Root protection area for a multi-stem tree, calculated

A root protection area for a multi-stem tree is calculated from a single combined stem diameter, not from the largest stem and not from the sum of the stems. BS 5837:2012 sets out the method: for a tree with two to five stems, take the square root of the sum of the squares of each stem diameter, then treat that figure as the stem diameter and apply the standard multiplier of 12 to get the radius. For a tree with more than five stems, use the square root of the mean stem diameter squared multiplied by the number of stems.

The arithmetic is easy. The mistakes are in the measuring and in the presentation, which is where a tree officer sends drawings back.

Where the standard defines the calculation

BS 5837:2012, on trees in relation to design, demolition and construction, sets the root protection area as the area equivalent to a circle with a radius of 12 times the stem diameter. That is a minimum area to be protected, not a prediction of where roots are, and the difference matters when you come to argue about the shape.

Stem diameter is measured at 1.5 metres above ground level. The standard also gives the adjustments for awkward trees: where a tree forks below 1.5 metres, measure immediately below the fork. Where the ground slopes, take the measurement relative to the higher side. Where a swelling or a graft union sits at measuring height, measure at the nearest sound point below it and record what you did.

For veteran and ancient trees, the standing advice is more demanding than the standard. The buffer expected around a veteran tree is at least 15 times the stem diameter, or five metres beyond the canopy edge, whichever is greater. A multi-stem veteran therefore gets a combined diameter calculation followed by the larger multiplier, and that combination produces an area that often rules out development on part of the site.

Measuring stem diameter on a single stem

Two practical points before the multi-stem case.

Use a diameter tape rather than a ruler and a calculation. Measuring circumference and dividing by pi introduces an error at every tree and the errors are not random, because tapes get pulled tight over bark ridges.

Record the measurement in millimetres, and record the height at which it was taken. A survey schedule that gives 310 without saying whether that is millimetres of diameter at 1.5 metres is the commonest reason a tree survey gets queried. Councils normally expect this work from a suitably qualified arboriculturist and professional review before submission is strongly advised.

The combined stem method

For a tree with two to five stems, the combined diameter is:

the square root of (d1 squared plus d2 squared plus d3 squared, and so on)

For a tree with more than five stems, the combined diameter is:

the square root of (the mean stem diameter squared, multiplied by the number of stems)

Both formulae do the same thing, which is to convert several stems into the single stem of equivalent cross-sectional area. That is why you cannot simply add the diameters. Adding them overstates the area by a large margin, and a report that does so is usually rejected because the resulting root protection area swallows the site.

Measure every stem that arises below 1.5 metres as part of the multi-stem count. A stem that divides above 1.5 metres is a branch for these purposes and is not counted separately.

An illustrative calculation for a three stem tree

Take a multi-stem field maple in a garden, with stem diameters at 1.5 metres of 240 millimetres, 310 millimetres and 180 millimetres. This example is illustrative.

So the protected area is a circle of radius 5.18 metres around the stem group, covering about 84 square metres. Round the radius to the nearest 0.1 metre on drawings and state the area to two significant figures. Do not present the radius to three decimal places, because it implies a precision the method does not have.

Compare that with the wrong answers. Using the largest stem alone gives a radius of 3.72 metres and an area of 43 square metres, about half the protection required. Adding the diameters gives 730 millimetres, a radius of 8.76 metres and an area of 241 square metres, nearly three times too much. Both errors appear in submitted drawings regularly, and the second is as much of a problem as the first because it makes an acceptable layout look impossible.

For a stem group with more than five stems, the mean method gives a slightly different figure from the sum of squares. Seven stems averaging 153 millimetres produce a combined diameter of 404 millimetres, a radius of 4.85 metres and an area of 74 square metres. Use whichever formula the standard specifies for the stem count rather than choosing the one that suits the layout.

The cap on the area

BS 5837 caps the root protection area at 707 square metres, which is a circle of radius 15 metres. That corresponds to a stem diameter of 1,250 millimetres, so the cap only bites on very large trees.

On multi-stem trees it bites sooner than people expect, because the combined diameter of a large coppice stool can reach that figure. A hornbeam stool with eight stems averaging 450 millimetres produces a combined diameter well over a metre, and the cap becomes the operative constraint.

Two points on the cap. It applies to the area, so where you cap the area, say so and give the uncapped figure as well. And the cap does not license working close to the stem: the protected area still has to be distributed sensibly around the tree, and the near-stem zone is the part that matters most.

Changing the shape of the area on site

A circle is the default, not a requirement. Where there is sound arboricultural reason to think the rooting is asymmetric, the shape can be modified while the area is held constant. Common reasons include a building foundation or a retaining wall on one side, a made-up road or car park over compacted formation, a watercourse, or a documented obstruction such as a services trench.

Three rules keep a modified area defensible. State the evidence for the asymmetry rather than asserting it. Keep the total area unchanged and show both figures on the drawing. And keep the modified shape a sensible polygon around the stem rather than a thin corridor running away from the building line.

Get the modification agreed with the tree officer before the layout depends on it. A layout that only works with a reshaped area, proposed for the first time at determination stage, invites a refusal. Where the tree has to survive construction as well as design, retaining a tree through the construction programme deals with the ground protection, the access route and the sequencing that make the calculated area mean something on site.

Presenting the calculation so an officer can check it

The tree survey schedule should carry, for every tree, the reference number, species, stem diameter at 1.5 metres in millimetres, number of stems where relevant, the combined diameter where calculated, the radius, the area, and the retention category. Put the arithmetic in the schedule rather than in an appendix, so a reader can reproduce it in 30 seconds.

Then show the area on the tree constraints plan at a stated scale, with the stem position dimensioned from a fixed point. Where the shape has been modified, show the default circle as a dashed line behind the modified polygon. That single drawing convention removes most of the argument.

Finally, make sure the landscape drawings agree with the arboricultural ones. A Landscape Strategy showing new planting inside a protected area, or a drainage layout with a soakaway in it, undoes the calculation. On street frontages the same conflict appears with utilities, and street trees, highway works and utility trenching is where the coordination usually fails.

Get the measurement right, show the working, and the number stops being contentious. Enter your postcode on PlanScope to see which tree and landscape documents your scheme is likely to need.

This is general guidance, not legal advice; check the position with your local planning authority or a qualified professional before relying on it. PlanScope provides AI-assisted draft reports for planning applications. Reports should be reviewed before submission. We do not guarantee planning approval.