To calculate a root protection area, multiply the tree's stem diameter (measured at 1.5m above ground) by 12 to get the RPA radius — then cap the resulting area at 707 square metres for large trees. That is the BS 5837:2012 formula in one line. Everything else on this page is about applying it correctly: measuring in the right place, handling multi-stem and veteran trees, converting girth to diameter, and turning the number into a usable constraint on a plan.
If you're new to the concept, start with what is a root protection area?. This guide is the maths.
The formula
BS 5837:2012 (clause 4.6) defines the RPA as a circle whose radius = 12 × stem diameter, with two things you must get right:
- Measure the stem diameter at 1.5m above ground level — diameter at breast height (DBH). Not the base flare, not the canopy spread. If you only have the girth (circumference), divide it by pi (3.14159) to get the diameter. On sloping ground, take the 1.5m from the higher side; where the trunk forks or bulges at 1.5m, surveyors adjust the measurement point per the standard.
- Cap the area at 707 square metres. For a stem diameter above roughly 1.25m, a straight 12× radius produces an unrealistically huge circle, so the standard caps the RPA at 707m² — the area of a 15m radius circle.
Two forms of the calculation are useful, and you'll switch between them:
- RPA radius (m) = 12 × stem diameter (m) — gives you the circle to plot.
- RPA area (m²) = π × radius² — gives you the number to check against the 707m² cap.
A quick sense-check table (standard, non-veteran trees):
| Stem diameter | RPA radius | RPA area | Notes |
|---|---|---|---|
| 150mm (0.15m) | 1.8m | ~10m² | Small tree, often Category C |
| 250mm (0.25m) | 3.0m | ~28m² | |
| 400mm (0.40m) | 4.8m | ~72m² | |
| 500mm (0.50m) | 6.0m | ~113m² | Mature tree |
| 750mm (0.75m) | 9.0m | ~254m² | Large mature tree |
| 1,250mm (1.25m) | 15.0m | ~707m² | At the cap threshold |
| 1,400mm (1.40m) | (16.8m) | capped to 707m² | Cap applied |
Worked examples
Example 1 — a mature oak, 500mm stem diameter
- Radius = 12 × 0.5 = 6.0m
- Area = 3.14159 × 6.0² = 113m²
- Below the cap, so the RPA is a 6m-radius circle of 113m².
Example 2 — a small tree, 250mm stem diameter
- Radius = 12 × 0.25 = 3.0m
- Area = 3.14159 × 3.0² = 28m²
Example 3 — measured by girth, 1,570mm (1.57m) girth
- Diameter = 1.57 ÷ 3.14159 = 0.5m (500mm)
- Radius = 12 × 0.5 = 6.0m — identical to Example 1, just measured differently.
Example 4 — a large tree hitting the cap, 1,400mm stem diameter
- Radius = 12 × 1.4 = 16.8m → area = 3.14159 × 16.8² = 887m² — over the cap.
- Apply the cap: RPA = 707m², plotted as a 15m-radius circle.
Multi-stem trees
Where a tree divides into several stems below 1.5m, you do not simply add the diameters together — that overstates the RPA badly and no tree officer will accept it. BS5837 uses a combined (notional) stem diameter: the square root of the sum of the squares of the individual stem diameters.
For a tree with three stems of 200mm, 300mm and 250mm:
- Sum of squares = 200² + 300² + 250² = 40,000 + 90,000 + 62,500 = 192,500
- Combined diameter = √192,500 = 439mm (0.439m)
- RPA radius = 12 × 0.439 = 5.3m
That is meaningfully smaller than the 9m radius you'd get by naively summing the stems (750mm × 12). Where a tree has more than about five stems, the standard shifts to a simpler proxy — the mean stem diameter multiplied by the square root of the number of stems — to avoid the calculation becoming unwieldy.
Veteran and ancient trees
Ancient and veteran trees are treated as irreplaceable habitat under national planning policy, and they get an enhanced RPA: 15 × stem diameter, or the canopy edge plus 5m, whichever is the larger. The point is to be generous, not economical — the standard 707m² cap does not constrain them in the same way. So a veteran oak with a 1m stem diameter has an RPA radius of 15 × 1 = 15m (before even considering the canopy-plus-5m alternative), and a spreading crown could push the protected zone wider still.
Ancient woodland is handled separately again: a minimum 15m buffer from the woodland boundary is expected, and larger where other impacts extend further. These enhanced figures materially shrink the developable area of a site, which is exactly why they must be identified at survey stage, not discovered late.
When the circle becomes a polygon
The circle is only the default shape. Roots do not grow into solid obstructions, so where a suitably qualified arboriculturist can demonstrate that rooting is asymmetric — a wall, road, riverbank, or existing building hard against one side — the RPA can be re-plotted as a polygon of the same area, redistributed to where roots can realistically grow. Worked through: an oak with a 113m² circular RPA sitting tight against a Victorian terrace can't be rooting into the house, so that area is reallocated to the open garden side, producing a lopsided polygon that still encloses 113m². This is a recorded professional judgement, justified in the survey — never a quiet trick to fit a foundation.
Requirements are set locally — check your council
The RPA formula is national: BS5837:2012 is a UK-wide British Standard, so the 12× calculation is the same in every authority. But BS5837 is guidance, not law — it becomes binding only when your local planning authority adopts it through its validation list or imposes it via a planning condition, and councils differ in how strictly they scrutinise RPA plotting, how much justification they want for a polygon, and how readily they accept construction inside an RPA. What a tree officer in Manchester waves through, one in Bristol or Nottingham may question — so the calculation is only half the job; presenting it in a way your authority accepts is the other half.
PlanWatch tracks live tree-related planning activity per council, so you can see how RPAs and tree constraints are being handled in real applications near you — start at the tree-surveys hub and check your area before you rely on a number. And note the usual scope caveat: this is England-centric guidance; Scotland, Wales and Northern Ireland apply the same BS5837 calculation but sit within different statutory planning frameworks.
From numbers to a plan
A calculated RPA only does its job once it is plotted to scale on a drawing so you can see the true developable area. That is what a tree survey and its tree constraints plan deliver, and it is why the RPA should be worked out before the layout is fixed — designing first and calculating later is the classic route to a refusal or a costly redesign. If your numbers show the scheme intruding into an RPA, read can you build in a root protection area? for the engineered, no-dig options, and see the full BS5837 survey for how these figures feed the arboricultural impact assessment and the wider application.
The formula here is the BS5837:2012 standard method. For a specific site, have the measurements taken and the RPAs plotted by a suitably qualified arboriculturist — find a tree surveyor.