Why is the radius twelve times the stem diameter?

It is the standards' proxy for how far the roots a tree cannot afford to lose extend, taken from the one dimension that can be measured quickly and repeatably. A 620 mm (24.4 in) stem gives a radius of 7.44 m (24.4 ft) and an area of about 174 m² (1,873 sq ft) — the same figure in both units, because twelve times a diameter in inches is a radius in feet — a far larger patch of ground than the crown suggests on a young tree, and often a smaller one on an old, spreading one.

How do I measure a tree with several stems?

Measure each stem at the standard height — 1.5 m (4 ft 11 in) for BS 5837, 1.4 m (4 ft 7 in) for AS 4970 — and combine them. Up to five stems combine as the square root of the sum of their squares; above five, BS 5837 uses the mean diameter times the square root of the number. Three stems of 200, 300 and 250 mm (7.9, 11.8 and 9.8 in) combine to 438.7 mm (17.3 in), a radius of 5.26 m (17.3 ft).

What happens above 707 m²?

BS 5837 caps the area there, which is a circle of 15 m (49 ft) radius — reached by any stem over about 1.25 m (49 in). AS 4970 caps the radius at 15 m directly and also sets a 2 m (6 ft 7 in) minimum, so a small tree still gets a protected zone worth fencing.

Can the protected area be a different shape from a circle?

Yes, under both standards, where the arboriculturist finds the roots constrained or displaced — by a building, a road, a change in level — and the area stays the same. The circle is what the arithmetic gives before anyone has looked at the ground; the report fixes the final shape, and the fencing follows the report.

Materials & Quantities

Tree Root Protection Area Calculator (BS 5837 RPA and AS 4970 Notional Root Zone)

The root protection area BS 5837 sets from a tree's stem diameter, or AS 4970's root zones, for one stem or several, and how far works sit from its edge.

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Standard

The British standard's root protection area, or the Australian standard's notional root zone.

Both start from twelve times the stem diameter. BS 5837 measures the stem at 1.5 m (4 ft 11 in) and caps the AREA at 707 m² (7,610 sq ft); AS 4970 measures at 1.4 m (4 ft 7 in), holds the RADIUS between 2 m (6 ft 7 in) and 15 m (49 ft), and adds a structural root zone for the tree's stability. In AS 4970:2025 the figure is the notional root zone, the starting point from which the project arborist sets the tree protection zone.

Number of Stems

Trees that fork below the measuring height are treated as several stems combined into one diameter.

Two to five stems combine as the square root of the sum of their squares, which gives the diameter of a single stem with the same total cross-section. For more than five, BS 5837 uses the mean diameter times the square root of the count, which is the same thing for stems of equal size.

Stem Diameter

The stem's diameter at 1.5 m (4 ft 11 in) above ground for BS 5837, or 1.4 m (4 ft 7 in) for AS 4970; the first stem of a forked tree.

Measure the girth with a tape and divide by π, or use a diameter tape. On sloping ground take the height from the upper side. The diameter is of the stem, not of the crown you can see, and the crown is no guide to where the roots are.

Distance from the Stem to the Nearest Works (0 to skip)

From the centre of the stem to the nearest edge of the excavation, trench or structure.

Measure on plan to the closest point the works reach, including the working space and any batter, not just the line of the foundation on the drawing.

Radius of the protected area

24 ft

High confidence

Twelve times the stem diameter as the radius of a circle. BS 5837 lets the arboriculturist change the circle's shape to follow the roots actually present, keeping the area the same, so the circle is the starting geometry rather than the only one. The nearest works sit outside the protected circle.

Stem diameter: 24 in
Root protection area: 1,809.56 ft²
Distance from the stem to the works: 30 ft
Works beyond the edge (negative: inside it): 6 ft

Then change the inputs to see how far the answer moves.

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How this was calculated

Formula source(s)

BS 5837:2012 Trees in relation to design, demolition and construction, 4.6.1 and Annexes C and D: the root protection area is a circle whose radius is twelve times the stem diameter measured at 1.5 m above ground, capped at 707 m²; for two to five stems the combined diameter is √(d1² + d2² + …), and for more than five the mean stem diameter × √(number of stems)
AS 4970:2025 Protection of trees on development sites (the second edition, which superseded AS 4970-2009): notional root zone radius = 12 × the diameter at standard height, 1.4 m, no less than 2 m and no more than 15 m, stems combined as √(Σd²); structural root zone radius = (D × 50)^0.42 × 0.64 from the diameter D just above the root buttress, no less than 1.5 m

Inputs used

Standard: BS 5837:2012 — root protection area (UK)
Number of Stems: One stem
Stem Diameter: 24 in
Stem 2 Diameter (0 if none): 11.75 in
Stem 3 Diameter (0 if none): 9.75 in
Stem 4 Diameter (0 if none): 0 in
Stem 5 Diameter (0 if none): 0 in
Mean Stem Diameter: 6 in
Number of Stems (count): 8
Trunk Diameter Above the Root Buttress (0 to skip): 28 in
Distance from the Stem to the Nearest Works (0 to skip): 30 ft

Intermediate steps

Stem diameter: 24 in
Root protection area: 1,809.56 ft²
Distance from the stem to the works: 30 ft
Works beyond the edge (negative: inside it): 6 ft

Final result24 ft

Confidence note: Twelve times the stem diameter as the radius of a circle. BS 5837 lets the arboriculturist change the circle's shape to follow the roots actually present, keeping the area the same, so the circle is the starting geometry rather than the only one. The nearest works sit outside the protected circle.

