Volume of common 3D shapes — dimensions in any length unit.
V = (4/3)πr³ | V = a³ | V = πr²h | V = (1/3)πr²h | V = l × w × h | V = (1/2) × b × h_t × l
Each geometric solid has its own volume formula. The six most common solids and their formulas are listed below. All dimensions must be in the same unit before calculating; the result will be in the corresponding cubic unit.
V = πr²h = π × (5)² × 12 = π × 25 × 12 = π × 300 ≈ 3.14159265 × 300 ≈ 942.48 cm³
Result: Volume ≈ 942.48 cm³ (or approximately 0.942 liters)
A cylinder with a radius of 5 cm and a height of 12 cm can hold approximately 942.48 cm³ of material — equivalent to just under one liter. This is useful for sizing containers, pipes, tanks, and cylindrical packaging. Remember: if you change the units of your inputs (e.g., inches instead of centimeters), the output will automatically be in the corresponding cubic unit (in³).
Volume measures the three-dimensional space that an object occupies or can contain. It is one of the most practical concepts in geometry, used daily in engineering, cooking, construction, medicine, and science.
Cubic Units: Volume is always expressed in cubic units because it captures length × width × height simultaneously. Common units include cm³, m³, mm³, in³, ft³, and liters (1 L = 1,000 cm³).
Consistent Units: Before plugging numbers into any formula, convert all measurements to the same unit. Mixing centimeters and meters, for example, will produce a wildly incorrect answer.
Radius vs. Diameter: For spheres, cylinders, and cones, the formula requires the radius (half the diameter). A common mistake is entering the diameter instead of the radius, which would overestimate the volume by a factor of up to 8 for spheres.
π (Pi): Rounded to 3.14159 for most practical purposes; use the full precision constant (3.14159265358979…) for scientific work.
Volume and surface area are related but different. Volume tells you how much space is inside an object; surface area tells you how much material covers the outside. For example, doubling the radius of a sphere multiplies its volume by 8 (2³) but only multiplies its surface area by 4 (2²).
V = (4/3)π(7)³ = (4/3) × 3.14159 × 343 ≈ 1,436.76 cm³.
Multiply its length × width × height. For example, a box that is 10 cm × 5 cm × 3 cm has a volume of 150 cm³.
V = π × (1)² × 2 ≈ 6.283 m³, which equals approximately 6,283 liters.
Yes. A cone with the same base radius and height as a cylinder has exactly 1/3 its volume. This is a fundamental geometric relationship.
Use V = (1/2) × base × triangle_height × prism_length. For example, if b = 4 cm, h_t = 3 cm, and l = 10 cm, then V = 0.5 × 4 × 3 × 10 = 60 cm³.
You can enter dimensions in any unit — centimeters, meters, millimeters, inches, feet, or yards. The result will be in the corresponding cubic unit (e.g., cm³ if you enter centimeters). Some calculators also offer a conversion to liters or gallons.
This calculator covers common geometric solids. For truly irregular shapes, methods such as water displacement (Archimedes' principle) or numerical integration are used. If your shape can be broken into combinations of common solids, calculate each part separately and add the volumes.
Divide by 1,000. For example, 942.48 cm³ ÷ 1,000 = 0.94248 liters. Conversely, 1 liter = 1,000 cm³.
Volume refers to the total space an object occupies, while capacity typically refers to how much a container can hold. In practice they are numerically equal for hollow containers; capacity is often expressed in liters or gallons while volume uses cubic units.
Because volume scales with the cube of the radius (r³). Doubling r means the new volume is (2r)³ = 8r³ — eight times the original. This is why small changes in radius have a large effect on volume.
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