Tree ring area formula
A tree ring is an annulus — a circle with a hole. Area = π × (R² − r²), where R is outer radius and r is inner radius (keep mulch off the trunk).
Example: mulch from 1 ft from trunk to 5 ft from trunk. Outer R = 5 ft, inner r = 1 ft. Area = 3.14 × (25 − 1) = 75.4 sq ft. At 3 inches depth: 75.4 × 0.25 = 18.9 cu ft ≈ 0.7 cubic yards.
For quick estimates when the trunk zone is small, use π × R² if R is measured to the drip line — error is modest on large rings.
Multiple trees and odd shapes
Calculate each ring separately, then add cubic yards for one delivery. Oval rings: use average radius or split into two half-ovals.
Grouped plantings under one canopy can be one large circle instead of individual rings — simpler math and a healthier root zone mulch blanket.
- Young tree: 3–4 ft outer radius is common
- Mature shade tree: extend to drip line when feasible
- Keep 3–6 inches bare around trunk flare
- Flat 2–4 inch depth — never mounded against bark
From square feet to bags or bulk
Divide cubic feet by 27 for yards; multiply yards by ~13.5 for standard 2 cu ft bags (half-bags do not exist — round up).
Three 6-ft-diameter rings at 3 inches total about 0.8 cubic yards — often cheaper as bags than a bulk minimum. Run all rings in our mulch calculator with custom bed dimensions.