Soil Volume Required for a Target Canopy
A tree's mature size is set by the soil it has, not by the species on the plan.
Example
You enter
- Intended mature canopy diameter (ft) 25
- Soil per sq ft of canopy (cu ft) 2
- Tree pit length (ft, 0 to skip) 5
- Tree pit width (ft) 5
- Tree pit depth (ft) 3
- Fraction of that soil roots can actually use 1
You get
- Canopy area (ft²) 490.874
- Soil required (ft³) 981.748
- Soil required (cy) 36.361
- Pit volume (ft³) 75
- Usable pit volume (ft³) 75
- Provision (%) 7.63944
- Supported canopy (ft) 6.90988
Details, formula, and sources
A tree's mature size is set by the soil it has, not by the species on the plan, and the arithmetic is brutal once it is written down. Guidance commonly puts the requirement at one and a half to two cubic feet of usable soil per square foot of intended canopy projection, and canopy area goes as the SQUARE of the diameter -- so a tree meant to reach twenty five feet across needs the better part of a thousand cubic feet of soil. A five by five foot pit three feet deep is seventy five. THAT IS EIGHT PERCENT OF WHAT THE PLAN ASKS FOR, and the tree does not fail: it grows to what its soil supports and stops, which is read as a species problem or a maintenance problem years later. The supported canopy is reported here beside the requirement, because it is the honest description of what has actually been built. COMPACTED SOIL IS NOT SOIL. Soil compacted to support paving is compacted past the density roots can penetrate, so a large volume of engineered subgrade beneath a sidewalk contributes nothing, and a pit whose walls are compacted is a container rather than an opening. That is what the usable fraction is for, and it is often the difference between a design that reads adequate and one that is. THE SOLUTIONS ARE STRUCTURAL RATHER THAN HORTICULTURAL, which is why this belongs in the site design and not in the planting detail. Connected trenches let several trees share a volume none of them could have alone; structural soil carries load through a stone skeleton with soil in its voids; suspended pavement carries the paving on a structure and leaves uncompacted soil beneath it. All of them cost money at construction and all of them are cheaper than replacing a street tree every fifteen years, which is what the alternative actually costs. A volume comparison against a ratio the reader supplies. The ratio itself varies with species, climate, soil type, rainfall and whether the tree is irrigated, and published guidance spans a wide range -- a number at the low end of it is not a safe default. It does not design the soil, specify its composition, drainage or organic content, or address the rooting depth that is actually available above a water table or a hardpan. It does not evaluate structural soil or suspended pavement systems, which have their own design and their own effective volumes, and it does not address the aeration, irrigation and drainage that decide whether a volume of soil is usable at all. The urban forestry standard in use, the landscape architect, and a qualified arborist govern.
canopy projection area = pi/4 x the mature canopy diameter squared; soil required = that area x the entered cubic feet of usable soil per square foot of canopy; and the canopy a given pit actually supports is that relation inverted on the usable pit volume.
The urban soil volume guidance by name -- commonly 1.5 to 2 cubic feet of usable soil per square foot of intended mature canopy projection. The ratio varies with species, climate, soil type, rainfall and irrigation and is ENTERED; published guidance spans a wide range and a number at the low end is not a safe default. Soil compacted for paving support is not soil roots can use, which is what the usable fraction is for. It does not design the soil or evaluate structural soil and suspended pavement systems. The urban forestry standard in use, the landscape architect, and a qualified arborist govern.
One area and one multiplication; no urban forestry manual is reproduced.
Estimate. AHJ and licensed professional govern.
Field names used by the API: canopy_diameter_ft, soil_per_canopy_ft3_per_ft2, pit_length_ft, pit_width_ft, pit_depth_ft, usable_fraction, canopy_area_ft2, soil_required_ft3, soil_required_cy, pit_volume_ft3, usable_pit_volume_ft3, provision_pct, supported_canopy_ft
- The ratio is entered it varies with species, climate, soil, rainfall and irrigationthe urban forestry standard in use
- Compacted soil does not count soil compacted for paving support is past what roots can penetratethe landscape architect
- It does not design the soil composition, drainage, aeration and rooting depth decide usabilitya qualified arborist