Normal Volume Calculator Online
Volume Calculator
Calculate the volume of various three-dimensional shapes with automatic real-time calculations
Select Shape and Enter Dimensions
Volume measures the three-dimensional space a shape occupies, expressed in cubic units such as cubic feet, cubic meters, or liters. This calculator covers the most common 3D shapes and gives you the formula alongside the result. Volume calculations come up in construction (ordering concrete, fill, or gravel), cooking, shipping package sizing, aquarium capacity, and science lab work. Knowing the right formula for each shape saves time and prevents costly over- or under-ordering.
Volume Formulas for Common 3D Shapes
Each three-dimensional shape has its own formula derived from its geometry. A box multiplies three dimensions. A cylinder applies the circle area formula to a height. Cones and pyramids are one-third the volume of their corresponding prisms, because they taper to a point.
| Shape | Formula | Variables |
|---|---|---|
| Rectangular Box | V = l × w × h | length, width, height |
| Cube | V = s³ | side length |
| Cylinder | V = π × r² × h | radius, height |
| Sphere | V = (4/3) × π × r³ | radius |
| Cone | V = (1/3) × π × r² × h | radius, height |
| Pyramid | V = (1/3) × base area × h | base area, height |
| Ellipsoid | V = (4/3) × π × a × b × c | three semi-axes |
Volume Unit Conversions
Volume units scale by the cube of the linear unit, which surprises many people. One foot equals 12 inches, but one cubic foot equals 1,728 cubic inches (12 cubed, not 12 times). Always cube the conversion factor when switching between volume units. This matters most when ordering bulk materials like concrete or gravel, where the difference between cubic feet and cubic yards is a factor of 27.
1 cubic foot = 1,728 cubic inches 1 cubic yard = 27 cubic feet 1 gallon = 231 cubic inches = 0.134 cubic feet 1 liter = 1,000 cubic centimeters = 0.0353 cubic feet 1 cubic meter = 35.31 cubic feet = 1,000 liters
Practical Volume Applications
Construction projects use cubic yards for concrete, gravel, and fill dirt. Aquariums and tanks are sized in gallons or liters. Shipping boxes are measured in cubic inches or cubic centimeters for dimensional weight pricing. Swimming pool volumes are usually in gallons. Knowing how to convert between these units prevents ordering too much or too little material for a project.
| Application | Typical Unit Used |
|---|---|
| Concrete / fill material | Cubic yards |
| Swimming pool capacity | Gallons (US) or liters |
| Aquarium size | Gallons or liters |
| Shipping box (freight) | Cubic inches or cm³ |
| Engine displacement | Cubic centimeters (cc) or liters |
| Liquid recipes (US) | Cups, pints, quarts, gallons |
Irregular Volumes
For shapes that do not match a standard formula, you have two options. First, break the shape into standard components, calculate each volume separately, and add them together. Second, use water displacement: submerge the object in a graduated container and measure how much the water level rises. The displaced volume equals the object volume. This is the Archimedes method, used for over 2,000 years to measure irregular objects accurately.
Frequently Asked Questions
How do I calculate the volume of a cylinder?⌄
Volume = π × r² × h. First calculate the base area using the circle formula (π × r²), then multiply by the cylinder's height. Use the radius, not the diameter. Example: a cylinder with a 3-inch radius and 10-inch height has a volume of π × 9 × 10 = 90π ≈ 282.7 cubic inches. For real-world applications like storage tanks, convert the cubic inches result to gallons by dividing by 231.
How many cubic feet are in a cubic yard?⌄
27 cubic feet. Since 1 yard equals 3 feet, a cubic yard equals 3 × 3 × 3 = 27 cubic feet. This matters practically when ordering concrete or topsoil: your measurements are usually in feet, but materials are sold by the cubic yard. Divide your cubic footage total by 27 to get the cubic yards to order. Add 10% for waste and settling to avoid running short.
How do I calculate how much concrete I need?⌄
Measure the slab area in feet (length × width), then multiply by the depth in feet (convert inches to feet by dividing by 12). This gives cubic feet. Divide by 27 to get cubic yards. Add 10% for waste and settling. Example: a 10×12 ft slab at 4-inch depth = 10 × 12 × (4/12) = 40 cubic feet = 1.48 cubic yards. Order 1.6 cubic yards. Most concrete trucks hold 8-10 cubic yards minimum, so small projects often use ready-mix bags instead.
What is the volume of a sphere?⌄
V = (4/3) × π × r³. Use the radius (half the diameter), not the diameter, and cube it. Example: a basketball with a 4.7-inch radius has a volume of (4/3) × π × 4.7³ = (4/3) × π × 103.8 ≈ 434 cubic inches. A sphere with twice the radius has eight times the volume (since radius is cubed), not twice -- this is a common mistake when scaling spherical containers.
How do I convert liters to gallons?⌄
Multiply liters by 0.264172 to get US gallons. Divide US gallons by 0.264172 (or multiply by 3.78541) to get liters. Quick reference: 1 liter ≈ 0.264 gallons, 4 liters ≈ 1.057 gallons (slightly more than 1 gallon), 10 liters ≈ 2.64 gallons. Note: UK gallons are different from US gallons. 1 UK gallon = 4.546 liters, compared to 1 US gallon = 3.785 liters.