Tree Protection Calculator: Estimate Root Protection Area

This calculator works out the Root Protection Area (RPA) for a tree, which is the minimum ground area that must be kept undisturbed during construction to avoid damaging the tree’s roots. You enter the tree’s trunk diameter (measured at 1.5 m above ground) and the calculator returns the RPA radius and total area, based on the standard method used in arboriculture. The result is a circle centred on the tree trunk, and it is the first step in designing protective fencing or a no-dig surface.

Formula

The standard formula for Root Protection Area comes from British Standard 5837:2012, which is widely used in the UK and many other countries as a baseline for tree protection on development sites.

RPA radius (m) = (trunk diameter in cm / 100) × 12

RPA area (m²) = π × (RPA radius)²

Where:

• Trunk diameter is measured in centimetres at 1.5 m above ground level (or just above the root flare if the tree is multi-stemmed).
• The factor 12 converts the diameter in metres to a radius in metres. This is a simplified version of the BS5837 formula, which actually uses a factor of 12 for most trees but adjusts it for trees with a diameter over 60 cm or under 10 cm.
• π is approximately 3.14159.

For example, a tree with a 30 cm trunk diameter has an RPA radius of 3.6 m and an area of about 40.7 m².

Worked Example

Let’s use the default values from the calculator: trunk diameter = 30 cm.

1. Convert the diameter to metres: 30 cm ÷ 100 = 0.30 m
2. Multiply by 12: 0.30 × 12 = 3.6 m (this is the RPA radius)
3. Square the radius: 3.6² = 12.96 m²
4. Multiply by π: 12.96 × 3.14159 ≈ 40.7 m²

So for a 30 cm diameter tree, the Root Protection Area is a circle with radius 3.6 m and area 40.7 m². The calculator shows the same result.

What Is Root Protection Area and Why Does It Matter?

Root Protection Area is a concept from arboriculture that defines the zone around a tree where roots are concentrated and where soil disturbance should be minimised. Most tree roots grow in the top 60–100 cm of soil and spread widely, often extending well beyond the canopy drip line. The RPA is a practical approximation of that root zone, based on trunk diameter because trunk size correlates with root spread.

Construction activities such as digging trenches, laying paving, compacting soil with heavy machinery, or changing drainage can sever roots, compact the soil, and ultimately kill the tree. The RPA is used by architects, planners, and tree officers to decide where buildings, roads, and services can go, and to specify protective fencing before work begins.

The RPA is not a fixed legal boundary, but it is a widely accepted standard. Many local planning authorities in the UK require a tree protection plan that shows the RPA for every retained tree. Outside the UK, similar concepts exist, such as the Tree Protection Zone (TPZ) in Australia and New Zealand, which uses a similar calculation.

How to Measure Trunk Diameter Correctly

The accuracy of the RPA depends entirely on the trunk diameter measurement. Here are the key points:

• Measure at 1.5 m above ground level on the uphill side of the tree, or just above the root flare if the tree is on a slope.
• Use a diameter tape (a tape that reads circumference divided by π) or a standard tape measure and divide the circumference by π (3.14159).
• For multi-stemmed trees, measure each stem at 1.5 m, then calculate the combined diameter using the formula: D = √(d₁² + d₂² + … + dₙ²), where d is each stem diameter.
• If the tree is on a slope, measure from the highest ground level at the base.
• For very large trees (over 60 cm diameter), the BS5837 factor reduces from 12 to a value that gives a smaller RPA, but for most trees the factor 12 is used.

If you are not confident measuring, a professional arborist can do it, but the measurement itself is simple enough for preliminary planning.

Common Mistakes and Limitations

The most common mistake is using the trunk circumference instead of the diameter. A tape measure gives circumference, which is about three times the diameter. If you accidentally enter 90 cm instead of 30 cm, the RPA radius becomes 10.8 m instead of 3.6 m, a ninefold difference in area. Always convert circumference to diameter first.

Another mistake is measuring at the wrong height. The standard is 1.5 m, but many people measure at ground level where the trunk is often wider, resulting in an overestimated RPA. Conversely, measuring higher up the trunk gives a smaller diameter and underestimates the RPA.

