Pier, Caisson & Sonotube Concrete: Volume Formulas, Bell Footings, and Bag Counts

Pier, Caisson & Sonotube Concrete: Volume Formulas and Worked Examples

A drilled pier (also called a caisson or bored pile) is a cylindrical concrete foundation element installed by drilling a hole in the ground and filling it with concrete. They're used where a shallow spread footing would require an impractically large footprint, where soil bearing capacity improves significantly with depth, or where frost depth makes conventional footings expensive.

Sonotubes are a trade name for round fiber-board tubes used as forms for small-diameter piers — the most common solution for residential deck foundations, pergola posts, and fence structures requiring below-grade anchoring.

Use the Pier/Caisson Concrete Calculator and Sonotube Calculator for instant volumes. This guide explains the geometry behind the calculations.

Types of Pier Foundations

Straight-Shaft Pier

The simplest type: a uniform-diameter cylinder from grade to bearing stratum.

Volume = π × r² × h

Where r = shaft radius (half the diameter), h = shaft depth. This is the standard sonotube geometry.

Bell-Bottom (Belled) Caisson

A drilled shaft with a flared base (the "bell"). The bell increases the bearing area at the bottom without requiring a larger shaft throughout. It's used where the bearing stratum has limited depth and maximum bearing capacity is needed.

Total Volume = Shaft Volume + Bell Volume
Shaft Volume = π × r_shaft² × h_shaft
Bell Volume  = (π × h_bell / 3) × (r_bell² + r_shaft² + r_bell × r_shaft)

The bell volume formula is the frustum (truncated cone) formula. h_bell is the height of the bell, r_bell is the radius at the base, r_shaft is the shaft radius (= bell top radius).

Stepped Pier

Two or more uniform cylinder segments of different diameters stacked vertically. Calculate each segment separately and sum.

Total Volume = π × r₁² × h₁ + π × r₂² × h₂ + ...

Sonotube / Deck Pier — Worked Example

Scenario: Deck with 8 piers. Sonotube diameter = 12 inches, depth = 48 inches (4 ft).

Shaft radius: 12/2 = 6 inches = 0.5 ft

Volume per pier: V = π × (0.5)² × 4 = π × 0.25 × 4 = 3.14 ft³ per pier

Total for 8 piers: V = 8 × 3.14 = 25.14 ft³ = 0.93 yd³

Bags of 80-lb premix (0.60 ft³/bag): 3.14 / 0.60 = 5.2 → 6 bags per pier (round up) Total: 8 × 6 = 48 bags (or order 1 yd³ of ready-mix)

Bell-Bottom Caisson — Worked Example

Scenario: A commercial building column requires a belled caisson bearing on stiff clay at 12 ft depth.

Shaft: 18 inches diameter = 1.5 ft → r_shaft = 0.75 ft, depth = 10 ft
Bell: 36 inches diameter = 3.0 ft → r_bell = 1.5 ft, height = 2 ft

Shaft volume: V_shaft = π × (0.75)² × 10 = π × 0.5625 × 10 = 17.67 ft³

Bell volume (frustum formula): V_bell = (π × 2 / 3) × ((1.5)² + (0.75)² + 1.5 × 0.75) = (π × 2 / 3) × (2.25 + 0.5625 + 1.125) = (2.094) × 3.9375 = 8.24 ft³

Total caisson volume: V = 17.67 + 8.24 = 25.91 ft³ = 0.96 yd³

Order 1 yd³ per caisson (or batch 3–4 caissons together for a more economical 3–4 yd³ pour).

Sonotube Size Reference — Bags per Hole at Common Depths

Diameter	Depth	Volume (ft³)	40 lb bags	60 lb bags	80 lb bags
8"	24" (2 ft)	0.70	3	2	2
8"	36" (3 ft)	1.05	4	3	2
10"	36" (3 ft)	1.64	6	4	3
10"	48" (4 ft)	2.18	8	5	4
12"	36" (3 ft)	2.36	8	6	4
12"	48" (4 ft)	3.14	11	7	6
12"	60" (5 ft)	3.93	14	9	7
16"	48" (4 ft)	5.59	19	13	10
16"	60" (5 ft)	6.98	24	16	12
18"	48" (4 ft)	7.07	24	16	12
24"	48" (4 ft)	12.57	42	28	21

Bag counts rounded up. Yield: 40 lb = 0.30 ft³, 60 lb = 0.45 ft³, 80 lb = 0.60 ft³.

For custom sizes or deeper piers, use the Pier/Caisson Calculator directly.

