Hole Volume Calculator - Cylinder, Rectangle, Cone & More
Calculate the exact volume of any excavated hole in cubic feet, cubic yards, and liters. Works for post holes, concrete piers, bell-bottom footings, rectangular foundation pits, and tapered drilled shafts. Returns concrete bag counts and soil haul-away weight automatically.
⛏️ Hole Volume Calculator
Rebar Weight Chart
US Standard Rebar Sizes (#2–#18) with Weight, Diameter & Area
View Chart →How the Calculator Works — 5 Formulas Explained
Each hole shape uses a distinct geometric formula. The calculator applies the correct one based on your selection, then converts the result to cubic feet, cubic yards, liters, and cubic inches simultaneously.
Cylindrical Hole
V = π × r² × h
The most common shape for post holes and concrete piers. r = radius (diameter ÷ 2) in feet. h = depth in feet. A 12-inch diameter, 3-foot deep hole holds 2.356 cubic feet.
Rectangular Hole
V = L × W × D
L = length, W = width, D = depth, all in feet. A 4-foot × 4-foot × 3-foot footing hole holds 48 cubic feet, or 1.78 cubic yards.
Conical Hole
V = (1/3) × π × r² × h
Exactly one-third the volume of a cylinder with the same radius and depth. Rare in construction practice but applies to auger-drilled pile tips and some blasted rock shapes.
Truncated Cone (Frustum)
V = (π×h/3) × (R² + R×r + r²)
R = bottom (bell) radius, r = top radius, h = depth. Bell-bottom caissons use this shape to increase bearing area at depth without enlarging the shaft. See the concrete pier calculator for full pier design.
Elliptical Hole
V = π × a × b × h
a = semi-major axis (half-length), b = semi-minor axis (half-width), h = depth. Applies to hand-dug holes that are oval rather than circular, or oblong excavations with rounded ends.
Unit Conversions Used by This Calculator
- 1 cubic yard = 27 cubic feet
- 1 cubic foot = 1,728 cubic inches
- 1 cubic foot = 28.317 liters
- 80 lb concrete bag = 0.60 cubic feet yield (ACI, manufacturer TDS)
- 60 lb bag = 0.45 cubic feet | 40 lb bag = 0.30 cubic feet
Concrete Bag Coverage Reference
The table below shows how many bags of each size fill common post hole dimensions. Values include 10% waste and are based on a full cylindrical hole (no post deducted). For net volume after post deduction, use the calculator above.
| Hole Diameter | Depth | Volume (ft³) | 40 lb Bags | 60 lb Bags | 80 lb Bags | Common Use |
|---|---|---|---|---|---|---|
| 8 in | 24 in | 0.70 | 3 | 2 | 2 | Mailbox, sign post |
| 10 in | 36 in | 1.80 | 7 | 5 | 4 | Standard fence post |
| 12 in | 36 in | 2.59 | 10 | 7 | 5 | Gate post, deck post |
| 12 in | 48 in | 3.46 | 13 | 9 | 7 | Heavy gate, frost-line post |
| 16 in | 48 in | 6.15 | 23 | 16 | 12 | Deck footing, pergola |
| 18 in | 60 in | 9.62 | 36 | 24 | 18 | Sonotube pier, flagpole |
| 24 in | 72 in | 22.62 | 84 | 56 | 42 | Large column, bridge pier |
All bag counts are rounded up to the nearest whole bag and include 10% waste. Bag yields: 40 lb = 0.30 ft³, 60 lb = 0.45 ft³, 80 lb = 0.60 ft³. Source: ACI guidelines and manufacturer technical data sheets.
What Is Hole Volume and When Does It Matter?
Hole volume is the three-dimensional space enclosed by an excavation. It drives two separate material estimates: how much concrete, gravel, or fill you need to put in, and how much soil you need to haul out.
Getting this wrong in either direction costs money. Under-ordering concrete means returning to the hardware store mid-pour, which ruins concrete that has already begun to set. Over-ordering gravel by 30% on a 50-hole fence installation adds hundreds of dollars in wasted material. On commercial jobs, the excavation calculator and haul-away estimates determine truck count, which directly affects the project schedule.
The sonotube calculator and the circular concrete calculator both depend on accurate hole volume as their starting point. The formulas on this page are their geometric foundation.
