Volume Calculator
Choose a shape, enter your dimensions, and see the formula, the substituted numbers, and step-by-step math.
Enter all dimensions using the same unit. The result will be shown in cubic units.
Your Volume
Calculate the volume of cubes, rectangular prisms, cylinders, cones, spheres, pyramids, capsules, frustums, ellipsoids, tubes, and more. See the formula, your numbers substituted into it, unit conversions, and step-by-step explanations.
Choose a shape, enter your dimensions, and see the formula, the substituted numbers, and step-by-step math.
Enter all dimensions using the same unit. The result will be shown in cubic units.
Volume measures how much three-dimensional space is inside an object or shape. Think about a box. Length tells you how far the box extends in one direction. Width gives you another direction. Height gives you the third. Volume combines all three dimensions to describe the amount of space inside the box. That is why volume is measured in cubic units.
If a box measures 5 centimeters by 4 centimeters by 3 centimeters, its volume is 5 × 4 × 3 = 60 cm³. The little ³ means cubed. It tells you the answer represents three-dimensional space rather than a simple length or a flat area. You can imagine 60 tiny cubes, each measuring 1 cm × 1 cm × 1 cm, filling the box. That is what 60 cubic centimeters means.
Area measures two-dimensional surface. Volume measures three-dimensional space. A rectangle with length 5 and width 4 has area 5 × 4 = 20 square units. If that rectangle becomes the base of a box with height 3, the volume is 20 × 3 = 60 cubic units.
Think of it this way: area asks, "How much flat space is covered?" Volume asks, "How much space is inside?" This distinction is important because square units and cubic units are not interchangeable. If your problem is specifically asking for the amount of flat surface inside a two-dimensional shape, use the Area Calculator.
For a rectangular prism, Volume = Length × Width × Height. Formula: V = lwh. Suppose Length = 10 cm, Width = 4 cm, Height = 3 cm. Substitute: V = 10 × 4 × 3. Multiply: 10 × 4 = 40. Then: 40 × 3 = 120 cm³.
Another way to understand this is to first find the area of the base. 10 × 4 = 40 cm². Then imagine stacking that base through 3 centimeters of height. 40 × 3 = 120 cm³. That base area × height idea appears again and again in volume formulas.
A prism has a consistent cross-section extending through its length or height. The basic volume idea is Volume = Base Area × Height. Written: V = Bh. B represents the area of the base. h represents the distance the base extends through the prism. This explains why Rectangular Prism: V = lwh. The base area is lw.
A triangular prism works the same way. The triangle's area is 1/2 bh. Then multiply that area by the prism's length. Triangular Prism: V = 1/2 bhL. Once you understand base area × height, you do not have to memorize every prism formula as an unrelated rule.
Base Area × Height
Triangle Base Area × Prism Length
A cylinder follows the same Base Area × Height idea. Its base is a circle. Area of a circle: πr². Stack that circular area through height h. Therefore: V = πr²h.
Example: Radius = 5 cm, Height = 13 cm. Formula: V = π(5²)(13). Square the radius: 5² = 25. Multiply: 25 × 13 = 325. So V = 325π. Decimal: V ≈ 1,021.02 cm³.
Notice that the formula uses radius, not diameter. If you are given diameter, divide by 2 first. Diameter = 10, Radius = 5.
Radius measures from the center of a circle or sphere to its outside edge. Diameter measures all the way across through the center. Therefore: Diameter = 2 × Radius, and Radius = Diameter ÷ 2.
If a sphere has diameter 12, its radius is 6. Using 12 as the radius would make the answer dramatically too large. This is one of the most common mistakes in circle, cylinder, cone, and sphere problems.
A cone uses V = 1/3 πr²h. Compare that with a cylinder: Cylinder: V = πr²h. Cone: V = 1/3 πr²h. If a cone and cylinder have exactly the same radius and height, the cone's volume is one-third of the cylinder's volume.
Example: Radius = 3, Height = 8. Cylinder: π × 3² × 8 = 72π. Cone: 1/3 × 72π = 24π. That relationship makes the formula easier to remember.
V = πr²h
V = 1/3 πr²h
A pyramid follows a similar rule. General Pyramid: V = 1/3 Bh. B is base area, h is vertical height. A square pyramid with base side s has base area s². Therefore: V = 1/3 s²h. A rectangular pyramid uses V = 1/3 lwh.
The important word is vertical height. Do not automatically use the slanted edge of a pyramid as its height. The volume formula uses the perpendicular distance from the base to the top point.
Sphere volume: V = 4/3 πr³. Suppose diameter = 9 mm. First find radius: 9 ÷ 2 = 4.5 mm. Then: V = 4/3 π(4.5³). 4.5³ = 91.125. Then: 4/3 × 91.125 = 121.5. So V = 121.5π ≈ 381.70 mm³.
Notice the radius is cubed. That means sphere volume changes very quickly as radius increases. If radius doubles, r becomes 2r. Then (2r)³ = 8r³. So doubling the radius makes the sphere's volume eight times as large.
