Bore Hole Volume Calculator and Formula

A bore hole volume calculator estimates the space inside a drilled hole from its diameter and depth. Enter both measurements in the same unit system, and it returns the hole’s volume, usually in cubic feet or cubic metres, before any allowance for irregular walls or soil expansion.

Formula

A straight, round bore hole is treated as a cylinder. Its volume is the area of the circular opening multiplied by the hole’s depth:

V = π × (D ÷ 2)² × H

• V is volume, in cubic feet (ft³) when the inputs are in feet.
• D is the hole diameter, in feet.
• H is the hole depth, in feet.
• π is approximately 3.14159.

The calculator’s second result converts cubic feet to US liquid gallons using 1 ft³ ≈ 7.48052 US gallons. The gallon figure is a volume conversion, not a separate estimate of how much material a particular job requires. If you work in metric units, use the same formula with diameter and depth in metres; the result is in cubic metres. One cubic metre is 1,000 litres.

Worked Example

Using the calculator’s default values, the hole is 1 ft in diameter and 10 ft deep. The radius is half the diameter:

• Radius = 1 ft ÷ 2 = 0.5 ft.
• Cross-sectional area = π × (0.5 ft)² = π × 0.25 ft² ≈ 0.785398 ft².
• Volume = 0.785398 ft² × 10 ft ≈ 7.85398 ft³.
• Rounded to two decimal places, the bore hole volume is 7.85 ft³.
• Approximate US gallons = 7.85398 ft³ × 7.48052 ≈ 58.766 ft³? No: the conversion is gallons per cubic foot, so the result is 58.77 US gal.

The unit shown in the multiplication is US gallons; the intermediate number 7.85398 is cubic feet. The calculator displays approximately 58.77 US gal after conversion.

What Bore Hole Volume Means

The result is the geometric volume of an ideal cylinder with the entered diameter and depth. It describes the space bounded by the bore’s sides and bottom. It does not automatically account for soil or rock removed, material that falls back into the hole, groundwater, a casing, or a shape that widens or narrows with depth.

For example, a nominal 1-foot-diameter, 10-foot-deep hole has a calculated volume of about 7.85 cubic feet. If its diameter is actually 1.1 feet throughout, the volume rises to about 9.50 cubic feet. That is roughly a 21% increase: because diameter is squared in the formula, a modest diameter difference can matter more than the same percentage difference in depth.

People use bore hole volume estimates when planning drilling, filling, grouting, or other work that depends on the space in a hole. The calculation is a starting point, not a guarantee of the quantity of material needed. The appropriate allowance depends on the work and ground conditions.

How to Measure and Use the Calculator

1. Measure the bore’s diameter across its opening, preferably at more than one direction if it may not be round.
2. Measure the depth from the opening to the bottom, using the same length unit as the diameter.
3. Enter the diameter and depth. This calculator uses feet and returns cubic feet and US gallons.
4. For metric measurements, calculate with metres, or convert both measurements to feet first. Do not mix feet and inches in one calculation.
5. Use the result as the ideal empty-hole volume, then consider the actual hole profile and the needs of the job.

To convert inches to feet, divide by 12. For instance, a 6-inch diameter is 0.5 ft. In metric, a 150 mm diameter is 0.15 m. Keep units consistent throughout the calculation so the squared area and final volume have the right dimensions.

Common Errors and Limits

• Using diameter as radius: the formula requires radius, which is half the diameter. Squaring the full diameter makes the answer four times too large.
• Mixing units: if depth is entered in feet but diameter in inches, convert one before using the formula.
• Assuming a perfect cylinder: a tapered, stepped, rough, or collapsed hole has a different volume. One diameter cannot fully describe it.
• Confusing hole volume with material volume: material may compact, settle, displace water, or occupy a different volume after placement. A simple cylinder calculation cannot predict those effects.
• Rounding too early: retain the full precision of the radius and area until the final result. The displayed answer is rounded to two decimal places.

For a hole whose diameter changes with depth, divide it into sections and calculate each section separately, then add the volumes. For sections that are approximately cylindrical, use each section’s representative diameter and length. A conical section can be estimated with V = (1/3)πr²h; more complex profiles need measurements or a suitable geometric model.

Choosing Units and Interpreting Results

Use cubic feet or cubic metres for three-dimensional volume, not square feet or square metres, which measure area. In US customary units, 1 cubic foot is about 7.48052 US liquid gallons. A US gallon is not the same as an imperial gallon, so specify which gallon unit is intended when sharing results. In metric units, 1 m³ equals 1,000 litres; 1 litre equals 0.001 m³.

Check whether the dimensions are measured at the drilled opening or refer to a tool’s nominal size. A drilling tool’s stated diameter may not equal the final hole diameter, especially in variable ground. If accurate material quantities matter, use measurements and guidance appropriate to the specific drilling and filling method rather than treating the geometric estimate as an order quantity.

Frequently Asked Questions

How do I calculate the volume of a bore hole?
For a round, uniform hole, multiply π by the square of its radius and then by its depth: V = πr²h. Use the same length unit for radius and depth; the answer is in that unit cubed.

How many gallons does a bore hole hold?
First calculate its volume in cubic feet, then multiply by about 7.48052 for US gallons. A 1-foot-diameter hole that is 10 feet deep holds about 58.77 US gallons geometrically.

Does the calculator use diameter or radius?
Enter diameter. The calculator divides it by two to obtain the radius used in the cylinder formula.

Can I use inches and feet together?
Not without converting first. Convert inches to feet by dividing by 12, or convert all dimensions to inches and interpret the resulting volume in cubic inches.

Is the calculated volume the amount of fill I need?
Not necessarily. It is the ideal volume of the hole’s empty cylindrical space. Irregular dimensions, ground conditions, settling, placement methods, and material behavior can change the quantity required.

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in d | Hole diameter | ft | 1 | 0
in h | Hole depth | ft | 10 | 0
out v | Bore hole volume | ft^3 | pi * (d / 2)^2 * h | 2
out g | Approximate volume | US gal | v * 7.48052 | 2