Three trunks that each measure 12 cm across produce a Vaughan bylaw Diameter of about 20.78 cm. A tree can reach the 20 cm private-tree threshold even when none of its trunks does on its own.
Vaughan doesn’t add the trunk diameters together. It squares the diameters of the three largest trunks, adds those squares, and takes the square root.
Three Trunks Use One Diameter
Start at 1.37 m above the existing grade. Measure each trunk outside the bark at that height. Then select the three largest trunk diameters and use this formula:
Diameter = sqrt(d1^2 + d2^2 + d3^2)
For three 12 cm trunks, the calculation is:
sqrt(12^2 + 12^2 + 12^2) = sqrt(432) = 12*sqrt(3) ≈ 20.78 cm
The exact result, sqrt(432), is greater than 20 cm before any rounding. Check each 12 cm trunk separately and you’d miss the tree’s bylaw Diameter.
Vaughan’s enacted Tree Protection By-law defines ordinary Diameter at 1.37 m above existing grade. The City’s Tree Protection Protocol also gives the multi-stem formula. For the height, use the bylaw’s 1.37 m definition.
The Fourth Trunk Stays Out
A fourth trunk doesn’t enter Vaughan’s multi-stem formula. If a tree has four trunks that each measure 10 cm, use only three of them:
sqrt(10^2 + 10^2 + 10^2) = sqrt(300) = 10*sqrt(3) ≈ 17.32 cm
The exact result, sqrt(300), is below 20 cm. Adding the selected trunks would produce 30 cm. Adding all four would produce 40 cm. Neither number is the bylaw Diameter.
If the trunks differ in size, pick out the three largest before you calculate. Don’t average them, add them, or include a fourth. Our tree diameter measurement guide covers the basic circumference-to-diameter method and measurement point.
The 20 cm Rule Is Private
The 20 cm trigger belongs to Vaughan’s non-public-tree rule. If a private tree has a Diameter or Base Diameter of 20 cm or more, it can’t be injured or destroyed without authorization through a Tree Permit or Tree Protection Agreement. The bylaw also excludes Regional Woodlands and exempts emergency work and pruning of no more than 25 percent of live branches.
Public trees follow a separate rule. Vaughan defines a Public Tree as one with at least 50 percent of its main stem on Public Lands, and public trees are regulated at any size. If ownership is unclear, a result below 20 cm is not permission to proceed.
Check the Vaughan permit guide for the application route.
The bylaw itself allows Vaughan’s Director of Forestry to require an arborist report for a Tree Permit application. The City’s permit page requires one for every permit type except the Dead, Hazardous, or Emerald Ash Borer permit, which needs no report.
One Result Affects Later Planning
Once you’ve checked the threshold, keep that calculated Diameter handy. Where Vaughan’s diameter-based replacement schedule applies, the aggregate Diameter selects the replacement band. For the three 12 cm trunks, sqrt(432) sits in the printed 20 cm through 30 cm band and corresponds to one replacement tree.
Where the site can’t fit every replacement tree, staff decide case by case whether to take a fee in lieu. The 2026 cash-in-lieu amount is $600. The protocol multiplies the replacement count by the current year’s tree replacement fee (s.4.2), and Fees By-law 051-2026 sets that fee. The City’s dead, hazardous, or ash permit route is excluded from canopy replacement under the protocol. Public-tree compensation follows a separate method.
The same aggregate Diameter points you to the minimum Tree Protection Zone row. Both worked examples fall in the 10 cm through 29 cm row, but that doesn’t give every site the same protection-zone distance. The standard column gives 1.8 m for that row. The naturalized-area column requires the drip line or 3.6 m, whichever is greater, and Vaughan can require a larger zone. The table sets a starting minimum for the site review.
Base Diameter Means a Cut Tree
Base Diameter isn’t Vaughan’s normal standing-tree measurement. The bylaw uses it when a tree has already been cut down to less than 1.37 m above existing grade. In that case, measure outside the bark at ground level beside the base.
For a standing tree, ordinary Diameter is the measurement at 1.37 m. The City’s application guidance can still request both base and breast-height inventory fields. That doesn’t move the legal standing-tree threshold to ground level. Keep the two measurements separate when you read a form or prepare an inventory.
The Bylaw Sets the Measurement
The formula comes from Tree Protection By-law 177-2025, in force since June 24, 2025 and consolidated December 2, 2025, and from the 2025 Tree Protection Protocol.
Getting the Vaughan Measurement Right
Measure every stem outside the bark at 1.37 m. Record the individual readings, then run the three largest through the square-root formula. Keep the unrounded result for the threshold comparison. If the tree is close to 20 cm, ownership is unclear, or the planned work enters its protection zone, settle those points before work starts.
The Arborist Group provides ISA Certified Arborist assessments and prepares tree removal permit reports with site plans and photographs when Vaughan requests that documentation. Contact us with the Vaughan property address, photos of the tree, and each stem reading so we can confirm the measurement and report scope.