not a random number. It is the golden ratio used in art and design.

So what you get is that you cut the first segment when it reaches 10cm. The second segment is then left to grow until it reaches 6,2cm and cut back. And on and on: Segment 3 at 3.8, and segment 4 at 2.4cm. Due to the process explained in {why bonsai loose taper} you see that the final segment diameters are now 12,6 – 7,6 – 4,5 – 2,4. I will leave the more complex calculations of getting the final segments to have a ratio of 0.618 to someone else. (If you do work it out in spreadsheet automated formulas, please let me know).

Formulas for trunk segments
Formulas for trunk segments

How tall will my bonsai be?

This is up for grabs in a way. It really is up to you what you like. There is a whole category of bonsai called Sumo Bonsai. Sumo bonsai are bonsai that are extreme stocky. Typically, the tree is as high as the trunk is thick, up to 3 times as high as the trunk is thick. Most bonsai however will have a height of 6 to 12 times the diameter of the trunk. So in our example 75,5 to 151 cm tall. Do keep in mind: The final height for the tree is NOT the height of the last chop. I would recommend putting that 20-30% lower, allowing for top of canopy branching to develop.

Where can I put the first branch?

Typically the first branch comes at about 1/3 of the tree height. Not that if we take the inverted golden ratio (1/0,618 = 1,618) we get a good indication of how high that is: You want the ratio between the crown and the bare trunk to approach the golden ratio. The trunk is therefore the tree height divided by 2,618. This makes the ratio between crown and trunk 1,618. So in our example, a normal bonsai with a stout trunk will have a final height of ~75 cm, with the first branch at ~29cm.

Get the calculations!?

Mathematics for bonsai trunk segments
Mathematics for bonsai trunk segments

So.. These tables are nice. But would it not be nice to be able to do these for yourself? Of course, you can create your own spreadsheet. Please find the formula’s used in the figure below. Feel free to use them. Alternatively, I offer the spreadsheet in excel format for download here. That is right. You can download the full spreadsheet used to create these statistics and use it.

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