Cubic Yard Mound Calculator: Volume & Cost

A cubic yard mound calculator estimates the volume of a pile of material (soil, gravel, sand, mulch) shaped roughly like a cone or a rounded mound, and often converts that volume into weight or cost. You enter the mound’s base width, length, and height (or just diameter and height for a circular pile), and the calculator returns the volume in cubic yards, plus optional tons and total price. This page explains the math behind the estimate and how to use it for ordering bulk materials.

Formula

The calculator uses a simple geometric model: a mound is treated as a fraction of a rectangular box (or a cylinder) that the pile would fill if it were flat-topped. The standard formula is:

Volume (cubic feet) = Base Width × Base Length × Height × Shape Factor

Then convert to cubic yards by dividing by 27 (since 1 yard = 3 feet, so 1 yd³ = 27 ft³).

• w = base width (ft)
• l = base length (ft)
• h = height (ft)
• m = shape factor: 0.33 for a cone (typical loose pile), 0.5 for a dome (rounded, flatter pile)
• d = material density (lb/ft³) — see typical values below

For a circular pile, use the same formula with width = length = diameter. The shape factor accounts for the fact that a pile slopes down on all sides, so it doesn’t fill the full box.

Worked Example

Using the defaults: width = 10 ft, length = 10 ft, height = 4 ft, shape = cone (0.33), density = 100 lb/ft³.

1. Volume in cubic feet: 10 × 10 × 4 × 0.33 = 132 ft³
2. Convert to cubic yards: 132 ÷ 27 = 4.89 yd³
3. Weight: 4.89 yd³ × 27 ft³/yd³ × 100 lb/ft³ = 13,203 lb
4. Convert to tons: 13,203 ÷ 2000 = 6.60 US tons

The calculator shows 4.89 yd³ and 6.60 tons for the default inputs.

Why Shape Factor Matters

Real piles are never perfect cones. Loose soil dumped from a truck forms an angle of repose — the steepest angle the material can hold without sliding. That angle varies by material: dry sand sits at about 34°, gravel at 30–40°, and damp clay can be steeper. The cone factor of 0.33 approximates a 45° slope, which is close for many materials. A dome factor of 0.5 is better for piles that are deliberately flattened or compacted, like a stockpile that has been pushed by a loader.

If you need a more precise volume for a stockpile, surveyors use the prismoidal formula or 3D scanning, but for ordering mulch or topsoil, the cone estimate is usually within 10–15%.

Typical Material Densities

Weight matters because trucks are often limited by weight, not volume. Use these approximate densities (lb/ft³) for common materials:

• Topsoil (loose): 75–90
• Sand (dry): 90–110
• Gravel (loose): 95–120
• Crushed stone: 100–135
• Mulch (shredded bark): 20–30
• Compost: 40–60

When in doubt, ask your supplier for the bulk density of the specific material. A cubic yard of mulch weighs far less than a cubic yard of gravel, so the same mound volume can mean very different truck loads.

How to Measure a Mound

To get a usable estimate, measure the pile at its widest point (the base) and its tallest point. For irregular piles, take two width measurements at right angles and average them. For length, measure the longest horizontal distance across the base. Height should be measured vertically from the ground to the peak — not along the slope.

For a circular pile, measure the diameter (distance across the center) and use that for both width and length. If the pile is not symmetric, treat it as an ellipse: use the average of two diameters.

Common Mistakes and Misconceptions

One frequent error is confusing cubic yards with square yards (area). A cubic yard is 3 feet long × 3 feet wide × 3 feet high — 27 cubic feet. A square yard is only 9 square feet. Another mistake is using the slope length instead of vertical height. If you measure along the side of the pile, you get a much larger number and overestimate volume.

Also, don’t forget that a pile of loose material settles after being dumped. A fresh pile may measure 4 feet high, but after a day it might be 3.5 feet. If you’re ordering material to fill a hole or a garden bed, order a little extra (5–10%) to account for compaction and spillage.

Cost and Ordering Considerations

Bulk materials are sold by the cubic yard, but delivery trucks have weight limits. A standard dump truck carries 10–14 cubic yards of soil, but only 8–10 cubic yards of gravel because of weight. Use the weight estimate to check if your order might exceed truck capacity or require a smaller load.

For cost, multiply the cubic yard volume by the per-yard price. Many suppliers also charge a delivery fee that is per mile or a flat rate. Always confirm whether the price includes delivery and whether there is a minimum order (often 1–3 cubic yards).

If you’re spreading material to a certain depth (e.g., 3 inches of mulch over a garden bed), you don’t need a mound calculator — use the area (length × width) times the depth in feet, then divide by 27 to get cubic yards. That formula is: (length × width × depth in feet) / 27.

Frequently Asked Questions

How many cubic yards is a typical pickup truck load?

A full-size pickup truck bed (8 ft long, 5 ft wide, 2 ft deep) holds about 2.5–3 cubic yards if heaped. A level load is about 2 cubic yards. However, weight limits often mean you can carry less: a half-ton truck can only hold about 1.5 cubic yards of gravel (weighing ~2,700 lb) before exceeding payload capacity.

What is the formula for a cone-shaped pile?

The exact formula for a cone is V = (1/3) × Ï€ × r² × h, where r is the radius of the base and h is the height. For a pile with a 10 ft diameter and 4 ft height, that gives (1/3) × 3.14 × 5² × 4 = 104.7 ft³, or 3.88 yd³. Our calculator’s cone factor (0.33) gives 4.89 yd³ for the same base dimensions, because it uses the full base rectangle rather than a circle — a more conservative estimate for irregular piles.

How do I convert cubic feet to cubic yards?

Divide the number of cubic feet by 27. For example, 135 ft³ ÷ 27 = 5 yd³. This works because 1 yard = 3 feet, so 1 yd³ = 3 × 3 × 3 = 27 ft³.

Why does my supplier’s estimate differ from the calculator?

Suppliers often measure piles with a laser or GPS, or they use a different shape factor (e.g., 0.4 or 0.5) depending on how the pile was made. Also, they may include the volume of the base that isn’t perfectly flat. Differences of 10–20% are normal. If you’re ordering, ask the supplier how they measured and whether their estimate includes compaction.

Can I use this for a pile of snow or compost?

Yes, the volume calculation works for any material. The density will vary widely: fresh snow is about 5–15 lb/ft³, while compacted snow can be 30–40 lb/ft³. Compost is typically 40–60 lb/ft³. Just enter the appropriate density for your material.

Related

• Area Calculator in Feet: How to Use It
• Area Calculator Cubic Feet: How to Find Volume
• Area Calculator Feet and Inches: How to Use It

in w | Base width | ft | 10 | 0
in l | Base length | ft | 10 | 0
in h | Height | ft | 4 | 0
in d | Material density | lb/ft³ | 100 | 0
sel m | Shape | Cone=0.33, Dome=0.5
out cy | Volume | yd³ | (w * l * h * m) / 27 | 2
out tons | Estimated weight | US tons | cy * d * 27 / 2000 | 2