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Volume Calculator
Our free volume calculator works out how much space a shape holds, in cubic inches, cubic feet, cubic centimeters, or cubic meters. Pick a shape — a rectangular box, a cylinder, a sphere, or a cone — enter your measurements, and the volume appears right away, with the formula and each step shown.
Use the radius (half the diameter), not the diameter. All measurements must use the same unit.
| Formula | V = l × w × h |
| Calculation | 2 × 3 × 4 = 24 |
| Volume | 24 ft³ |
How it works
Volume is the amount of three-dimensional space an object takes up. If area tells you how much paint covers a wall, volume tells you how much water fills a tank, how much concrete fills a footing, or how many moving boxes fit in a storage unit. In the United States it is usually measured in cubic inches, cubic feet, or cubic yards, and in metric work in cubic centimeters or cubic meters.
Each shape has its own formula, but the idea is the same: multiply the measurements that define the shape, using pi (about 3.14159) for anything round. A rectangular box is the simplest case — length times width times height. A cylinder is the area of its circular base, pi times the radius squared, times its height. A sphere uses four-thirds pi times the radius cubed, and a cone is exactly one-third of the cylinder with the same base and height, which is why its formula is one-third pi r squared h.
The most common mistake is mixing units or using the diameter where the radius belongs. If a pipe is 6 inches across, its radius is 3 inches — using 6 would make the answer four times too big, because the radius is squared. Likewise, if the length is in feet and the height is in inches, convert one to match the other first. This calculator keeps it simple: pick one unit for every measurement, and the answer comes out in the matching cubic unit, such as ft³ for feet or cm³ for centimeters.
Volume is a practical number in everyday American life. Movers quote storage units in cubic feet, so a 10-by-10-foot unit with an 8-foot ceiling holds about 800 cubic feet. Concrete and mulch are sold by the cubic yard — 27 cubic feet — so a patio slab 10 feet by 12 feet and 4 inches thick needs about 1.5 cubic yards of concrete. Aquariums are rated in gallons, and one cubic foot of water is about 7.48 gallons, which is how a tank's size turns into a weight your floor has to carry.
Worked example
A family in Texas is packing for a move and wants to know how much a standard moving box holds. The box measures 2 feet long, 3 feet wide, and 4 feet tall. Select "Rectangular box" and "Feet" in the calculator, then enter 2, 3, and 4.
The formula for a box is V = l × w × h. Step 1 — multiply length by width: 2 × 3 = 6 square feet, the area of the base. Step 2 — multiply by the height: 6 × 4 = 24. The box holds 24 cubic feet. That is the same answer the calculator shows for 2 × 3 × 4 ft: 24 ft³. For a sense of scale, that is roughly the size of a large moving box that can hold about a dozen folded moving blankets, or around 180 gallons of water if it were a tank — far more than most people guess from the outside dimensions.
FAQ
How do you calculate the volume of a box?
Multiply length times width times height: V = l x w x h. A box that is 2 feet long, 3 feet wide, and 4 feet tall has a volume of 2 x 3 x 4 = 24 cubic feet. All three measurements must use the same unit.
What is the volume formula for a cylinder?
The volume of a cylinder is pi times the radius squared times the height: V = pi x r squared x h. Measure the radius (half the diameter) and the height in the same unit, then multiply.
How do you calculate the volume of a sphere?
The volume of a sphere is 4/3 times pi times the radius cubed: V = (4/3) x pi x r cubed. For example, a sphere with a radius of 3 inches has a volume of (4/3) x 3.14159 x 27, which is about 113.1 cubic inches.
What is the difference between volume and surface area?
Volume measures how much space is inside a three-dimensional object, in cubic units such as cubic feet. Surface area measures the total area of the outside of the object, in square units such as square feet. A shipping box needs volume for what fits inside and surface area for how much cardboard it takes to build.
How many cubic feet are in a cubic yard?
There are 27 cubic feet in a cubic yard, because a yard is 3 feet and 3 x 3 x 3 = 27. Concrete, mulch, and topsoil in the United States are usually sold by the cubic yard, so divide a volume in cubic feet by 27 to convert it.