About

Estimating fill material for cylindrical forms - sonotubes, round footings, tanks, culverts - demands precise volume in cubic yards because that is the unit suppliers quote and trucks deliver. A miscalculation of r by even 1 in on a 36 in diameter column changes the volume by roughly 5%, which across 40 piers means an entire extra yard of concrete you did not order. This calculator applies V = π × r² × h, converts the result into cubic yards using the exact factor 1 yd = 3 ft = 36 in, and cross-reports in cubic feet, cubic meters, gallons, and liters so you can validate against spec sheets in any system.

The tool assumes a perfect right circular cylinder. Real-world pours lose material to over-excavation, form bulge, and waste; most contractors add 5 - 10% overage. Enter the interior dimensions of the form, not the exterior, unless you are calculating displacement. Pro tip: for half-filled horizontal tanks, this calculator gives the full cylinder; you must halve the result manually or adjust the height to the fill level.

Formulas

The volume of a right circular cylinder is computed from its radius and height.

V = π × r² × h

Where V is the volume, r is the radius of the circular base, h is the height (or length) of the cylinder, and π ≈ 3.14159265.

If the user provides diameter d instead of radius:

r = d2

To convert the computed volume into cubic yards, all linear dimensions must first be expressed in yards. The conversion factor from any input unit to yards:

V_yd³ = π × (r × f_unit→yd)² × (h × f_unit→yd)

Where f_unit→yd is the linear conversion factor. For feet: f = 13. For inches: f = 136. For meters: f = 1.09361. For centimeters: f = 0.010936.

Additional volume conversions from cubic yards:

V_ft³ = V_yd³ × 27

V_m³ = V_yd³ × 0.764555

V_gal = V_ft³ × 7.48052

V_L = V_m³ × 1000

Reference Data

Input Unit	To Yards Factor	To Feet Factor	To Meters Factor	To Inches Factor
Feet	0.333333	1	0.3048	12
Inches	0.027778	0.083333	0.0254	1
Yards	1	3	0.9144	36
Meters	1.09361	3.28084	1	39.3701
Centimeters	0.010936	0.032808	0.01	0.393701

Common Cylinder	Diameter	Height	Approx. Cubic Yards
Sonotube 8"	8 in	48 in	0.065
Sonotube 10"	10 in	48 in	0.101
Sonotube 12"	12 in	48 in	0.145
Sonotube 14"	14 in	48 in	0.198
Sonotube 16"	16 in	48 in	0.258
Sonotube 18"	18 in	48 in	0.327
Sonotube 24"	24 in	48 in	0.581
Sonotube 36"	36 in	48 in	1.308
Round Footing 18"	18 in	12 in	0.082
Round Footing 24"	24 in	12 in	0.145
Cistern 48"	48 in	72 in	4.712
Culvert 30"	30 in	120 in	1.818
Water Tank 6 ft	6 ft	8 ft	8.378
Grain Bin 12 ft	12 ft	10 ft	41.888
Pool (round) 15 ft	15 ft	4 ft	26.180

Frequently Asked Questions

This calculator accepts either. Use the toggle to switch between radius and diameter input mode. If you select diameter, the tool divides by 2 internally to obtain the radius r before applying V = πr²h. Sonotube and pipe specifications almost always list diameter, so diameter mode is the typical choice for construction work.

Industry practice is to add 5 - 10% overage. Concrete is lost to spillage, over-excavation of the hole, form bulge under hydrostatic pressure, and residual material left in the truck chute. For critical pours where a short load means a cold joint, some contractors go as high as 15%. Ready-mix suppliers typically sell in 0.25 yd³ increments, so always round up to the next quarter yard.

Temperature does not change the geometric volume you must fill, but it affects workability and slump. In hot weather (above 30 °C), concrete sets faster and may not flow fully into a narrow form, causing voids that require more material to patch. In cold weather (below 5 °C), air-entrained mixes are specified, which have slightly higher volume per unit weight but do not change the cubic-yard requirement. The calculated geometric volume remains accurate regardless of temperature.

Volume depends on the square of the radius. Doubling the diameter quadruples the cross-sectional area. For example, a 12 in diameter sonotube at 4 ft height holds about 0.145 yd³. A 24 in diameter at the same height holds about 0.581 yd³ - four times as much, not two. This nonlinear relationship is why precise measurement of the cylinder diameter matters far more than precise measurement of height.

Yes. A horizontal cylinder has the same volume formula as a vertical one. Enter the pipe length as the height h and the interior pipe diameter as the diameter. The orientation does not affect the volume. If the pipe is only partially filled (e.g., a storm drain at half capacity), you need a partial cylinder (segment) formula, which this calculator does not cover. In that case, calculate the full cylinder and multiply by the fill fraction.

Standard-weight concrete (normal mix with gravel aggregate) weighs approximately 4050 lb/yd³ or about 2400 kg/m³. Lightweight concrete ranges from 2700 to 3200 lb/yd³. This calculator outputs volume only. Multiply the cubic yard result by the density of your specific mix to estimate total weight, which is critical for structural load calculations and truck axle limits (most ready-mix trucks carry a maximum of 10 yd³).