🧊 Volume Calculator
Volumes for 8 solid shapes, with each formula shown.
Volume
How to Use the Volume Calculator
Pick the shape, enter its dimensions in your chosen units, and calculate. The exact formula with your numbers substituted is shown under the result.
Select the 3D shape closest to your object.
Enter the dimensions. Radius vs diameter is labeled where it matters.
Read the volume in cubic units, plus the formula working.
Volume Formulas
Sphere: (4/3)πr³. Cube: s³. Box: l×w×h. Cylinder: πr²h. Cone: (1/3)πr²h. Square pyramid: (1/3)b²h. Triangular prism: (1/2)bhl. Capsule: (4/3)πr³ + πr²h (sphere plus cylinder). Notice the pattern: prisms and cylinders are base area × height; pyramids and cones are one-third of that.
Practical Uses
Concrete for a slab: box volume in feet ÷ 27 = cubic yards to order. Aquarium capacity: gallons = cubic inches ÷ 231. Soil for a planter: box volume in cubic feet directly. Hot tub chemicals dose by gallons: cylinder volume × 7.48. Moving boxes: sum box volumes and compare against truck cubic footage. In every case, measure twice and keep units consistent: mixing inches and feet is the classic error.
Unit Conversions
Metric: 1 m³ = 1,000 liters; 1 cm³ = 1 milliliter. Imperial: 1 ft³ = 7.48052 gallons = 28.3168 liters; 1 in³ = 0.004329 gallons. 1 gallon = 231 in³ exactly (US). When a recipe or manual gives mixed units, convert everything to one unit before calculating: 2 feet 6 inches is 30 inches, not 2.6 feet.
Frequently Asked Questions
What is the volume of a sphere?
V = (4/3)πr³. For radius 3: (4/3) × π × 27 = 36π ≈ 113.1 cubic units. The sphere holds the most volume for the least surface area of any shape, which is why bubbles and planets are round.
How do you calculate cylinder volume?
V = πr²h: base area times height. A cylinder with radius 2 and height 5 holds π × 4 × 5 = 20π ≈ 62.8 cubic units. This is the formula behind every can, tank, and pipe capacity calculation.
What is the volume of a cone vs a cylinder?
A cone holds exactly one-third of the cylinder with the same base and height: V = (1/3)πr²h. This 3:1 ratio is easy to verify by filling: three cones of water fill the cylinder. The same third applies to pyramids vs prisms.
How do I convert between volume units?
1 cubic meter = 1,000 liters = 35.31 cubic feet = 264.17 gallons. 1 cubic foot = 7.48 gallons = 28.32 liters. This calculator lets you pick the unit family; multiply the cubic result by the conversion factor for the exact unit you need.
What is the difference between volume and surface area?
Volume measures 3D space inside (cubic units), surface area measures the 2D skin outside (square units). They scale differently: doubling a shape's size multiplies volume by 8 but surface area by 4. That is why small animals lose heat faster and why crushed ice melts quicker than cubes.