What this calculation does not cover

It sets out the standard's geometry from the diameter you measured. It does not assess the tree's condition, its species' tolerance of root loss, or whether a Tree Preservation Order, a conservation area or a planning condition applies — those sit with the arboricultural report and the planning authority.
A circle about the stem. Roots follow the ground, not the geometry: a kerb, a building, a watercourse or a change in level can confine them to one side, and the arboriculturist may reshape the protected area to match, keeping its area.
A tree's roots also affect the ground well beyond the protected area. On shrinkable clay the foundations near it are a separate question, set by the soil's volume change potential, the species' water demand and its mature height — see the modified plasticity index calculator.

Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.

Sources checked 2026-09-22 · v1.0.0

Regulatory standards & verification citations2

BS 5837:2012 Trees in relation to design, demolition and construction, 4.6.1 and Annexes C and D: the root protection area is a circle whose radius is twelve times the stem diameter measured at 1.5 m above ground, capped at 707 m²; for two to five stems the combined diameter is √(d1² + d2² + …), and for more than five the mean stem diameter × √(number of stems)
AS 4970:2025 Protection of trees on development sites (the second edition, which superseded AS 4970-2009): notional root zone radius = 12 × the diameter at standard height, 1.4 m, no less than 2 m and no more than 15 m, stems combined as √(Σd²); structural root zone radius = (D × 50)^0.42 × 0.64 from the diameter D just above the root buttress, no less than 1.5 m

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These guides cover the work this quantity is for — the first ones run this calculator inside the section that raises the question.

Setting Foundation Depth Near Trees on Shrinkable Clayuses this calculator
On shrinkable clay the tree sets the dig, not the load — how species, distance and plasticity index become a trench depth, and what goes on its faces.
Clearing and Grubbing a Wooded Lot

How to calculate tree root protection area (BS 5837 RPA and AS 4970 notional root zone) in 12 steps

StandardThe British standard's root protection area, or the Australian standard's notional root zone.
Number of StemsTrees that fork below the measuring height are treated as several stems combined into one diameter.
Stem DiameterThe stem's diameter at 1.5 m (4 ft 11 in) above ground for BS 5837, or 1.4 m (4 ft 7 in) for AS 4970; the first stem of a forked tree.
Stem 2 Diameter (0 if none)The diameter of stem 2, measured at the same height as the first; leave at 0 if the tree has fewer stems.
Stem 3 Diameter (0 if none)The diameter of stem 3, measured at the same height as the first; leave at 0 if the tree has fewer stems.
Stem 4 Diameter (0 if none)The diameter of stem 4, measured at the same height as the first; leave at 0 if the tree has fewer stems.
Stem 5 Diameter (0 if none)The diameter of stem 5, measured at the same height as the first; leave at 0 if the tree has fewer stems.
Mean Stem DiameterThe average diameter of the stems of a many-stemmed tree or coppice stool.
Number of Stems (count)How many stems the tree has at the measuring height.
Trunk Diameter Above the Root Buttress (0 to skip)For AS 4970's structural root zone: the trunk diameter just above the flare at the base.
Distance from the Stem to the Nearest Works (0 to skip)From the centre of the stem to the nearest edge of the excavation, trench or structure.
Radius of the protected areaThe tool computes the radius of the protected area from those figures and shows the formula, its sources, and a confidence rating alongside it.

Frequently asked questions

Why is the radius twelve times the stem diameter?: It is the standards' proxy for how far the roots a tree cannot afford to lose extend, taken from the one dimension that can be measured quickly and repeatably. A 620 mm (24.4 in) stem gives a radius of 7.44 m (24.4 ft) and an area of about 174 m² (1,873 sq ft) — the same figure in both units, because twelve times a diameter in inches is a radius in feet — a far larger patch of ground than the crown suggests on a young tree, and often a smaller one on an old, spreading one.
How do I measure a tree with several stems?: Measure each stem at the standard height — 1.5 m (4 ft 11 in) for BS 5837, 1.4 m (4 ft 7 in) for AS 4970 — and combine them. Up to five stems combine as the square root of the sum of their squares; above five, BS 5837 uses the mean diameter times the square root of the number. Three stems of 200, 300 and 250 mm (7.9, 11.8 and 9.8 in) combine to 438.7 mm (17.3 in), a radius of 5.26 m (17.3 ft).
What happens above 707 m²?: BS 5837 caps the area there, which is a circle of 15 m (49 ft) radius — reached by any stem over about 1.25 m (49 in). AS 4970 caps the radius at 15 m directly and also sets a 2 m (6 ft 7 in) minimum, so a small tree still gets a protected zone worth fencing.
Can the protected area be a different shape from a circle?: Yes, under both standards, where the arboriculturist finds the roots constrained or displaced — by a building, a road, a change in level — and the area stays the same. The circle is what the arithmetic gives before anyone has looked at the ground; the report fixes the final shape, and the fencing follows the report.

Preliminary estimate, not certified engineering. This tool produces an indicative quantity calculation for planning purposes only — it is not a certified structural analysis, a guaranteed material takeoff, or a substitute for building department approval. Always verify measurements on-site and have a licensed contractor or structural engineer review any load-bearing, code-sensitive, or safety-critical work before purchasing materials or starting construction. Spotted an arithmetic or standards error? Report it to contact@craftquantities.com with your inputs — a confirmed fix gets a permanent check of its own, so the same mistake cannot come back.