A hemisphere is half of a sphere. Sphere: V = 4/3 πr³. Half: V = 2/3 πr³. This is useful for domes, rounded containers, and geometric models containing half-spherical sections.
Real objects are not always simple cubes or cylinders. A capsule combines a cylinder with two hemispherical ends. Two hemispheres together form one sphere. So Capsule Volume = Cylinder Volume + Sphere Volume.
A tube or hollow cylinder can be calculated by Outer Cylinder minus Inner Empty Cylinder. A conical frustum is a cone with its top cut off. Its formula uses both large radius and small radius. An ellipsoid looks like a stretched or compressed sphere.
The important lesson is that complicated-looking volume problems often become easier when you identify the basic shapes inside them.
Sometimes the volume is already known. Instead of calculating volume, you need to work backward. Example: Rectangular Prism Volume = 2,016 cm³, Length = 8 cm, Width = 14 cm, Height = unknown.
Start: V = lwh. Substitute: 2,016 = 8 × 14 × h. Multiply: 8 × 14 = 112. So: 2,016 = 112h. Divide: 2,016 ÷ 112 = 18. Height = 18 cm.
Notice: volume was measured in cm³, but the missing height is cm. A linear dimension should not have cubic units. The calculator's Missing Dimension mode works backward like this automatically.
Suppose a cube measures 1 meter on every side. Volume: 1 m × 1 m × 1 m = 1 m³. Now convert each meter into centimeters. 1 m = 100 cm. The same cube is 100 cm × 100 cm × 100 cm. Volume: 100 × 100 × 100 = 1,000,000 cm³.
This means 1 m³ = 1,000,000 cm³. You cannot convert cubic units by applying a linear conversion only once. The conversion factor must be cubed. This is why mixing units without converting them first can create huge errors.
Volume describes the amount of three-dimensional space. Capacity often describes how much a container can hold. Metric volume has especially convenient relationships. 1 cm³ = 1 milliliter. 1,000 cm³ = 1 liter. 1 m³ = 1,000 liters.
That is why a Volume Calculator can be useful for containers, tanks, packing, construction, storage, and liquids. However, always check whether the dimensions describe the inside or the outside of a container. Wall thickness can make a difference when you are trying to calculate actual usable capacity.
If the main task is converting an already-known measurement between units rather than finding geometric volume, use the Unit Converter.
Some objects are made from more than one simple solid. Suppose a solid is made from a rectangular prism plus a square pyramid. Find the volume of the prism. Find the volume of the pyramid. Then add them.
If an object has a hollow section, calculate the full outer volume and subtract the empty section. The important rule is: add material, subtract empty space. This can turn a complicated object into several easy calculations.
Using area instead of volume. Area uses square units. Volume uses cubic units.
Forgetting to cube the radius for a sphere. Sphere formula uses r³, not r².
Using diameter as radius. Always check whether the measurement goes center to edge or edge to edge.
Forgetting the one-third. Cones and pyramids require 1/3.
Using slant height. Cone and pyramid volume formulas use perpendicular vertical height.
Mixing units. Do not multiply centimeters, meters, and inches without converting first.
Forgetting cubic units. If dimensions are in feet, volume is ft³.
Rounding too early. Keep enough precision during intermediate calculations and round at the end.
A very reliable process is:
Step 1: Identify the 3D shape. Is it a prism, cylinder, cone, sphere, pyramid, or another solid?
Step 2: Write the correct formula. Do not start multiplying numbers until you know which measurements the formula needs.
Step 3: Substitute the values. Put the given dimensions into the formula.
Step 4: Calculate. Follow the order of operations.
Step 5: Include cubic units. Your final volume needs mm³, cm³, m³, in³, ft³, or another appropriate cubic unit.
Third Space Learning also teaches volume by first identifying the formula, substituting the known values, calculating the result, and then including the correct units. Their volume formula guide and worked examples provide another useful educational explanation of this process.
Area measures two-dimensional space. Volume measures three-dimensional space. If you need the space inside a box, cylinder, sphere, cone, or other solid, use this Volume Calculator. If you need the amount of flat surface inside a rectangle, circle, triangle, or other 2D shape, use the Area Calculator.
If you are working specifically with triangles before using them as the base of a prism or pyramid, the Triangle Calculator can help calculate missing triangle measurements. For floors, rooms, walls, and other flat measurements where the primary question is square footage rather than cubic volume, use the Square Footage Calculator. These tools answer related but different geometry questions.