🏗️ Post & Pier Holes
Standard fence posts require cylindrical holes 2.5 to 3 times the post diameter. A 4-inch post needs a 10-inch to 12-inch hole. Depth should reach below the local frost line — 36 to 48 inches in most of the continental US, deeper in northern states.
🏛️ Footing Excavations
Rectangular footing pits for residential foundations typically measure 12 inches wider and 6 inches deeper than the footing dimensions to allow for formwork. Include this overage in your hole dimensions before calculating volume.
🔔 Bell-Bottom Caissons
Drilled piers with a belled base (frustum shape) increase the bearing area at the bottom of the pier without increasing the shaft diameter. The bell diameter is typically 2 to 3 times the shaft diameter. Use the truncated cone formula for accurate concrete volume.
🚛 Soil Haul-Away
Excavated soil expands by 10-80% depending on type. Sandy loam swell averages 12%. Clay averages 25%. Rock averages 60%. A 10-cubic-yard clay excavation generates approximately 12.5 cubic yards of loose material, requiring two standard 10-yard dump trucks.
Sample Calculations — Three Real-World Scenarios
Fence with 15 Identical Post Holes
Shape: Cylinder
Diameter: 10 inches (0.833 ft)
Depth: 42 inches (3.5 ft)
Quantity: 15 holes
Post: 4×4 lumber (3.5 in actual)
r = 0.833 ÷ 2 = 0.417 ft
Single hole = π × 0.417² × 3.5 = 1.91 ft³
Post volume = 0.292 × 0.292 × 3.5 = 0.298 ft³
Net concrete = 1.91 - 0.298 = 1.612 ft³ × 15 holes = 24.18 ft³
+ 10% waste = 26.60 ft³ = 0.985 cu yd
80 lb bags: 26.60 ÷ 0.60 = 45 bags
At $8.50/bag average, material cost is approximately $382. The fence post concrete calculator includes post spacing and total linear footage for full fence estimates.
Deck Footing — Bell-Bottom Caisson
Shape: Truncated Cone
Top diameter: 12 inches (1.0 ft) at surface
Bottom diameter: 24 inches (2.0 ft) at base
Depth: 48 inches (4.0 ft)
Quantity: 6 piers
R = 1.0 ft, r = 0.5 ft, h = 4.0 ft
V = (π × 4 / 3) × (1.0² + 1.0×0.5 + 0.5²)
V = 4.189 × (1.0 + 0.5 + 0.25) = 4.189 × 1.75
Single pier = 7.33 ft³
6 piers = 6 × 7.33 = 43.98 ft³ + 10% = 48.38 ft³ = 1.79 cu yd
80 lb bags = 48.38 ÷ 0.60 = 81 bags
The belled base increases bearing area by 4× compared to a straight 12-inch shaft, improving load distribution on soft soils. See the concrete pier calculator for full pier design with rebar.
Foundation Pit — Soil Haul-Away
Shape: Rectangular
Length: 28 ft
Width: 22 ft
Depth: 5 ft
Soil type: Clay (25% swell)
Bank volume = 28 × 22 × 5 = 3,080 ft³ = 114.1 cu yd
Clay swell factor = 1.25
Loose volume = 114.1 × 1.25 = 142.6 cu yd
Truck loads (10 yd trucks) = 142.6 ÷ 10 = 15 loads
Soil weight (clay ~100 lb/ft³) = 3,080 × 100 = 308,000 lb = 154 tons
Order trucks by loose volume, not bank volume. Underestimating loose volume by even 15% strands a truck waiting for a full load. The backfill calculator handles material needed to refill after construction.
Calculation Mistakes That Cost Money on Job Sites
These five errors appear repeatedly in post-pour calls to concrete suppliers and material return lines. Each one is avoidable with the right numbers before you order.
⚠️ Error 1 — Measuring Diameter at the Surface Only
Hand-dug holes widen toward the bottom due to shovel angle. A hole measured as 10 inches at the top may be 13 to 14 inches at the base. Auger-drilled holes are more consistent, but always measure at two depths on hand-dug work and use the average. Underestimating diameter by 2 inches on a 36-inch deep hole reduces calculated volume by roughly 22%.
⚠️ Error 2 — Skipping the Post Deduction
Filling a 12-inch, 36-inch deep hole around a 4×4 post without deducting the post volume over-orders by about 0.30 ft³ per hole. On a 20-hole fence project, that adds up to 6 ft³ of wasted concrete — nearly half a cubic yard at $130–$160 per yard delivered. Use the post deduction field in the Advanced Options.
