Volume Calculator: Find the Volume of 3D Shapes
Volume measures the three-dimensional space occupied by an object. Whether you need the volume of a box for shipping, a cylinder for a water tank, or a sphere for a ball, our Volume Calculator handles all common 3D shapes. Enter the required dimensions and get the volume in your choice of cubic units, with visual representations and formulas displayed. Use our Volume Calculator to estimate your costs.
Volume Formulas for Common Shapes
Each 3D shape has a specific formula. A rectangular prism (box) is length × width × height. A cylinder is π × r² × h. A sphere is 4/3 × π × r³. A cone is 1/3 × π × r² × h. A pyramid is 1/3 × base area × height. The calculator supports all these and more: cube, rectangular prism, sphere, cylinder, cone, pyramid, torus, ellipsoid, and triangular prism.
For irregularly shaped objects, you can use the water displacement method in a graduated cylinder, but for regular shapes, these formulas provide exact volumes.
Using the Volume Calculator
Select the shape from the dropdown menu. Enter the required dimensions — for a box, enter length, width, and height; for a cylinder, enter radius and height; for a sphere, enter radius. Choose your unit of measurement (inches, feet, centimeters, meters, etc.). The calculator shows the volume in cubic units and provides a cross-sectional view of the shape.
You can convert between different cubic units (cubic inches to cubic feet, cubic meters to liters, etc.) and calculate the liquid capacity of containers in gallons or liters.
Practical Applications
Shipping and Logistics
Calculate the volume of packages to determine shipping class and costs. Dimensional weight pricing means larger-volume packages may be charged based on volume rather than actual weight.
Aquariums and Pools
A rectangular aquarium measuring 48 × 18 × 20 inches has a volume of 48 × 18 × 20 = 17,280 cubic inches. Convert to gallons: 17,280 / 231 = 74.8 gallons. This tells you how much water and what size filter and heater you need.
Construction
A concrete slab measuring 10 × 12 × 0.5 feet (6 inches thick) needs 10 × 12 × 0.5 = 60 cubic feet. Convert to cubic yards: 60 / 27 = 2.22 cubic yards. Concrete is typically ordered by the cubic yard.
Unit Conversion Reference
- Cubic inches to cubic feet: Divide by 1,728
- Cubic feet to cubic yards: Divide by 27
- Cubic inches to gallons: Divide by 231
- Cubic feet to gallons: Multiply by 7.481
- Liters to gallons: Divide by 3.785
- Cubic meters to liters: Multiply by 1,000
- Cubic centimeters to milliliters: 1 cm³ = 1 mL
Real-World Example
You need a cylindrical water tank with a 3-foot radius that holds at least 500 gallons of water:
- Target volume in cubic feet: 500 gallons / 7.481 = 66.83 cubic feet
- Volume formula: V = π × r² × h, so h = V / (π × r²)
- Required height: h = 66.83 / (π × 9) = 66.83 / 28.27 = 2.36 feet
- Check: π × 9 × 2.36 = 66.8 cubic feet = 499.6 gallons
A spherical ball with radius 6 inches has volume: 4/3 × π × 6³ = 4/3 × π × 216 = 904.78 cubic inches = 0.524 cubic feet.
Worked Example: Comparing Shapes of the Same Dimensions
Enter a 3-foot radius and 5-foot height, then switch between the cylinder and cone options to see how the same dimensions produce very different volumes. The cylinder computes as π × r² × h = π × 9 × 5 = 141.37 cubic feet. The cone applies its one-third factor, so the same inputs return 47.12 cubic feet — exactly one-third of the cylinder, no matter what radius and height you enter. That relationship is baked into the formulas themselves: a cone or pyramid is always one-third of the corresponding prism or cylinder with identical base and height.
The unit conversion in the calculator turns those cubic feet into useful planning numbers. Convert 141.37 cubic feet to gallons using the 7.481 factor and you get about 1,058 gallons — roughly the capacity of a standard residential water tank. Convert the same volume to liters and you get about 4,003 liters, a number that matches international product specifications. For a sphere with a 6-inch radius, the calculator evaluates 4/3 × π × 6³ = 904.78 cubic inches, which converts to 0.52 cubic feet or 14.8 liters — a helpful figure when a ball or storage tank's capacity is listed in liters abroad.
These worked examples reveal a practical habit: always enter dimensions in the same unit, then let the calculator handle the conversion. Mixing feet for radius and inches for height produces a result that is off by a factor of 12, and no formula display will catch it. Select your measurement unit first, enter every dimension consistently, and use the output unit toggle to get the volume in the form your project actually needs.
Start Calculating
Use our Volume Calculator below to find the volume of any 3D shape for construction, shipping, or science projects. Also check our Area Calculator for 2D measurements and our Concrete Calculator for construction material estimates.
Related Calculators
Use our Volume Calculator Guide together with related tools such as Area Calculator, Combination Calculator, Derivative Calculator to plan more accurately. Each calculator runs instantly in your browser with step-by-step guidance.
Written by the CalcMaster Pro Editorial Team — financial, health, and DIY tools reviewed for accuracy. All calculators run on standard, widely accepted formulas. Always confirm final numbers with a qualified professional for decisions that require official figures.