Volume Calculator

Volume is the amount of three-dimensional space a solid occupies, and it is always measured in cubic units. A cube with 5 cm edges holds 5 × 5 × 5 = 125 cm³; a sphere with a 6 cm radius holds about 904.8 cm³; a soda can roughly 3 cm across and 10 cm tall holds about 282.7 cm³ (a little over a quarter of a liter). This volume calculator covers the seven shapes you meet most often - cube, rectangular box, sphere, cylinder, cone, square pyramid and triangular prism - and shows the formula, the volume, the surface area where it is simple, and the equivalent capacity in liters and gallons.

The formulas at a glance

Every shape has its own formula, but they all return a result in the cube of whatever length unit you measure in. Pick a shape in the calculator and the matching formula appears automatically:

The letters mean: s = edge length, l/w/h = length, width and height, r = radius (half the diameter), b = base edge or triangle base, hₜ = the triangle's own height, and L = the prism's length. The constant π (pi) ≈ 3.14159 appears only in shapes with a circular cross-section.

What volume actually means

If you imagine filling a solid with tiny unit cubes - say 1 cm cubes - the volume is simply how many of those cubes fit inside. That is why the unit is "cubic": you are counting in three directions at once. Doubling a single length does not double the volume; for a cube it multiplies the volume by eight (2³), because all three dimensions scale together. Keeping that "third power" intuition in mind explains why small changes in radius or edge length can change a volume dramatically.

How to use this volume calculator

You only need a shape and a few measurements to get an answer:

1. Pick the shape from the grid at the top (cube, box, sphere, cylinder, cone, pyramid or triangular prism). The input fields change to match it.
2. Choose your length unit - millimeters, centimeters, meters, inches or feet. Use the same unit for every measurement.
3. Enter the dimensions. For round shapes, enter the radius (half the diameter), not the diameter.
4. Read the result. The big number is the volume in cubic units; supporting cards show surface area and capacity in liters and gallons.

The result updates instantly as you type, so you can experiment - for example, see how a cylinder's volume changes when you increase the radius versus the height.

Worked example 1: a rectangular box

Suppose you have a moving carton that is 10 in long, 4 in wide and 6 in tall. Using V = l × w × h, the volume is 10 × 4 × 6 = 240 in³. To convert to cubic feet, divide by 1,728 (since 12³ = 1,728 cubic inches per cubic foot): 240 ÷ 1,728 ≈ 0.139 ft³. The box's surface area is 2 × (10·4 + 10·6 + 4·6) = 2 × (40 + 60 + 24) = 248 in², which tells you how much cardboard wraps around it.

Worked example 2: a cylinder and a cone

A cylindrical water tank with a 3 m radius and 4 m height holds V = π × 3² × 4 = π × 9 × 4 ≈ 113.1 m³, which is 113,097 liters - about 29,877 US gallons. Now picture a cone with the same base and height: its volume is exactly one-third, V = 1/3 × π × 3² × 4 ≈ 37.7 m³. That one-third relationship between a cone and a cylinder (and between a pyramid and a prism) is one of the most useful facts in solid geometry - it lets you estimate a cone's volume just by finding the matching cylinder and dividing by three.

Worked example 3: a sphere

A basketball has a radius of roughly 12 cm. Its volume is V = 4/3 × π × 12³ = 4/3 × π × 1,728 ≈ 7,238 cm³, or about 7.24 liters. Notice that because the radius is cubed, a ball with twice the radius would hold eight times as much air. The sphere also has the smallest surface area for a given volume of any shape, which is why bubbles and droplets are round.

Common shapes and their volumes (reference)

This table summarizes each shape, what you measure, the formula, and what you would need for surface area. Use it as a quick lookup when you are away from the calculator:

In the cone and pyramid surface-area formulas, ℓ is the slant height (the distance up the sloping face), not the vertical height.

Unit conversions you will actually use

Because volume is a cubed quantity, conversions are larger than people expect. These are the ones that come up most often:

• 1 cm³ = 1 milliliter, so 1,000 cm³ = 1 liter.
• 1 m³ = 1,000 liters ≈ 264.2 US gallons.
• 1 ft³ ≈ 28.317 liters ≈ 7.481 US gallons.
• 1 US gallon ≈ 3.78541 liters = 231 cubic inches.
• 1 ft³ = 1,728 in³ (because 12³ = 1,728).

Who this calculator is for

• Students checking geometry and pre-algebra homework on solids.
• DIY and home projects - figuring out how much concrete, soil, water or aggregate fills a space.
• Aquarium and pool owners converting tank dimensions into liters or gallons.
• Shippers and movers estimating the cubic feet a carton or container holds.
• Cooks and brewers sizing pots, kegs and containers by capacity.