⚠️ Error 3 — Using Bank Volume for Haul-Away Trucks
Bank volume is the amount of material in the ground before excavation. Loose volume is what you actually load into trucks. Clay soil at 25% swell means 10 cubic yards of excavation generates 12.5 cubic yards of loose material. Ordering based on bank volume leaves you one truck short on a typical residential foundation dig.
⚠️ Error 4 — Ordering No Waste Factor on Ready-Mix
Ready-mix trucks cannot return partial loads once mixed. A 0% waste factor means any spillage, over-dig, or mixing variation leaves you short. ACI guidelines and most estimators recommend a minimum 10% waste on poured concrete. Use 15% for rocky or irregular soil conditions where hole walls are uneven.
⚠️ Error 5 — Using Nominal Lumber Dimensions for Post Deduction
A 4×4 post is actually 3.5 × 3.5 inches. A 6×6 is 5.5 × 5.5 inches. Using nominal dimensions (4 × 4 = 16 in²) instead of actual dimensions (3.5 × 3.5 = 12.25 in²) over-deducts post volume by 30%. Always use actual (dressed) dimensions in the post deduction fields. Per the American Softwood Lumber Standard (PS 20-20), nominal and actual dimensions differ for all dimensional lumber.
Frost Lines, Codes, and Delivery Planning
Frost Depth by US Region
Post holes must extend below the local frost line to prevent heaving. The post hole calculator and this tool both use depth as a direct input — verify your local frost depth before finalizing hole dimensions.
| Region | Example States | Frost Depth (in) | Min Post Hole Depth |
|---|---|---|---|
| Deep South | FL, LA, southern TX | 0 – 6 in | 24 in min (code) |
| Mid-South | TN, AR, GA, SC | 6 – 18 in | 30 – 36 in |
| Mid-Atlantic | VA, MD, PA, OH | 18 – 36 in | 42 in |
| Midwest | IL, IA, MO, IN | 36 – 48 in | 48 in |
| Upper Midwest / Northeast | MN, WI, MI, NY, VT | 48 – 60 in | 54 – 60 in |
| Mountain / Northern Plains | MT, ND, SD, WY, ID | 60 – 72 in | 66 – 72 in |
Frost depth data from NOAA climate normals and IRC Table R301.2. Always verify with your local building department — site-specific conditions vary.
Ready-Mix Delivery Planning
Ready-mix plants typically have a minimum order of 1 cubic yard, with short-load fees for orders under 4–5 yards (typically $50–$100 extra per yard under minimum). Most standard mixer trucks hold 8–10 cubic yards. Use the concrete yardage calculator to confirm total volume before calling a plant.
📋 What to Tell Your Ready-Mix Supplier
- Total volume in cubic yards (use this calculator's output)
- Concrete mix design: 3,000 PSI standard for footings and post holes (ACI 318-19 §19.2.1.1)
- Slump requirement: 4–5 inches for footings and columns (ASTM C143)
- Pour date and time — plants need 24–48 hours notice
- Access limitations: truck length, gate width, site grade
- Air entrainment requirement if freeze-thaw exposure applies (ACI 318-19 Table 19.3.3.1)
Sonotube and Cardboard Form Sizing
When using sonotube forms, the hole diameter must exceed the form diameter by at least 2 inches on each side for proper backfill compaction. A 12-inch sonotube requires a 16-inch hole minimum. The concrete volume inside the tube is calculated as a cylinder using the tube's inside diameter, not the hole diameter.
Frequently Asked Questions
Use the formula V = π × r² × h, where r is the radius (half the diameter) and h is the depth, both in feet. For a 12-inch diameter, 36-inch deep hole: r = 0.5 ft, h = 3 ft, V = 3.1416 × 0.25 × 3 = 2.356 cubic feet (0.087 cubic yards). Always measure diameter at the top of the hole — hand-dug holes typically widen slightly toward the bottom.
An 80 lb bag yields approximately 0.60 ft³, a 60 lb bag yields 0.45 ft³, and a 40 lb bag yields 0.30 ft³ (per Quikrete and Sakrete TDS, consistent with ACI guidelines). For a 10-inch diameter, 36-inch deep post hole with a 4×4 post: gross hole volume = 1.636 ft³, deduct post volume (0.292 × 0.292 × 3 = 0.256 ft³), net = 1.38 ft³. Add 10% waste: 1.518 ft³ ÷ 0.60 = 3 bags of 80 lb concrete. Use the Advanced Options above to let the calculator do this automatically.
