Critical Root Zone Encroachment Percent
How much of a tree's critical root zone a construction limit line cuts off, judged against species tolerance.
Example
You enter
- DBH (in) 20
- Radius factor 1
- Construction limit-line distance from trunk (ft) 5
- Species tolerance intermediate
You get
- Protection radius 20
- CRZ encroachment 34.3%
- Threshold (%) 30
Details, formula, and sources
A limit line at distance d slices a segment R^2 x acos(d/R) - d x sqrt(R^2 - d^2) out of the circle; encroach = segment / (pi x R^2) x 100. A wall 5 ft from a 20-in tree (R = 20 ft) encroaches 34% - fine for a tolerant species (40%), over the line for intermediate (30%) and sensitive (20%): same cut, three verdicts. Move it to 12 ft and it drops to 14%. A planning screen, not a tree-preservation permit.
radius = radius_factor x DBH; segment = radius^2 x acos(d/radius) - d x sqrt(radius^2 - d^2) for a limit line at distance d; encroach_pct = segment / (pi x radius^2) x 100; over when encroach_pct > threshold (tolerant 40 / intermediate 30 / sensitive 20).
Critical root zone encroachment (ANSI A300 Part 5 tree protection; arboriculture practice), by name.
The CRZ encroachment geometry and the species tolerance guides are published arboriculture practice; a qualified arborist and the local ordinance govern.
Estimate. AHJ and licensed professional govern.
Field names used by the API: dbh_in, radius_factor, limit_distance_ft, species_tolerance, radius_ft, encroach_pct, threshold_pct
- Single limit line encroachment is the circular segment beyond one straight limit line; multiple sides are cumulativeANSI A300 Part 5 / arboriculture practice
- Species tolerance acceptable encroachment ~40% tolerant, ~30% intermediate, ~20% sensitive (Matheny & Clark tolerance ratings)Matheny & Clark