Section one
Why a growth model is needed at all
A BS5837 survey records a tree as it stands. A development, by contrast, is designed once and then lived in for decades. The gap between those two timescales is where most avoidable conflict between trees and buildings begins: a canopy drawn at its surveyed size looks comfortably clear of a window, and fifteen years later it is not.
The pending revision to BS5837 addresses this by asking for canopy extents at nominal snapshots of 0, 10, 20 and 30 years, so that layout, daylight, shading and pruning liability can all be tested against the tree the occupier will actually live with. That is a sound requirement, and it creates an immediate practical problem: growth rates for amenity trees in the United Kingdom are poorly published, and the software that offers to model them tends not to show its working.
Our position is that a projection nobody can check is worth very little in a planning context. Every rate, modifier and transition rule used here is stated on this page, traced to a named source, and applied identically to every tree in every survey we issue. If a local planning authority, a design team or another consultant disagrees with a number, they can see which number to argue with.
What this model is not. It is not a prediction of any individual tree's future size, and it is not a substitute for a condition assessment. It projects canopy spread only; it says nothing about a tree's health, structural integrity or safe useful life expectancy, and it cannot anticipate pruning, disease, drought, root severance or the failure of a limb. It is a consistent, defensible planning assumption, applied evenly, so that comparisons between trees and between design options are meaningful.
Section two
The method in five stages
The sequence below runs from a surveyor standing under the tree to the projected canopy outlines that appear on the tree constraints plan. Nothing in it is hidden from the client: the same five stages are described in the report appendix that accompanies every drawing.
Survey the tree as it stands
Canopy spread is measured to each of the four cardinal points, not as a single average radius, so an asymmetric or wind-shaped crown is recorded as asymmetric. Life stage and a growth potential rating are assigned at the same time.
Select the base growth rate
Each life stage carries an annual radial growth rate in metres per year, derived from published allometric data rather than from a rule of thumb. Growth slows markedly as a tree matures.
Apply the three modifiers
Direction of growth, the surveyor's judgement of growth potential, and the tree's progression through later life stages during the projection window are each applied to the base rate.
Grow each direction separately
North, east, south and west are projected independently from their surveyed measurements, so the shape recorded in the field is carried forward rather than being averaged away.
Four canopy outlines per tree
Snapshots at 0, 10, 20 and 30 years, drawn as individual canopies and as a combined extent for the whole survey, issued on the constraints plan and in the schedule.
Show the working: the projection formula
Each of the four cardinal radii is projected independently. For a given direction:
The model is deliberately additive rather than exponential. Canopy radius in mature amenity trees does not grow as a fixed percentage of itself, and a compounding model applied over thirty years produces implausible extents for the largest trees, which are precisely the trees where accuracy matters most on a constraints plan.
Section three
Where the growth rates come from
There is no published table of lateral canopy growth rates for United Kingdom amenity trees that can simply be adopted. What does exist is a body of allometric work relating stem diameter to crown radius, and a long-standing field rule for annual stem growth. The rates used here are built by combining the two, then tested against the raw data that underpins the allometry.
Three sources, used for three different things
- Fennell and Fay (2024), Handbook of UK Urban Tree Allometric Equations and Size Characteristics. Around 15,400 records across 23 species, giving power-law equations relating stem diameter to crown radius. Used as the primary relationship.
- The OBARD v1.3 dataset, the raw measurements underlying that handbook. Analysed directly rather than through the fitted equations, as an independent empirical check.
- Mitchell's Rule (1974), the long-standing field assumption for annual girth increment in open-grown trees. Used to convert an allometric relationship into an annual rate.
The step that is easy to get wrong
An allometric equation gives crown radius for a given stem diameter. It does not give a growth rate, and the two are not interchangeable. A rate has to be obtained by difference: take the crown radius predicted at the tree's actual current stem diameter, take the radius predicted at that diameter plus one year's increment, and subtract. Substituting the annual increment directly into the equation instead returns the crown radius of a seedling and produces rates roughly an order of magnitude out.
How good is the evidence, plainly
Not very. That is worth saying openly, because the alternative is to imply a precision that does not exist, and because everybody working on this problem is drawing on the same thin material.
