cone volume calculator
A cone volume calculator uses V = ⅓ × π × r² × h. A cone with a 6 ft base diameter and 8 ft height holds 75.40 ft³, which is 2.793 yd³ or about 564 gallons.
How to find the volume of a cone
A cone volume calculator finds how much a pointed, round-based shape holds. Square the radius, multiply by pi and by the height, then take one-third. V = ⅓ × π × r² × h. A cone with a 6 ft base diameter and 8 ft height holds 75.40 cubic feet, which is 2.793 cubic yards or about 564 gallons.
Enter the base diameter and the vertical height in feet. The calculator returns cubic feet, cubic yards, gallons, and liters.
The formula in plain words
- Radius is half the base diameter. It is easier to measure the full width across, so the calculator asks for diameter and halves it.
- π × r² is the area of the round base.
- × height would give a cylinder.
- × ⅓ accounts for the taper. Every horizontal slice shrinks as you climb, and those slices add up to one-third of the cylinder.
Unit conversions use 27 ft³ per cubic yard, 7.48052 gallons per ft³, and 3.78541 liters per gallon.
Worked examples
Example 1: Conical form or hopper, 6 ft diameter, 8 ft tall
- Radius: 6 ÷ 2 = 3 ft
- Volume: ⅓ × π × 3² × 8 = 24π = 75.40 ft³
- Cubic yards: 75.40 ÷ 27 = 2.793 yd³
- Gallons: 75.40 × 7.48052 = 564.0 gal (2,135.0 L)
Example 2: Gravel pile left by a dump truck, 12 ft across, 5 ft tall
- Radius: 12 ÷ 2 = 6 ft
- Volume: ⅓ × π × 6² × 5 = 60π = 188.50 ft³
- Cubic yards: 188.50 ÷ 27 = 6.981 yd³
- At about 1.4 tons per yard: 6.981 × 1.4 ≈ 9.8 tons
Example 2 is a quick way to check a delivery. If you ordered 10 tons and the pile measures like this, the load is about right.
Cone volume reference
| Base diameter × height | Cubic feet | Cubic yards | Gallons |
|---|---|---|---|
| 3 × 2 ft | 4.71 | 0.175 | 35.3 |
| 4 × 6 ft | 25.13 | 0.931 | 188.0 |
| 6 × 8 ft | 75.40 | 2.793 | 564.0 |
| 10 × 4 ft | 104.72 | 3.879 | 783.4 |
| 8 × 12 ft | 201.06 | 7.447 | 1,504.0 |
| 20 × 7 ft | 733.04 | 27.150 | 5,483.5 |
Doubling the diameter quadruples the volume. Doubling the height only doubles it. That is why a wide, low pile can hold more than a tall, narrow one.
Where cones show up on a job
- Stockpiles of sand, gravel, mulch, and salt dropped from a conveyor or truck bed.
- Hoppers and silos with a conical bottom, where the cone section is added to a cylinder above it.
- Funnel-shaped forms and spun concrete caps.
- Conical tank bottoms on water and feed tanks. Add the cone to the straight-walled section from the cylinder calculator.
How to measure a real cone
- Diameter: stretch a tape straight across the base through the centre. For a pile, measure at ground level in two directions at right angles and average them.
- Height: measure straight up from the ground to the peak. On a pile, lay a straight board from the peak to a level point and measure down, or use a level and a rod.
- Do not use slant height. The sloped side is always longer than the true height and would overstate the volume.
- Hoppers: measure inside dimensions if you want the capacity, outside dimensions if you want material for the shell.
Common mistakes
- Entering the radius as the diameter. That makes the answer four times too big.
- Forgetting the one-third. Without it, you have a cylinder’s volume.
- Treating a flat-topped pile as a cone. Use the frustum volume calculator instead.
- Treating a long windrow as a cone. Ridge-shaped piles need the stockpile volume calculator.
Related calculators
Compare against the cylinder volume calculator for straight-sided tanks, or convert a pile’s yards to weight with the cubic yards to tons calculator.
Frequently asked questions
What's the formula for cone volume?
Volume is one-third of pi times the radius squared times the height: V = ⅓ × π × r² × h. With a 6 ft base diameter (3 ft radius) and 8 ft height, that is ⅓ × 3.1416 × 9 × 8 = 75.40 cubic feet.
Why is a cone exactly one-third of a cylinder?
As you slice a cone from base to tip, each slice's area shrinks with the square of its distance from the point. Adding up all those shrinking slices gives exactly one-third of a cylinder with the same base and height. A 6 × 8 ft cylinder holds 226.19 ft³; the matching cone holds 75.40 ft³.
How do I estimate a gravel or sand pile's volume?
Measure the pile's diameter at the ground and its height at the peak, enter both, and read the cubic yards. A 12 ft wide, 5 ft tall pile is 188.50 ft³, or 6.981 yd³. At about 1.4 tons per yard for gravel, that is roughly 9.8 tons.
Does this work for a cone-shaped hopper or funnel?
Yes. The formula is the same whether the point faces up or down. Measure the diameter across the wide end and the straight vertical height to the tip, not the slanted side length.
What if my pile isn't a perfect cone?
Real piles are lopsided or flattened on top. For a flat-topped pile use the frustum calculator, and for a long ridge-shaped pile use the stockpile calculator. For a slightly uneven cone, average two or three diameter readings taken at different angles.
How is this different from the frustum calculator?
A cone tapers to a point. A frustum is a cone with its top cut off flat, so it has two diameters, top and bottom. Truncated piles, buckets, and tapered planters are frustums.
Estimates only. Verify quantities with your supplier before purchasing.