Article — Hole Volume Calculator
Hole volume calculator: cubic feet, yards, and gallons for any excavation
A hole volume calculator returns the cubic feet, cubic yards, cubic metres, gallons, and litres in a cylindrical, rectangular, or conical excavation. For a cylindrical hole, volume = π × r² × h. A 12-inch diameter hole 4 ft deep holds 3.14 ft³ (0.116 yd³) — about 23 US gallons or seven 60-lb bags of concrete. For rectangular pits, volume = length × width × depth.
Whether you are pouring footings, digging a French drain, or sizing a koi pond, the underlying question is the same: how much material fills this hole? The calculator handles three shapes that cover almost every common case, but picking the right shape and entering the right dimensions matters more than the formula. A 5% measurement error compounds with a 5% over-order to mean either short pours or wasted material.
Cylindrical hole volume formula
Cylindrical holes are the easiest to calculate and the most common in residential construction. Volume equals π times the radius squared times the depth. The radius is half the diameter — a 12-inch diameter hole has a 6-inch (0.5 ft) radius.
V_cyl = π × r² × h cylindrical holeV_rect = L × W × D rectangular pitV_frust = (π h / 3)(r&sub1;² + r&sub1;r&sub2; + r&sub2;²) tapered holegallons = ft³ × 7.48 liquid volumeFor everyday post holes, memorise the answer for a 12-inch diameter at 4 ft deep: 3.14 ft³. Scale linearly with depth and quadratically with diameter. Double the depth, double the volume. Double the diameter, quadruple the volume. A 24-inch diameter at the same 4 ft depth holds 12.6 ft³ — four times the original.
Rectangular pit volume
Rectangular excavations cover foundation footings, utility trenches, planter boxes, and pool pits. Length times width times depth, all in the same unit. A 3 ft square footing 4 ft deep is 36 ft³, or 1.33 cubic yards. A 1 m × 30 m × 0.6 m utility trench holds 18 m³.
When the hole is wider at the top than the bottom (sloped sides for safety), the rectangular formula over-estimates by about 5 to 10%. For more accuracy, average the top and bottom dimensions and multiply by depth, or model the shape as a frustum.
Conical and frustum hole volume
A frustum is a cone with the top cut off — the shape of a bell-bottom pier, a tapered koi pond, or a deep excavation with sloped sidewalls. Volume = (π × h / 3) × (r&sub1;² + r&sub1;r&sub2; + r&sub2;²), where r&sub1; and r&sub2; are the top and bottom radii.
OSHA regulations require sloped sidewalls for any excavation deeper than 4 feet in soil that is not stabilised. The slope must be 1.5:1 (horizontal:vertical) in soft soil, 1:1 in firm soil. A 6 ft deep, 4 ft wide trench in soft soil actually opens to 22 ft wide at grade and holds 60% more soil than its bottom footprint suggests. The frustum formula models this accurately; the rectangular formula understates it.
Hole volume for fence posts
Fence post and mailbox holes are the most-Googled hole volume question. The standard sizes: 8-inch diameter by 24 inches deep for mailbox posts (0.7 ft³); 10-inch by 36 inches for wood fence posts (1.64 ft³); 12-inch by 48 inches for deck footings (3.14 ft³). The deeper holes give frost-line protection in cold climates — concrete poured above the frost depth heaves every winter.
- 8 in × 24 in = 0.70 ft³ (mailbox)
- 10 in × 36 in = 1.64 ft³ (wood fence post)
- 12 in × 48 in = 3.14 ft³ (deck footing)
- 12 in × 36 in = 2.36 ft³ (vinyl fence post)
- 16 in × 48 in = 5.59 ft³ (heavy gate post)
- 24 in × 48 in = 12.57 ft³ (sign or sonotube pier)
Concrete needed by hole volume
A 60-lb bag of premix concrete yields about 0.45 ft³ of cured concrete. A 12-inch by 48-inch hole (3.14 ft³) needs 7 bags. An 80-lb bag yields 0.60 ft³, so the same hole needs only 5 bags of the larger size.
Bag math works up to about 10 ft³ per project (roughly 20 bags). Beyond that, ready-mix delivery becomes cheaper per cubic foot despite the short-load fee. Ready-mix trucks sell by the cubic yard with a typical minimum of 1 yd³ (27 ft³) plus delivery; short-load fees apply below 5 yd³.
Fill weight and disposal
The weight of fill material matters when you have to move it. Concrete is the densest common fill at 2,400 kg/m³ (150 lb/ft³). A 1 m³ pit filled with concrete weighs 2,400 kg — that is roughly half a small car. Sand is 1,600 kg/m³, gravel 1,500, topsoil 1,300.
One cubic foot of concrete weighs 150 lb. A standard wheelbarrow holds 3 ft³ (450 lb) but is awkward at full load. Plan 3 to 4 wheelbarrow trips per cubic foot of concrete from the mixer to the form. Long pours need helpers or a concrete pump; lone pours over 10 ft³ are exhausting.
Hole volume in gallons
Septic tanks, drywells, and rainwater catchments are measured in gallons. The conversion: 1 ft³ = 7.48 US gallons; 1 m³ = 264 US gallons. A 4 ft diameter cylindrical drywell 6 ft deep holds 75 ft³ = 564 gallons before gravel fill. After 1-inch washed gravel fill (40% void space), it holds about 226 usable gallons.
For septic-tank sizing, residential code typically requires 1,000 gallons minimum for a 3-bedroom home, 1,250 for 4-bedroom. A 5 ft × 8 ft × 4.5 ft pit holds 180 ft³ = 1,346 gallons — just barely enough for a 1,000-gallon tank with backfill room around it.
Common hole volume calculation mistakes
Mixing units is the top mistake. Depth in inches and diameter in feet gives a number off by 12. Always convert before multiplying, or use the calculator’s per-input unit selectors. A 12-inch diameter at 4 ft deep is π × (0.5)² × 4 = 3.14 ft³ — not π × (6)² × 4 = 452 ft³.
Using diameter as radius is the second mistake. Cylindrical volume needs radius (half the diameter) squared, not diameter squared. A 12-inch diameter has a 6-inch radius. Forgetting to halve the diameter quadruples the calculated volume.
Hand-dug holes have irregular walls and a slight bell at the bottom from shovel sweeps. The actual volume is 5 to 10% greater than the calculated cylinder. Machine-bored holes are cleaner but still benefit from a 5% allowance. Running short on a concrete pour produces a cold joint that weakens the footing; over-order is the safer side to err on.
Ignoring the bell base on bottomed-out piers is the third mistake. Many footings have a wider bottom for bearing surface, which adds 20 to 30% to the volume. Use the frustum formula or add a flat-bottom cylinder for the bell explicitly.