There is no longitudinal study of amenity tree canopy growth in the United Kingdom of any useful size: no substantial population of trees measured, left alone, and measured again a decade later. What exists instead is cross-sectional data, many different trees measured once, from which growth has to be inferred by treating a large tree today as what a small tree today will become. That inference is sound in aggregate and unreliable for an individual, and no amount of statistical care removes the limitation.
The published allometry carries three further constraints worth stating. It covers a couple of dozen species, against the several hundred that turn up across a working survey archive. The threshold used to accept a fitted equation is permissive, so weak relationships sit in the same published table as strong ones and look alike. And the underlying measurements were taken for survey purposes rather than research purposes: crown spread is recorded to the nearest half metre, which for a small tree is a large fraction of the measurement itself.
The honest conclusion is that this evidence supports a defensible, consistent planning assumption. It does not support a claim to predict any particular tree, and we do not make one.
Testing it against fifteen years of our own surveys
Rather than take the published relationships on trust, we rebuilt them from our own archive. Every BS5837 survey spreadsheet produced by this practice and its predecessor over more than fifteen years was consolidated into a single dataset: around 10,650 individual tree records, of which some 9,740 survive outlier screening. Species names were normalised, dead and removed trees excluded, and crown radius taken as the mean of the four cardinal spreads.
Fitted on the same basis as the published work, that archive supports seventeen species at the sample size threshold the published Handbook itself uses, and a further twenty four at a lower, clearly flagged tier. Around three hundred more species appear too rarely to fit at all, which is its own useful finding about how amenity tree populations are actually composed. Pedunculate oak alone contributes over 1,700 usable records.
Eighteen species appear in both datasets, which allowed a direct comparison. That comparison produced the most useful result of the whole exercise, and it was not the one we expected.
Show the working: a 14.9 per cent difference that turned out not to exist
Compared species by species against the published coefficients, our fitted curves returned crown radii averaging 14.9 per cent smaller, with no comparable difference in height. Read at face value that is an interesting regional finding, and it would have been tempting to report it as one: trees in this part of the country carrying narrower crowns than the national picture.
It was not a regional effect. It was a definition. The published dataset records crown radius as a minimum bounding circle rather than as an average of the four cardinal spreads, and testing that field against the raw spread measurements confirms it is calculated as half the sum of the wider of the two opposing pairs. For any asymmetric crown, which is most of them, that produces a systematically larger figure than a four-direction mean.
Refitting the published raw data using our own definition collapsed the difference from 14.9 per cent to 0.8 per cent. There is no meaningful difference in tree size between the two datasets; the entire apparent effect was a mismatch in what the words meant.
We report this because it is the single most transferable lesson in the whole piece of work. Anyone combining allometric sources, and any software doing it invisibly, is exposed to exactly this class of error, and it is undetectable from the outputs alone. Both definitions are defensible; mixing them without noticing is not.
Show the working: how the archive was fitted
Relationships were fitted as log-log ordinary least squares, back-transformed with the standard bias correction, matching the published methodology so the two sets of coefficients are directly comparable rather than merely similar. Fits returning an R² below 0.2 were logged and dropped.
Two data-cleaning decisions are worth stating because they affect the result. Crown radius is the mean of the four cardinal spreads, after excluding records where any one direction exceeds four times the mean of the other three. That pattern is not a data error: it is the recording convention for a tree with a heavy lean or a swept stem, where the survey captures minimum canopy extent, and it affected under two per cent of records. Outlier bounds on height, diameter and crown radius mirror the published thresholds, so the same trees are in scope in both datasets.
Species-level results are not currently used to vary the growth rates in the model, for the reason given in the limits below: coverage is good for common species and absent for most others, and a refinement that applies to a third of the trees on a site is worse than a consistent assumption applied to all of them. The archive's present role is to test the published rates, not to replace them.
Show the working: deriving a rate from an allometric equation
For a tree of current stem diameter DBH, with an annual diameter increment
ΔDBH, the annual lateral growth of the crown is:
Mitchell's Rule gives an annual girth increment of roughly 20 mm for an open-grown tree, which is
about 0.64 cm of stem diameter per year once converted and scaled for typical amenity conditions.
That value sets ΔDBH, and the resulting rate is evaluated across the diameter
range associated with each life stage.