Soil swell (also called bulking factor) is the percentage by which excavated soil expands in volume once removed from the ground. Sandy loam swells 10–15%, clay soils swell 20–30%, and rock swells 40–80% (Engineering Toolbox, 2023). A 10-cubic-yard clay excavation produces approximately 12.5 cubic yards of loose material for haul-away. Order dump trucks based on loose volume — ordering based on bank volume will leave you one to two trucks short on a typical residential dig.
OSHA 29 CFR 1926 Subpart P requires all excavations 5 feet or deeper to have a protective system (sloping, shoring, or shielding) before any worker enters. For Type C soil (most common: sand, gravel, unstable ground), the maximum allowable slope is 1.5H:1V (34 degrees). Type B allows 1H:1V (45 degrees). Type A stable clay allows 0.75H:1V (53 degrees). Excavations over 20 feet deep require a protective system designed by a registered professional engineer. A competent person must classify soil type before work begins.
Divide cubic feet by 27. One cubic yard equals 27 cubic feet (3 ft × 3 ft × 3 ft). For example: 54 ft³ ÷ 27 = 2 cubic yards. Ready-mix concrete, gravel, and fill dirt are all sold by the cubic yard in the US, so always convert before calling a supplier. This calculator displays both cubic feet and cubic yards simultaneously in the results. See the cubic yard calculator for additional conversion tools.
A truncated cone (frustum) hole is wider at the bottom than at the top — the classic bell-bottom caisson shape. It uses the formula V = (π × h / 3) × (R² + R×r + r²) where R = bottom radius, r = top radius, and h = depth. Bell-bottom piers are drilled with a special belling tool after the shaft is complete. They are used when the bearing soil is at a specific depth and the engineer needs increased bearing capacity without enlarging the entire shaft. The bell diameter is typically 2–3 times the shaft diameter per standard drilled pier practice.
The quantity field multiplies one set of dimensions by the number of holes, so it handles multiple identical holes in a single calculation. For holes with different dimensions — for example, a fence with three different post sizes — run a separate calculation for each hole group and add the results together. For complete fence layout estimates including post spacing, linear footage, and concrete per run, the fence post concrete calculator handles mixed configurations directly.
Sources & Calculation Methodology
All formulas and reference data used in this calculator are drawn from publicly available engineering standards and manufacturer technical documentation. No values are estimated or interpolated without citation.
- ACI 318-19 — Building Code Requirements for Structural Concrete. American Concrete Institute, 2019. §19.2.1.1 (concrete strength requirements), §26.4 (mixing water), §26.10 (curing). Used for bag yield reference and curing time guidance. ACI 318-19 →
- OSHA 29 CFR 1926 Subpart P — Excavations. Occupational Safety and Health Administration. §1926.650–1926.652. Soil classification, slope requirements, and protective system criteria used in the Safety tab and OSHA depth alert. OSHA Subpart P →
- Engineering Toolbox — Soil and Rock Bulk Factors (2023). Swell percentages for sandy loam (10–15%), clay (20–30%), gravel (5–10%), and rock (40–80%) used in the haul-away estimator. Engineering Toolbox →
- Quikrete Technical Data Sheet — Concrete Mix No. 1101. Bag yield: 40 lb = 0.30 ft³, 60 lb = 0.45 ft³, 80 lb = 0.60 ft³. Used for all bag count calculations. Quikrete TDS →
- IRC Table R301.2 — International Residential Code 2021. Frost depth and ground snow load data by jurisdiction. Referenced in frost depth table. IRC 2021 →
- American Softwood Lumber Standard PS 20-20 — Nominal vs. actual dimension table for dimensional lumber (2×4, 4×4, 6×6). Referenced in Error 5 (post deduction nominal vs. actual). PS 20-20 →
- ASTM C143 / C143M — Standard Test Method for Slump of Hydraulic-Cement Concrete. Slump range 4–5 inches cited for footings and columns. ASTM C143 →
Reviewed by site author — Muhammad Ramzan Babar, Physics Researcher (PhD Candidate). Last reviewed: June 2026. Calculations run entirely in your browser. No data is transmitted or stored.
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