How to use the volume calculator
- Pick a shape. Use the circle for a cylinder, such as a round footing or a barrel.
- Enter the size, then the depth. For containers, measure the inside, since that is the space you can fill.
- Read the volume in the units you need. If something will fill the space, pick it from the list to see its weight and bag count.
The sphere has no depth, so its depth box is ignored. Every other shape is a flat outline pushed straight down, which builders call a prism.
Imperial or metric
The Imperial | Metric switch at the top of the calculator sets the units menus and which results come first: cubic yards, cubic feet and gallons for imperial, cubic meters and liters for metric. The page opens in the system your browser's region uses and remembers your choice. Switching keeps your numbers: a bare 10 in feet becomes 3.048 in meters, so the volume does not change.
A unit you type always wins over the menu, so you can enter 12'6", 12 ft 6 in, 150 in, 3.5 m, 3 m 20 cm or 80 cm in either system. Every factor is exact: a foot is exactly 0.3048 m, so a cubic foot is 0.028316846592 cubic meters and a cubic yard (27 cubic feet) is 0.764554857984 cubic meters. A U.S. gallon is exactly 3.785411784 liters, and a pound is exactly 0.45359237 kg.
The math: volume is base area times depth
A prism is a flat shape with a depth. Its volume is the area of the flat shape multiplied by the depth. The calculator finds the area first, converts everything to meters, multiplies, and then converts the answer back into the units you see.
| Shape | Base area | You enter |
|---|---|---|
| Square | s² | Side |
| Rectangle | length × width | Length and width |
| Circle (cylinder) | π × r² | Diameter |
| Oval | π × a × b | Length and width (a and b are half of each) |
| Hexagon | (3√3 ÷ 2) × s² ≈ 2.598 × s² | Side |
| Octagon | 2 × (1 + √2) × s² ≈ 4.828 × s² | Side |
| Five-point star | ≈ 1.1226 × R² | Across the points (R is half of it) |
| Sphere | volume = 4⁄3 × π × r³ | Diameter |
Here is the star worked through. A five-point star 2 ft across the points has R = 1 ft, so its area is 1.1226 sq ft. At 12 ft deep the volume is 1.1226 × 12 = 13.47 cubic feet. That is 0.499 cubic yards, about 100.8 gallons, or 0.38 cubic meters. Filled with water it would weigh about 840 pounds.
The same star in metric: 0.6 m across the points gives R = 0.3 m, so its area is 1.1226 × 0.09 = 0.101 square meters. At 3.6 m deep the volume is 0.101 × 3.6 = 0.364 cubic meters, or 363.7 liters.
The star is the one shape that needs explaining. "Across the points" means the width of the circle that touches all five tips. The inner corners sit at 0.382 of that radius, which is the ratio that makes the edges run straight from tip to tip.
How the depth scale works
Numbers like 13 cubic feet are hard to picture, so the drawing beside the calculator gives your shape a height. The footprint stays the same and the depth stretches to match each object. Pick "My depth" to see your own number next to a 6-foot person, or press the scale tour to zoom from a coin past houses, trees and Niagara Falls to Mount Everest.
Each step also shows the volume at that depth and compares large volumes with an Olympic swimming pool, which holds at least 2,500 cubic meters (50 m by 25 m by 2 m). A 2 ft star as deep as Everest holds about 0.37 of a pool.
| Object | Height used | Where it comes from |
|---|---|---|
| U.S. penny | 0.0598 in (1.52 mm) | United States Mint coin specifications |
| Horse | 5 ft at the shoulder | A 15-hand horse, where one hand is 4 in |
| Basketball rim | 10 ft | Regulation height for professional, college and high school play |
| One-story house | 14 ft | Typical: an 8 ft ceiling, the floor structure and about 5 ft of roof. Not a measured house |
| Two-story house | 22 ft | Home-height guides commonly give 20 to 25 ft |
| Utility pole | about 35 ft | A standard U.S. pole is about 40 ft long with about 6 ft underground |
| Big oak or maple | 75 ft | Sugar maples and large oaks reach 60 to 100 ft. A study of street maples in Rochester and Syracuse found mature trees averaging in the mid to upper 70s |
| Niagara Falls | 188 ft (57 m) | Horseshoe Falls, measured to the river. Some sources give 167 to 173 ft, depending on water flow and where it is measured |
| Statue of Liberty | 305 ft 1 in | National Park Service, ground to the tip of the torch |
| Coast redwood | about 380 ft (116 m) | Hyperion, the tallest known living tree |
| Empire State Building | 1,454 ft | To the tip of the antenna, from the building's operators |
| Mount Everest | 29,032 ft (8,848.86 m) | 2020 survey announced by China and Nepal |
What volume is used for
Volume tells you how much material a space needs or how much a container holds. Builders use it for round concrete footings and posts, planters and raised beds with six or eight sides, gazebo and hot tub pads, ponds, fire pits, rain barrels and tanks. The same math sizes a length of pipe or a drilled hole. Shops use it for packaging and shipping, and hobbyists use it for casting, molds and 3D printing.
Once you know the volume, weight and cost follow. Weight is volume times density. Cost is the volume in the unit the supplier sells, such as cubic yards of concrete or topsoil, times the price. The related calculators below cover the common materials with ordering details.
Where the fill weights come from
The fill list uses round figures in pounds per cubic foot: water 62.4, concrete 150, dry sand 100, gravel 105, topsoil 75 and mulch 22. In kilograms per cubic meter those are about 1,000, 2,400, 1,600, 1,680, 1,200 and 350. Water at room temperature is a standard physical value. The others are typical bulk densities of the kind suppliers publish. They change with moisture, compaction and the exact product, so treat them as planning numbers and ask your supplier for theirs. You can type your own density with the custom option.
Bag counts use a 2 cubic foot bag for mulch (about 57 liters) and an 80 pound bag of concrete mix (about 36 kg), which makes about 0.6 cubic feet. Bags are counted at the sizes they are sold in, in either system. The calculator adds nothing for settling, compaction or waste, so order a little extra of any loose material.
Measuring tips
Measure the inside of a container, not the outside, since walls take up room. If the floor slopes in a straight line, such as a pool that runs from shallow to deep, use the average depth. For a bottom that curves or steps, split the space into pieces, find each volume and add them. A cone or pyramid holds one third of the matching cylinder or box, which makes a quick check. You can mix units freely, such as a width in inches and a depth in feet.
Questions
What is the volume formula for a cylinder?
Multiply π by the radius squared, then by the depth. A cylinder 2 ft across and 3 ft deep is 3.1416 × 1 × 3 = 9.42 cubic feet, or about 70.5 gallons. Pick the circle shape and enter the diameter.
What is the difference between area and volume?
Area is flat space, measured in square feet. Volume is space with depth, measured in cubic feet. Divide cubic feet by 27 to get cubic yards, which is how concrete, soil and mulch are sold.
How many gallons are in a cubic foot?
A US gallon is 231 cubic inches and a cubic foot is 1,728 cubic inches, so a cubic foot holds about 7.48 gallons.
How do I find the volume of an irregular shape?
Break it into simple shapes, find each volume and add them. For a footprint with a curved edge, the oval or circle often gets close enough for a first estimate.
Can I use metric?
Yes. Press Metric at the top of the calculator to enter sizes in meters, centimeters or millimeters and see cubic meters and liters first. You can also type a unit into any box, such as 80 cm or 3.5 m, in either system. The page remembers your choice.
Can I find square footage with this?
Yes. The top-face area is shown in square feet and square meters under the volume. The square footage calculator covers more shapes and adding several areas together.