Show the working: the independent empirical check, and what it found
The same rates were derived a second time, without using the fitted equations at all. Records in the raw dataset were binned by stem diameter, the median crown radius taken for each bin, and the change in median radius from one bin to the next converted to an annual rate using the same diameter increment. Two findings came out of that exercise, and both are worth stating openly.
Crown radius is recorded coarsely. More than 97 per cent of crown radius measurements in the dataset fall on a multiple of 0.5 m, rising to over 99 per cent for trees under 10 cm stem diameter. For small trees this rounding is a substantial proportion of the measurement itself, and it is the single largest source of noise in the derived rates for young trees.
The fitted equations over-predict for small trees. Contrary to the direction of error we expected, empirical median crown radii ran roughly 15 to 30 per cent below the values the single power law predicts in the 10 to 20 cm diameter range. Averaging the two derivations, rather than taking either alone, produces the base rates used in the model.
Two further points affect confidence rather than the numbers themselves. The published dataset contains taxonomic synonym splits, with the same taxon appearing under two names, which artificially fragments sample sizes for those species. The acceptance threshold used for the published equations is also permissive, so we treat species below an R² of 0.5, or with a standard error above 0.3, as low confidence and rely on the life stage rate rather than any species-specific refinement.
Show the working: how the two end values were obtained
The empirical binning approach produces reliable values for the four central life stages, where sample sizes are large. It does not for newly planted trees, where crown radius rounding swamps the signal, or for veterans, where the sample is small and dominated by trees that have been managed. Those two values were obtained by fitting an exponential decay curve through the four central rates and reading off the ends, which keeps the whole series internally consistent rather than mixing derived and assumed numbers on the same scale.
Section four
The three modifiers
The base rate is a starting point, not an answer. Three modifiers are applied to it, each capturing something the raw allometry cannot: when in its life the tree is growing, which way it is growing, and what the surveyor judged about that particular tree on that particular site.
One: life stage, and the transitions between stages
Growth slows with age, and over a thirty year projection most young trees will not still be young at the end of it. Rates therefore step down as the tree passes from one life stage to the next during the projection window, rather than a single rate being applied for the full period. In the table below, a higher rate means faster canopy expansion.
| Life stage | Indicative stem diameter | Base rate (m per year) | Modelled duration from survey |
|---|---|---|---|
| Newly Planted | 1 to 5 cm | 0.160 | 10 years, then Young |
| Young | 5 to 20 cm | 0.120 | 20 years, then Early Mature |
| Early Mature | 20 to 40 cm | 0.080 | 20 years, then Mature |
| Mature | 40 to 80 cm | 0.060 | Stable across the window |
| Late Mature | 80 to 120 cm | 0.040 | Stable across the window |
| Veteran | Over 120 cm | 0.025 | Stable across the window |
Dead trees are excluded entirely. They carry no projection at any snapshot. Where a tree is recommended for removal on arboricultural grounds it is still projected, because the decision to remove it is the applicant's and the constraints plan has to show what is being given up.
Show the working: the transition assumption, and why it is conservative
The model assumes a tree enters its recorded life stage on the day of survey, and therefore has the full modelled duration of that stage ahead of it. A tree surveyed as Young is treated as having twenty years of Young growth remaining, then twenty of Early Mature, reaching Mature at year forty and so beyond the projection window.
In reality the tree is somewhere within its stage, not at the start of it, so the model tends slightly to over-project rather than under-project. On a constraints plan that is the right direction to err in: the cost of showing a canopy marginally larger than it turns out to be is a conversation at design stage, while the cost of showing one too small is a pruning application after the building is occupied.
Two: direction of growth
Canopies in the northern hemisphere do not expand evenly. Greater solar exposure on the southern face drives faster extension, and the effect is visible in almost any open-grown tree once you start looking for it. Each cardinal radius is therefore projected at its own adjusted rate, so the projected canopy leans south rather than inflating as a circle.
| Direction | Factor | Reason |
|---|---|---|
| North | × 0.80 | Least direct solar exposure, so the slowest face |
| East | × 1.00 | The reference condition the base rates describe |
| South | × 1.20 | Greatest solar exposure, so the fastest face |
| West | × 1.00 | The reference condition the base rates describe |
The effect is easiest to see rather than read: the interactive panel in the next section draws the four projected outlines in plan, and the southward lean appears within a couple of decades even on a crown that starts out symmetrical.
