Circular Mulch Calculator
Calculate mulch for a round bed by diameter or radius. Donut-shape option for tree rings.
Circular Mulch Calculator
Round beds and donut tree rings
Diameter vs Radius Input
A circle is measured by diameter or radius. The diameter is the straight line across the widest part of the bed. The radius is half the diameter. Measure the diameter with a tape across the center, then halve it for the radius. An 8 ft diameter bed has a 4 ft radius. The calculator above accepts the outer diameter and converts it to radius for you. For a tree ring, also measure the inner clearance diameter around the trunk so the calculator subtracts the bare center.
Formula πr² × Depth
A round bed uses the circle area formula: Area = pi x radius squared. Multiply the area by depth in inches and divide by 324 for cubic yards. An 8 ft diameter bed has a 4 ft radius, so the area is 3.14 x 4 x 4 = 50.3 sq ft. At 3 inches deep that is 50.3 x 3 / 324 = 0.47 cubic yards. This is the accurate method. Using length times width on a circle measures the square around it and overestimates mulch by 20 to 25 percent.
| Diameter | Area (πr²) | Cubic Yards (3") |
|---|---|---|
| 4 ft | 12.6 sq ft | 0.12 yd³ |
| 8 ft | 50.3 sq ft | 0.47 yd³ |
| 12 ft | 113 sq ft | 1.05 yd³ |
| 20 ft | 314 sq ft | 2.91 yd³ |
Donut/Ring Option
A tree ring is a donut, not a full circle. The trunk and a clearance zone sit in the bare center. Calculate the donut by subtracting the inner circle from the outer circle. A 6 ft outer ring with a 1 ft clearance has an outer area of 28.3 sq ft and an inner area of 0.8 sq ft, leaving 27.5 sq ft of mulch. At 3 inches deep that is 0.25 cubic yards. The International Society of Arboriculture (ISA) requires keeping mulch 3 inches off the trunk, so always use the donut option for tree rings.
How do I measure a round bed accurately?
Measure a round bed by finding the center and running a tape to the edge for the radius. If the center is planted, measure the full diameter across the widest line and halve it. Take two diameter measurements at right angles and average them if the bed is not a perfect circle. This average radius keeps the area estimate within 5 percent.
How much mulch for a 12 foot round bed?
A 12 ft diameter round bed has a 6 ft radius and a 113 sq ft area. At 3 inches deep it needs 1.05 cubic yards of mulch or 15 bags of 2 cubic feet. At 2 inches it needs 0.70 cubic yards. Add 10 percent for settling before ordering.
How to Lay Out a Round Bed
A round bed starts with a center stake and a string. Drive a stake at the center and tie a string to it at the radius length. Walk the string around the stake and mark the circle with paint or flour. Cut the edge along the mark with a spade. This string-compass method draws a perfect circle every time and gives you the exact radius for the mulch calculation in one step.
For a tree ring, set the inner clearance first. Measure 3 inches out from the trunk and mark the bare center circle, then run the string from the trunk for the outer edge. The mulch fills only the donut between the two circles. Keep the finished mulch flat, never mounded against the bark, because a mulch volcano rots the trunk. The International Society of Arboriculture (ISA) confirms that a wide flat ring out to the drip line feeds far more roots than a tall narrow pile near the trunk.
FAQ
Use Area = pi x radius squared, then multiply by depth and divide by 324. An 8 ft diameter bed at 3 inches deep needs 0.47 cubic yards of mulch.
Cubic Yards = pi x radius squared x depth in inches / 324. The radius is half the diameter. Do not use length times width, which overestimates by 20 to 25 percent.
A tree ring is a donut. Subtract the trunk-clearance circle from the outer circle. A 6 ft ring with a 1 ft clearance at 3 inches deep needs about 0.25 cubic yards.
Either works. The radius is half the diameter. Measure straight across for the diameter, then halve it for the radius. The calculator accepts the outer diameter.
Length times width measures the square around the circle and overestimates mulch by 20 to 25 percent. A round bed needs the pi r squared formula for an accurate count.
Drive a stake at the center and tie a string to it at the radius length. Walk the string around the stake and mark the circle with paint or flour. Cut the edge along the mark. This string-compass method draws a perfect circle and gives the exact radius for the calculation.
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