Do not leave knowing only "my answer is 523.6." Leave knowing: what volume measures; why volume uses cubic units; the difference between area and volume; that prism volume is based on base area times height; why cylinder volume uses πr²h; that cones and pyramids use one-third of the matching prism or cylinder relationship; that the sphere formula uses radius cubed; the difference between radius and diameter; the difference between vertical height and slant height; how to work backward from a known volume to find a missing dimension; why cubic-unit conversions are different from ordinary length conversions; how volume relates to capacity; how to break compound solids into simpler shapes; when to add volumes and when to subtract empty space; and which dimensions belong in the formula. Most importantly: you can see how the calculator arrived at your volume.
| Shape | Formula |
|---|---|
| Cube | V = a³ |
| Rectangular Prism | V = lwh |
| General Prism | V = Bh |
| Triangular Prism | V = 1/2 bhL |
| Cylinder | V = πr²h |
| Cone | V = 1/3πr²h |
| Sphere | V = 4/3πr³ |
| Hemisphere | V = 2/3πr³ |
| Square Pyramid | V = 1/3s²h |
| General Pyramid | V = 1/3Bh |
| Capsule | V = πr²L + 4/3πr³ |
| Spherical Cap | V = πh²(3R-h)/3 |
| Conical Frustum | V = 1/3πh(R²+Rr+r²) |
| Ellipsoid | V = πLWH/6 |
| Tube | V = πh(R²-r²) |
I need the three-dimensional space inside a solid, or I need to find a missing 3D dimension.
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Open Square Footage Calculator →I already know the measurement and need to convert it to another unit.
Open Unit Converter →What is volume?
Volume measures how much three-dimensional space a solid occupies or contains.
What units are used for volume?
Volume is usually measured in cubic units such as cm³, m³, in³, or ft³. Capacity may also be expressed in milliliters, liters, or gallons.
Why is volume measured in cubic units?
Because volume combines three dimensions: length, width, and height.
What is the difference between area and volume?
Area measures two-dimensional space. Volume measures three-dimensional space.
How do I calculate the volume of a cube?
Cube the side length: V = a³.
How do I calculate the volume of a rectangular prism?
Multiply length × width × height.
How do I calculate the volume of a cylinder?
Use V = πr²h.
How do I calculate the volume of a cone?
Use V = 1/3πr²h.
How do I calculate the volume of a sphere?
Use V = 4/3πr³.
How do I calculate the volume of a pyramid?
Multiply the base area by the perpendicular height and divide by 3.
Is diameter the same as radius?
No. Diameter is twice the radius.
How do I find radius from diameter?
Divide diameter by 2.
Can I enter diameter instead of radius?
Yes. The calculator converts diameter to radius automatically when that option is selected.
What does B mean in V = Bh?
B means the area of the base.
Why is a cone one-third of a cylinder?
For the same base radius and perpendicular height, a cone has one-third the volume of the corresponding cylinder.
Why is a pyramid one-third of a prism?
For the same base and perpendicular height, the pyramid has one-third the volume of the corresponding prism.
What height do I use for a pyramid?
Use the perpendicular vertical height, not the slant height.
Can I solve for a missing dimension?
Yes. Choose Missing Dimension and enter the known volume and other required measurements.
How do I find a missing rectangular-prism height?
Divide volume by length × width.
Can I calculate volume using negative dimensions?
No. Physical dimensions for these standard solids must be positive.
Can volume be zero?
A standard three-dimensional solid needs positive dimensions. A zero dimension would describe a degenerate shape rather than an ordinary 3D solid.
What is 1 cubic centimeter equal to?
1 cm³ equals 1 milliliter.
How many cubic centimeters are in a liter?
1,000 cm³.
How many liters are in one cubic meter?
1,000 liters.
Is 1 cubic meter equal to 100 cubic centimeters?
No. 1 m³ equals 1,000,000 cm³ because the conversion factor is cubed.
How do I calculate the volume of a hollow tube?
Subtract the inner-cylinder volume from the outer-cylinder volume.
How do I calculate a compound shape?
Break it into simpler solids, calculate each volume, then add material or subtract empty sections as appropriate.
Can this calculator convert volume units?
Yes. The result includes useful volume and capacity conversions.
Should I round π before calculating?
No. Keep π at full calculator precision and round the final answer.
What is the difference between volume and capacity?
Volume describes three-dimensional space. Capacity describes how much a container can hold.
Every dimension is validated before it is used: required fields must be positive, finite numbers, a Tube's Outer Radius must be greater than its Inner Radius, a Spherical Cap's height must be greater than 0 and no more than twice the sphere radius, and a Conical Frustum's large radius must be greater than or equal to its small radius. Diameter entries are converted to radius (radius = diameter ÷ 2) before any formula runs. Missing Dimension mode uses the same formulas solved algebraically for the requested variable; it is offered only for the shapes and variables listed above, where the inverse is a clean, closed-form equation. Shapes such as the Spherical Cap, whose inverse requires solving a cubic equation, are intentionally left out of Missing Dimension mode rather than approximated. Internal calculations keep full floating-point precision and use JavaScript's built-in value of π; only the displayed result is rounded, by default to two decimal places, with an option to show more decimals. Cubic and capacity unit conversions use standard SI and US customary definitions (1 inch = 2.54 cm, 1 foot = 12 inches, 1 yard = 3 feet, 1 US gallon = 3.785411784 liters), cubed where appropriate for volume.