Three: growth potential, assigned by the surveyor
The published data describes trees in aggregate. It cannot know that this particular lime is in a paved pit with three cubic metres of soil, or that this particular oak has an open field on two sides. Growth potential is the surveyor's judgement on that point, recorded in the field at the same time as the spread measurements, on a five point scale.
| Rating | Multiplier | Applied where |
|---|---|---|
| Very Low | × 0.60 | Severely constrained: a tree pit in paving, a heavily shaded understorey position, or a regime of repeated hard reduction that will keep the crown where it is |
| Low | × 0.80 | Restricted rooting volume, hard surfacing over much of the root area, or significant competition |
| Medium | × 1.00 | Typical amenity conditions; the default, and the condition the base rates themselves describe |
| High | × 1.20 | Open-grown, unconstrained rooting, no significant competition for light |
| Very High | × 1.40 | Exceptional: a young, vigorous tree of a fast species in open ground with no competition and no foreseeable constraint |
The two outer ratings are used sparingly. Most trees on most sites are Low, Medium or High, and a Very Low or Very High rating carries a note in the schedule saying why.
Section five
Try the model
The panel below runs exactly the calculation described above, with the same rates and modifiers. Enter a tree's surveyed spreads and see the four snapshots it would produce. Nothing is sent anywhere; the arithmetic runs in your browser.
| Direction | Year 0 | Year 10 | Year 20 | Year 30 |
|---|
On a real survey this runs across every tree at once, and the four snapshots are issued as separate drawing layers so a design team can switch between them. The arithmetic, though, is the arithmetic shown here: no species lookup, no hidden coefficient, nothing that cannot be reproduced with the tables further up this page.
Section six
Limits and caveats
Stated plainly, because a model whose limitations are buried is a model that will eventually be used for something it cannot do.
- It is not species specific
Rates are set by life stage, not by species. A field maple and a London plane at the same life stage and growth potential will project identically. This is a deliberate choice: the species-level equations that exist have wide confidence intervals and cover a minority of the species we survey, and a species refinement that is right for some trees and badly wrong for others is worse than a consistent assumption applied to all of them. Our own archive extends usable coverage to around forty species, which is better and still nowhere near the whole of a typical site.
- It is built from cross-sectional data
The underlying measurements are of many different trees at one moment, not of the same trees over time. Inferring a growth rate from that comparison assumes that a large tree today is what a small tree today will become, which is a reasonable assumption in aggregate and an imperfect one for any individual.
- It does not model management
Pruning, crown reduction, storm damage, root severance and decline all change canopy extent, and none of them appear in the projection. A projected canopy is the extent expected if the tree is left to grow.
- It does not model competition or a changing climate
Neighbouring canopies closing in, new buildings casting shade, and long-term shifts in growing season are all outside the model's scope. Over a thirty year window these are real effects, and the growth potential rating is the only place where any of them can be reflected.
- It tends to over-project rather than under-project
Because a tree is assumed to enter its life stage on the day of survey, and because growth potential is judged conservatively, the errors in the model mostly point the same way. That is intentional, and it is stated so that the direction of the bias is never a surprise.
- It is reviewable
Every rate on this page can be recalculated from the cited sources, and every projection in a report can be reproduced by hand from the schedule. Where better data becomes available, the rates change and the version of this page changes with them.
Section seven
Sources and version
- Fennell, J.T. and Fay, L. (2024) Handbook of UK Urban Tree Allometric Equations and Size Characteristics, v1.4. DOI 10.13140/RG.2.2.28745.04961. CC BY 4.0.
- OBARD v1.3, the raw dataset underlying the above, analysed directly for empirical bin rates.
- Mitchell, A.F. (1974) A Field Guide to the Trees of Britain and Northern Europe. Collins.
- Hirons, A.D. and Sjoman, H. (2019) Tree Species Selection for Green Infrastructure, Issue 1.3. Trees and Design Action Group.
- BS5837:2012, Trees in relation to design, demolition and construction. Survey extent at 4.4.2.1; estimated remaining contribution at 4.4.2.5.
Version 1.0 · September 2026 · first publication