Calculate Concrete in a Cylinder: Volume and Bags

To calculate concrete for a cylinder, multiply pi by the square of its radius and by its height: V = pi × r² × h. Enter the cylinder’s diameter and height in the same unit to get its volume, plus an estimate of how many concrete bags that volume requires.

Formula

The cylinder’s volume is pi times its radius squared times its height. Since the calculator asks for diameter, it first divides diameter by two to get the radius:

V = pi × (d / 2)² × h

• V = concrete volume, in cubic feet (ft³).
• d = cylinder diameter, in feet (ft).
• h = cylinder height or depth, in feet (ft).
• pi ≈ 3.14159.

To convert cubic feet to cubic yards, divide by 27, because one cubic yard equals 27 cubic feet. The bag estimate is V divided by the entered bag yield; rounding up gives a whole number of bags. Bag yields vary by product and package size, so replace the default yield with the yield stated on the bag or product information. This estimate assumes a complete fill with no waste.

Worked Example

Using the calculator’s defaults, the cylinder is 2 ft in diameter and 3 ft high. The assumed yield is 0.6 ft³ per bag.

1. Radius = diameter / 2 = 2 / 2 = 1 ft.
2. Volume = pi × 1² × 3 = 9.42478 ft³, which rounds to 9.42 ft³.
3. Cubic yards = 9.42478 / 27 = 0.34907 yd³, which rounds to 0.349 yd³.
4. Bags = 9.42478 / 0.6 = 15.70797; round up to 16 bags.

The cubic-yard result is a conversion of the same volume, not an additional amount of concrete. Bag count is only an estimate based on the entered yield.

How to Measure a Cylinder

Measure across the circular opening through its center to find the diameter. Measure the filled height from the bottom to the top of the concrete. Use the inside dimensions of a form if it has wall thickness; the outside dimensions would overstate the space being filled.

• For a cylindrical post hole, use the hole’s diameter and the depth that will actually contain concrete.
• For a round pier form, measure its internal diameter and the planned concrete height.
• For a cylinder lying on its side, use its circular end diameter and its length as the cylinder height in the formula.

If the form is not a true cylinder—for example, it narrows toward the bottom—the cylinder formula will not give an exact volume. Divide an irregular shape into simpler sections and calculate each section separately, or use a suitable geometric formula.

Choosing Units and Bag Yield

The calculator uses feet for diameter and height and reports volume in cubic feet and cubic yards. Measurements in inches must be converted first: divide inches by 12 to get feet. For instance, a 12-inch diameter is 1 ft, and a 30-inch height is 2.5 ft. Entering 12 and 30 as though they were feet would inflate the result dramatically.

Metric measurements work with the same formula, but all dimensions must use the same unit. With diameter and height in metres, the result is cubic metres; with both in centimetres, it is cubic centimetres. To convert cubic feet to cubic metres, multiply by 0.0283168. To convert cubic yards to cubic metres, multiply by 0.764555. Do not mix, for example, a diameter in inches with a height in feet without converting one of them.

Bag yield is the volume of mixed concrete produced by one bag, not necessarily the bag’s weight or the volume of its dry contents. Read the yield for the specific product and package size. If it is printed in litres, convert it to cubic feet by dividing litres by 28.3168, or convert the calculated volume to litres by multiplying cubic feet by 28.3168. Then divide the project volume by the converted yield and round up to a whole bag.

Allowances, Accuracy, and Common Mistakes

The mathematical result describes the exact volume of an ideal cylinder. Real excavations and forms may be uneven, and some material may be lost during mixing or placement. For planning, people commonly allow a modest extra amount, but the appropriate allowance depends on how accurately the form is measured and the job conditions. Add any allowance separately rather than changing the cylinder formula.

• Using radius as diameter: If you measure from the center to the edge, that is the radius. Enter twice that measurement as diameter, or calculate using V = pi × r² × h.
• Forgetting to square the radius: The radius is multiplied by itself before multiplying by height.
• Rounding too early: Keep the full volume during conversions and bag calculations; round the displayed amount only at the end.
• Assuming all bags yield the same amount: Use the yield shown for the actual product and bag size.
• Ignoring the form’s shape: A tapered or irregular hole can contain a different volume than a cylinder with the same top diameter and depth.

This calculator estimates volume and bag count; it does not determine a concrete mix design, strength, reinforcement, or whether a particular structure is suitable. Those requirements depend on the project and should be established separately.

Frequently Asked Questions

How do I calculate concrete for a cylinder?
Use V = pi × r² × h. Measure the radius and height in the same unit, square the radius, and multiply by the height and pi. If you measured diameter, divide it by two first.

How many cubic yards are in a cylindrical hole?
Calculate its volume in cubic feet, then divide by 27. For dimensions in feet, the direct expression is pi × (diameter / 2)² × height / 27.

Can I use diameter instead of radius?
Yes. Substitute half the diameter for the radius: V = pi × (diameter / 2)² × height. Do not square the full diameter, or the answer will be four times too large.

How many concrete bags do I need for a cylinder?
Divide the cylinder’s volume by the yield per bag, using matching units, then round up to a whole bag. Check the package yield because it varies with product and bag size.

Does the calculator include extra concrete for waste?
No. It calculates the ideal cylinder volume. Add a separate allowance if measurement uncertainty, an uneven excavation, or placement loss makes one necessary.

Related

• Building Costs Calculator NZ: Estimate Your Project
• Building Budget Calculator NZ: Estimate Your Build Cost
• Boysen Paint Calculator: Estimate Paint Needed

in d | Diameter | ft | 2 | 0
in h | Height | ft | 3 | 0
in y | Bag yield | ft^3 per bag | 0.6 | 0
out v | Concrete volume | ft^3 | pi * (d / 2)^2 * h | 2
out g | Concrete volume | yd^3 | v / 27 | 3
out b | Bags required | bags | ceil(v / y) | 0