Hole Volume Calculator - Round & Rectangular Holes

What is a hole volume calculator?

A hole volume calculator finds how much material fills, or must be dug out of, a cylindrical or rectangular hole. It multiplies the hole's dimensions using standard geometry formulas. The result helps with ordering concrete, renting a dumpster, or estimating how much soil a job will produce.

How to calculate the volume of a cylindrical hole

A cylindrical hole, such as a post hole or a well, is shaped like a short tube. Its volume comes from the formula for a cylinder:

$V = \pi \times r^2 \times h$

• $V$ is the volume
• $\pi$ is approximately 3.14159
• $r$ is the radius, the distance from the center of the hole to its edge
• $h$ is the depth of the hole

Most people measure across the top of a hole, which gives the diameter, not the radius. The radius is half the diameter. A hole measured at 12 inches across has a 6-inch radius. Using diameter ($d$) directly, the formula becomes:

$V = \pi \times \frac{d^2}{4} \times h$

How to calculate the volume of a rectangular hole

A rectangular hole, such as a foundation trench or a pool excavation, uses a simpler formula:

$V = l \times w \times d$

• $l$ is length
• $w$ is width
• $d$ is depth

Real excavations rarely have perfectly straight walls. Building codes often require sloped sides on deep trenches for safety, so the actual dug volume can exceed this simple calculation. The OSHA excavation standard sets slope requirements for trenches over 5 feet deep in the United States.

Worked examples

Cylindrical hole: fence post

A fence needs 20 post holes, each 30 cm across (15 cm radius) and 60 cm deep.

$V = \pi \times 15^2 \times 60 = 42{,}412 \text{ cm}^3 \approx 0.042 \text{ m}^3 \text{ per hole}$

For 20 holes, the total is about 0.85 cubic meters of soil, roughly 1.1 cubic yards.

Rectangular hole: shed foundation

A shed base needs a gravel bed 2.5 m long, 2 m wide, and 0.4 m deep.

$V = 2.5 \times 2 \times 0.4 = 2 \text{ m}^3$

That is about 2.6 cubic yards of soil to remove.

Rectangular hole: irrigation trench

A 500-foot irrigation trench is dug 12 inches (1 ft) wide and 18 inches (1.5 ft) deep.

$V = 500 \times 1 \times 1.5 = 750 \text{ ft}^3$

Dividing by 27 (cubic feet per cubic yard) gives about 28 cubic yards of soil.

Cylindrical hole: tree planting

A tree with a 24-inch root ball needs a hole roughly 48 to 60 inches across and about 24 inches deep. Using the low end (48-inch diameter, 24-inch radius) the volume is about 0.71 cubic meters. Using the high end (60-inch diameter, 30-inch radius) it is about 1.11 cubic meters. A mid-sized hole, around 54 inches across, holds close to 0.9 cubic meters of soil.

Converting between volume units

How to measure a hole accurately

For a cylindrical hole, measure the diameter across the widest point, then halve it to get the radius. Drop a tape measure straight down for the depth. For a tapered hole, measuring the narrowest point suits concrete estimates, since concrete fills every part; measuring the widest point suits soil removal, since it accounts for all the dug material.

For a rectangular hole, measure length and width at the top, and take several depth readings if the bottom is uneven, then average them. Keep every measurement in the same unit before calculating.

Where hole volume calculations are used

Foundation footings and utility trenches for water, gas, and electrical lines need a volume estimate to plan concrete or backfill. Pool excavations for an average in-ground pool remove tens of cubic yards of soil. In landscaping, tree and shrub planting holes, pond digs, and French drains all rely on the same two formulas. In agriculture, vineyard and orchard posts add up fast: a 5-acre vineyard with roughly 2,000 posts, each an 8-inch-diameter, 30-inch-deep hole, requires digging out around 50 cubic meters of earth in total.

Excavated soil also expands once it is dug up, typically by 20 to 40 percent depending on soil type, so the amount to be hauled away is usually larger than the volume of the hole itself.

A short history

The formula for a cylinder's volume was described by the Greek mathematician Archimedes around 250 BCE, and it is still the formula used today. The Rhind Mathematical Papyrus, an Egyptian document from around 1650 BCE, shows volume calculations used for grain storage, evidence that this kind of math has supported construction and farming for thousands of years.

Frequently asked questions

What is the formula for the volume of a cylindrical hole? $V = \pi \times r^2 \times h$, where $r$ is the radius and $h$ is the depth. If only the diameter is known, divide it by 2 to get the radius first.

What is the formula for the volume of a rectangular hole? $V = l \times w \times d$: length times width times depth.

What is the difference between radius and diameter? The diameter is the distance across a circle through its center. The radius is half of that, measured from the center to the edge. A 12-inch diameter hole has a 6-inch radius.

How much more soil comes out of a hole than the hole's volume? Dug soil loosens and expands, usually by 20 to 40 percent, depending on the soil type. A 2 cubic meter hole can produce 2.4 to 2.8 cubic meters of loose soil.

How do I convert cubic meters to cubic feet or cubic yards? Multiply cubic meters by 35.3147 for cubic feet, or by 1.30795 for cubic yards. The calculator above can also convert automatically.

What if the hole is not a perfect cylinder or rectangle? Break the shape into simpler sections and calculate each one separately, then add the results. A tapered hole is often estimated by averaging the top and bottom diameters and treating it as a cylinder.