Key terms explained

• Radius vs. diameter: the radius is half the diameter. Round-shape formulas use the radius, so halve the diameter first if that is what you measured.
• Height vs. slant height: "height" is the straight vertical distance; "slant height" runs up the sloping face of a cone or pyramid and is used only for surface area.
• Base area: the area of the flat bottom face. For prisms and cylinders, volume = base area × length/height.
• Cubic unit: a length unit raised to the third power (cm³, ft³, m³). Always cube the unit, not just the number.
• Capacity: how much a container holds, usually in liters or gallons - the same quantity as volume, just expressed in fluid units.

Tips for accurate measurements

• Keep one unit. Mixing inches and feet in the same calculation is the most common source of wrong answers - convert everything first.
• Measure to the inside when you want capacity (how much it holds) and to the outside when you want material or displacement.
• Use the radius for round shapes. If you only have the diameter, divide by two before entering it.
• Decompose complex objects. An L-shaped room or a bottle with a tapered neck is just two or three simple shapes added together.

Related concepts

Volume sits alongside a few other measurements you may need. Area is the two-dimensional space inside a flat shape (square units) - if you only need the floor space or a circular footprint, the Area Calculator and Circle Calculator handle those directly. Surface area is the total area of a solid's outer faces. Density ties volume to mass: mass = density × volume, so once you know a solid's volume you can estimate its weight if you know what it is made of. For real-world fill jobs, the specialist tools below convert a space into the material you need to buy.

Filling real spaces: from volume to materials

The most common reason people reach for a volume calculator is not homework - it is buying enough material to fill a space without overpaying for the surplus. Once you have the volume of an area, the rest is unit conversion and a small waste allowance. The trick is that landscaping and construction materials are sold in cubic yards or cubic feet, while many people measure their space in feet and inches, so the cube of the unit has to be handled carefully (recall 1 ft³ = 1,728 in³ and 1 cubic yard = 27 ft³).

For a rectangular slab or bed, the volume is simply length × width × depth, with the depth usually entered in inches and converted to a fraction of a foot. A patio that is 12 ft × 10 ft poured 4 in (0.333 ft) deep needs 12 × 10 × 0.333 ≈ 40 ft³, which is 40 ÷ 27 ≈ 1.48 cubic yards of concrete. Because materials settle, compact, and get wasted at the edges, professionals add roughly 5-10% on top of the bare volume. If you are pouring concrete, our Concrete Calculator applies exactly this logic and reports bags or yards; for loose fill, the Gravel Calculator, Mulch Calculator, and Cubic Yard Calculator turn the same depth-and-area math into a yardage you can order. This volume calculator is the underlying geometry; those tools wrap it in material-specific defaults and coverage rules.

Volume of liquids and containers

Liquid problems are just volume problems read in fluid units. A fish tank, a rain barrel, a stock pot, or a fuel can all have a geometric volume that you then express as capacity. Because 1 cm³ holds exactly 1 milliliter, a tank measured in centimeters converts to liters by dividing by 1,000, and to US gallons by dividing the liters by 3.78541. A rectangular aquarium that is 60 cm × 30 cm × 40 cm has a volume of 72,000 cm³ = 72 liters ≈ 19 US gallons - though the true water capacity is a little less once you subtract gravel, rocks, and the freeboard you leave at the top. For cylindrical containers such as drums, buckets, and water heaters, use V = π × r² × h and remember to measure the inside radius, not the outside, when you care about how much it holds. When a container tapers (a bucket that is wider at the top than the bottom), it is technically a frustum; a quick, slightly conservative estimate is to average the top and bottom radii and treat it as a cylinder, then round down so you do not overfill.

How scaling changes volume (and why it matters)

One of the most useful mental models in geometry is how volume responds to scaling. If you multiply every linear dimension of a solid by a factor k, the surface area grows by k² and the volume grows by k³. Double a box's length, width, and height and it holds eight times as much (2³ = 8), even though it only looks "twice as big." This single fact explains a surprising number of everyday observations: why a large pot of soup takes far longer to cool than a small one (volume grows faster than surface area, so there is relatively less surface to shed heat), why baby animals lose body heat more easily than adults, and why doubling the radius of a pizza gives you far more than twice the food. When you are sizing anything - a tank, a planter, a storage box - resist the temptation to estimate volume by eye, because the third-power growth means your intuition will almost always undershoot the real number.

A short history of measuring volume

The idea of measuring three-dimensional space is ancient. Egyptian scribes recorded formulas for the volume of a truncated pyramid (a frustum) on the Moscow Mathematical Papyrus around 1850 BCE, and the famous story of Archimedes leaping from his bath shouting "Eureka!" is about volume: he realized that an irregular object's volume equals the water it displaces, which let him test whether a crown was pure gold by comparing its density. That displacement method is still the most reliable way to measure a genuinely irregular solid, and it is why this calculator focuses on the regular shapes you can either measure directly or build an object from. The exact 1/3 factor linking a cone to its cylinder, and a pyramid to its prism, was proven rigorously by the Greeks and later by the integral calculus of Newton and Leibniz - the same calculus that gives the 4/3·π·r³ formula for a sphere. When you type a radius into the sphere field, you are using a result that took mathematicians two thousand years to nail down.