Volume Calculator
Find the volume of cubes, spheres, cylinders, cones and more
🧊 Shape & dimensions
📐 Volume
🧮 How it was calculated
Volumes use exact geometric formulas with π ≈ 3.14159. Capacity conversions use 1 cm³ = 1 mL and 1 US gallon ≈ 3.78541 L. Results are rounded for display.
Last updated June 2026
Method: Volumes use the exact, standard geometric formulas (cube s³, box l·w·h, sphere 4/3·π·r³, cylinder π·r²·h, cone 1/3·π·r²·h, square pyramid 1/3·b²·h, triangular prism ½·b·hₜ·L) with π ≈ 3.14159.
Included: Volume for seven common solids, surface area where it is well defined, and capacity conversions to liters and US gallons using exact factors (1 cm³ = 1 mL, 1 US gal ≈ 3.78541 L).
Not included: Irregular or compound solids, hollow-wall thickness, and non-standard shapes (ellipsoids, frustums, tori). Results are rounded for display.
Volume calculator: how much space is inside a shape
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:
- 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.
- Choose your length unit - millimeters, centimeters, meters, inches or feet. Use the same unit for every measurement.
- Enter the dimensions. For round shapes, enter the radius (half the diameter), not the diameter.
- 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 29,878 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:
| Shape | You measure | Volume formula | Surface area |
|---|---|---|---|
| Cube | edge s | s³ | 6s² |
| Rectangular box | l, w, h | l·w·h | 2(lw+lh+wh) |
| Sphere | radius r | 4/3·π·r³ | 4·π·r² |
| Cylinder | r, h | π·r²·h | 2·π·r(r+h) |
| Cone | r, h | 1/3·π·r²·h | π·r(r+ℓ) |
| Square pyramid | base b, h | 1/3·b²·h | b²+2b·ℓ |
| Triangular prism | b, hₜ, L | ½·b·hₜ·L | depends on sides |
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); 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 purely numeric work behind these formulas - powers, roots and percentages - the exponent, square-root and percentage calculators below pair naturally with this one.
⚠️ Common mistakes & edge cases
Using the diameter instead of the radius
Spheres, cylinders and cones all use the radius - half the diameter. Entering a diameter where a radius belongs makes the volume far too large (up to 8× for a sphere). Always halve the diameter first.
Mixing units
Measuring length in feet and height in inches gives a meaningless answer. Convert every dimension to the same unit before calculating, then convert the final cubic result if needed.
Confusing volume with surface area
Volume is cubic units (cm³) and tells you how much fits inside; surface area is square units (cm²) and tells you how much covers the outside. They are different quantities - don't report one for the other.
Forgetting to cube the unit when converting
There are 1,728 cubic inches in a cubic foot, not 12, because the conversion factor is cubed (12³). The same applies to cm-to-m (×1,000,000) and other unit changes.
❓ Frequently asked questions
How do you calculate the volume of a 3D shape?
Volume measures the amount of space inside a solid, in cubic units. Each shape has its own formula: a cube is s³, a rectangular box is length × width × height, a sphere is 4/3 × π × r³, a cylinder is π × r² × h, a cone is 1/3 × π × r² × h, a square pyramid is 1/3 × base² × height, and a triangular prism is the triangle's area (½ × base × height) times its length. Plug your measurements into the right formula and the answer comes out in cubic units of whatever length unit you used.
What units does volume use?
Volume is always in cubic units - the length unit raised to the third power. If you measure in centimeters the volume is in cubic centimeters (cm³); in feet it is cubic feet (ft³); in meters it is cubic meters (m³). One cubic centimeter equals one milliliter, and one cubic meter equals 1,000 liters, which is why this calculator can also show capacity in liters and US gallons.
What is the difference between volume and surface area?
Volume is the space contained inside a solid, measured in cubic units (like cm³). Surface area is the total area of all the outside faces of the solid, measured in square units (like cm²). A box has a volume telling you how much it can hold and a surface area telling you how much material wraps around it. They answer different questions and use different units, so never mix them up.
How do I find the volume of a cylinder?
Use V = π × r² × h. Measure the radius of the circular base (half the diameter) and the height. Square the radius, multiply by π (about 3.14159), then multiply by the height. For example, a can with a 3 cm radius and 10 cm height holds π × 3² × 10 ≈ 282.7 cm³, or about 0.283 liters.
How do I find the volume of a sphere?
Use V = 4/3 × π × r³. You only need the radius. Cube the radius, multiply by π, then multiply by 4/3. A sphere with a 6 cm radius has a volume of 4/3 × π × 6³ ≈ 904.8 cm³. If you know the diameter instead, divide it by two to get the radius first.
Is volume the same as capacity?
They are closely related but not identical. Volume is the geometric space a solid occupies; capacity is how much a container can hold, usually given in liters or gallons. For a hollow container with thin walls they are nearly the same. This calculator reports the geometric volume and also converts it to liters and US gallons so you can read it as capacity.
How do I find the volume of an irregular shape?
Break the object into simple shapes whose volumes you can calculate (boxes, cylinders, cones), find each one separately, then add them up. For truly irregular solids, water displacement works: submerge the object in a measured container and the rise in water level equals its volume. This calculator handles the standard geometric shapes you can decompose an object into.
What is π and why does it appear in volume formulas?
π (pi) is the ratio of a circle's circumference to its diameter, approximately 3.14159. It appears in the formulas for any shape with a circular cross-section - spheres, cylinders and cones - because their volume depends on the area of a circle (π × r²). Shapes with flat polygonal faces, like cubes, boxes and pyramids, do not use π.
How do I convert cubic centimeters to liters or gallons?
Divide cubic centimeters by 1,000 to get liters (since 1 liter = 1,000 cm³), because 1 cm³ equals exactly 1 milliliter. To get US gallons, multiply liters by 0.264172 (1 US gallon ≈ 3.78541 liters). For cubic feet, 1 ft³ ≈ 28.317 liters ≈ 7.481 US gallons. The calculator does these conversions for you.
Why is a cone exactly one-third of a cylinder?
A cone and a cylinder with the same base radius and height are related by a factor of three: the cone's volume is exactly 1/3 of the cylinder's. This is a classic result from calculus (integrating the area of the circular cross-sections). The same one-third relationship holds between a pyramid and a prism that share the same base and height.
💡 Good to know
Volume scales with the cube of length
Double every dimension and the volume grows eightfold (2³), not double. This is why a slightly bigger pot holds a lot more, and why a small change in a sphere's radius changes its volume so much.
A cone is one-third of its cylinder
A cone and a cylinder with the same base and height differ by exactly a factor of three. The same one-third rule links a pyramid to a prism - a handy shortcut for quick estimates.
1 cm³ = 1 milliliter, exactly
That clean relationship makes metric conversions easy: 1,000 cm³ = 1 liter, and 1 cubic meter = 1,000 liters. The calculator uses it to show capacity in liters and gallons.
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