Concrete Strength for Piers and Caissons

ACI 318-19 §10.5.1 (for nonprestressed compression members including columns and piers):

Condition	Minimum f'c
Cast-in-place pier, not exposed	3,000 psi (20.7 MPa)
Cast-in-place pier, exposed to weather	3,500 psi (24.1 MPa)
Drilled caisson in contact with soil	3,000 psi (20.7 MPa)
Marine or sulfate-bearing soil	4,000–4,500 psi

For residential deck piers using sonotubes, 3,000 psi bagged concrete (most brands) is appropriate. For structural caissons supporting columns in commercial construction, specify per the structural engineer of record — typically 4,000–5,000 psi with a designed mix.

Reinforcement in Piers

Most residential sonotube piers (deck, pergola, fence) are unreinforced or lightly reinforced — a central rebar dowel to connect the post hardware is the most common detail, not structural cage reinforcement.

Drilled caissons for structural support follow ACI 336.3R (Drilled Piers):

Minimum longitudinal reinforcement: 0.5% to 1.0% of gross cross-section area
For an 18-inch caisson (gross area = 254 in²), 0.5% = 1.27 in² → use 4 × #6 bars (1.76 in²)
Transverse (spiral or ties): typically #3 at 6-inch pitch in the top 3 shaft diameters, relaxed below

For structural caissons, always obtain a designed reinforcement layout from a licensed structural or geotechnical engineer. The soil profile, caisson depth, and load combination (axial + lateral) all affect the reinforcement.

Frost Protection for Shallow Piers

Residential deck piers must extend below the local frost depth — otherwise frost heave will lift the entire deck. Minimum frost depths by U.S. climate zone (ASCE 7-22 Figure C-1):

Region	Frost Depth
Southern states (Zone 1–2)	0–12 inches
Mid-Atlantic, Midwest, PNW	18–36 inches
Upper Midwest, Northern New England	42–60 inches
Minnesota, northern tier	60–72 inches

The sonotube tube itself is a form — remove the tube after concrete has set (typically 24–48 hours after pour) unless the manufacturer specifically rates it for buried use. Most standard sonotubes are intended to be stripped and will deteriorate if left in ground contact.

Common Mistakes Setting Piers

1. Drilling a smaller hole than the tube diameter. The drilled hole must be at least as large as the sonotube OD, not just the nominal ID. A 12-inch tube has a ~12.75-inch OD — drill 13 inches at minimum.

2. Not suspending the tube above the bottom of the hole. Concrete poured directly onto loose drilled cuttings at the bottom has a weak bearing surface. Clean the hole and set the tube 2–3 inches above any cuttings, or use a formed bell.

3. Setting post hardware before concrete reaches initial set. Wet concrete has no shear resistance — embedded post bases will shift. Wait at least 4 hours with fast-set mix (QUIKRETE Fast-Setting) or 24 hours with standard 60/80 lb mix before loading hardware.

4. Pouring into water-filled holes. Drilling into a water table without casing degrades concrete quality. Use a casing or dewater the hole before placement, or use tremie-placed concrete.

5. Ignoring bell geometry in volume estimates. For belled caissons, the bell can add 25–60% to the total volume. Failing to account for it produces a significant under-order.

Frequently Asked Questions

How deep should a deck pier be?

At minimum, below the local frost depth — typically 36–48 inches in the northern U.S. The pier must also bear on stable, undisturbed native soil. Many local codes specify minimum 12 inches of bearing into native soil below the frost depth. Check your municipality's building code.

What size sonotube for a 6×6 post?

A 10-inch or 12-inch diameter sonotube is standard for a 6×6 deck post. The wider 12-inch form gives more bearing area and is preferred in soft soil or for taller decks. Post hardware anchor bolts are typically set at the time of pour, before concrete reaches final set.

Can I pour sonotubes in winter?

Yes, with cold-weather precautions. Use fast-setting bagged concrete (it generates more heat during hydration) and insulate the tube top with a foam board or insulating blanket. Do not pour on frozen ground — the soil temperature affects curing speed and the frost-heave risk to uncured concrete.

What is the difference between a pier and a caisson?

In residential construction, the terms are often used interchangeably. Technically, a pier is a shorter, shallower concrete column typically cast in a tube form (sonotube), while a caisson is a deeper drilled element intended to reach bearing stratum below weak surface soils. Caissons may have belled ends; piers typically do not.

How many sonotubes come on a pallet?

Sonotubes are sold individually at most lumber yards. A 12-inch × 48-inch tube typically costs $12–$ 18 per tube. For large deck projects with many piers, buying a small quantity from a concrete products supplier is often cheaper than box-store pricing.

Use the Calculator

The Pier/Caisson Concrete Calculator computes shaft volume, bell volume, and total volume for any diameter, depth, and bell geometry — and returns the result in cubic feet, cubic yards, and number of bags (40/60/80 lb options).

For standard residential sonotubes, the Sonotube Calculator provides a simplified interface: diameter, depth, number of piers, and bag size.

Visit Concrete Calculator Max for the full suite of concrete foundation calculators.