Free tool · BS 5837:2012
RPA calculator: the BS 5837 root protection area
Enter the stem diameter at 1.5 m in millimetres, for a single or multi-stem tree. You get the root protection area radius and area, worked out the way BS 5837:2012 clause 4.6 sets out, with the working shown.
A guide, not a judgement. The RPA from this calculator is a starting point. The arboriculturist's assessment of the tree and the site, such as existing roads, buildings, slopes and soil, decides the final RPA and its shape.
Root protection area
- Radius
- Area
Working:
The radius is capped at 15 m, about 707 m².
The same calculation as Tree Atlas reports, rule rpa-v1. Radius to 0.01 m, area to 0.1 m².
How the RPA is worked out
BS 5837:2012 clause 4.6 gives the root protection area as a circle centred on the stem, with a radius of 12 times the stem diameter measured at 1.5 m above ground.
-
Single stem
Twelve times the stem diameter.
radius = 12 × Ø -
2 to 5 stems
Combine the stems: the square root of the sum of each stem diameter squared.
Ø = √(Ø₁² + Ø₂² + … + Øₙ²) -
More than 5 stems
The square root of the mean stem diameter squared, times the number of stems.
Ø = √(mean ز × n) -
Area and the cap
The area of the circle. The radius is capped at 15 m, an area of about 707 m².
area = π × radius²
Worked examples
| Stems (mm) | Combined Ø | Radius | Area |
|---|---|---|---|
| 480 | 480 mm | 5.76 m | 104.2 m² |
| 600 | 600 mm | 7.20 m | 162.9 m² |
| 300, 400, 500 | 707.1 mm | 8.49 m | 226.2 m² |
| 200, 250, 300, 350, 400, 450 | 796.1 mm | 9.55 m | 286.7 m² |
| 1300 | 1,300 mm | 15.00 m (capped) | 706.9 m² |
RPAs on the Tree Constraints Plan, from the survey
In Tree Atlas the RPA is worked out from the stem measurements as you type, multi-stem too, with this same calculation. The BS 5837 report, the Tree Constraints Plan and the DXF draw each RPA from the same records, so nothing is retyped.
Draw every RPA on the Tree Constraints Plan, from the survey
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