The RPA formula is a general guideline, not a precise map of root distribution. Roots are not evenly spread; they may be concentrated on one side due to soil conditions, obstacles, or prevailing winds. For high-value trees, a detailed root survey (e.g., using ground-penetrating radar) may be needed. Also, the RPA assumes a circular area, but in reality the root zone may be irregular. The formula is conservative in most cases, meaning it errs on the side of protection.

Finally, the RPA only addresses root protection. It does not account for the tree’s crown (canopy) which may need pruning for clearance, or for the tree’s stability in the ground. Those are separate considerations.

How to Use the RPA in Practice

Once you have the RPA, you use it to plan protective measures:

1. Install protective fencing at the RPA boundary before any construction begins. The fence should be at least 2 m tall and sturdy enough to resist being moved.
2. Keep the RPA free of construction materials, soil storage, and vehicle traffic. Do not allow any excavation, even shallow, within the RPA without an arborist’s advice.
3. If you must work within the RPA, use special techniques such as hand digging, air spading, or no-dig surfaces (e.g., cellular confinement systems) that allow roots to survive.
4. Do not change the ground level within the RPA. Adding or removing soil can suffocate roots or expose them to damage.
5. If tree roots are found during excavation, stop and consult an arborist. Roots larger than 25 mm in diameter should be cut cleanly with a sharp saw, not torn.

For small projects like a garden shed, you might not need full fencing, but you should still avoid digging within the RPA. For larger developments, the RPA is often shown on a site plan and becomes part of the planning conditions.

Alternatives and Variations

The BS5837 method is not the only way to estimate root protection. Other methods include:

• Tree Protection Zone (TPZ) used in Australia and New Zealand: radius = 12 × diameter (in metres) for most trees, similar to BS5837.
• Critical Root Zone (CRZ): often defined as a radius of 0.3 m per cm of trunk diameter, which is more conservative (i.e., larger) than the RPA.
• Root Protection Area based on canopy drip line: some guidelines use the outer edge of the tree’s crown as the protection boundary, which is simpler but can be inaccurate for trees with narrow or uneven canopies.
• Site-specific root mapping: for high-value or veteran trees, a detailed root investigation may be done to define exact root locations.

For most planning applications, the BS5837 RPA is the accepted baseline. If you are working outside the UK, check local regulations, as some countries have their own standards.

Frequently Asked Questions

What is the difference between RPA and TPZ?

RPA (Root Protection Area) is the term used in BS5837, while TPZ (Tree Protection Zone) is used in Australian and New Zealand standards. Both use the same basic calculation: radius = 12 × trunk diameter (in metres). The difference is mostly terminology and minor details in how the zone is applied. In practice, they are interchangeable for most trees.

What if the tree has multiple stems?

For multi-stemmed trees, measure each stem at 1.5 m above ground. Then calculate the combined diameter using the formula: D = √(d₁² + d₂² + … + dₙ²). Use this combined diameter in the RPA calculation. This accounts for the total root spread of the tree.

Can I build a shed or deck within the RPA?

It depends on the type of construction. A lightweight deck on posts that are hand-dug and placed between roots may be acceptable, but a concrete slab or deep footings will likely damage roots. You should consult an arborist and possibly use a no-dig construction method. Many local authorities will require a tree protection plan before approving any structure within the RPA.

Does the RPA change if the tree is in poor health?

The RPA is based on trunk diameter, not tree health. A tree in poor health may have a smaller or larger root system, but the RPA remains the same for planning purposes. However, an arborist may recommend a larger protection area for a tree that is stressed, or a smaller one if the tree is dying and will be removed.

Is the RPA a legal requirement?

In the UK, BS5837 is a British Standard, not a law. However, many local planning authorities require a tree protection plan that follows BS5837 as a condition of planning permission. If you damage a protected tree, you may face fines. Outside the UK, similar standards are often referenced in local regulations. Always check with your local planning department.

What does a 12 factor mean?

The factor 12 means that for every 1 metre of trunk diameter, the RPA radius is 12 metres. This is based on observations that root spread is typically 12–15 times the trunk diameter. The factor 12 is a conservative estimate that protects the majority of roots. For trees over 60 cm diameter, the factor may be reduced to 10 or less, but this calculator uses 12 for simplicity.

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in t | Trunk diameter at 1.5 m | cm | 30 | 0
out rpa_radius | RPA radius | m | t / 100 * 12 | 2
out rpa_area | RPA area | m² | pi * (t / 100 * 12)^2 | 2