Volume Calculator
Volume formulas depend on shape. A box uses length x width x height. A cylinder uses pi x radius squared x height.
Choose the solid shape
Choose the solid shape and enter the required dimensions. A box needs length, width and height. A cylinder needs radius and height. A sphere needs radius.
Use the same unit for every length. If the radius is in centimeters and height is in meters, convert first.
Use this for geometry homework, containers, boxes, tanks and rough material estimates. For real containers, remember that wall thickness and usable fill level can change practical capacity.
Volume means space inside
Volume measures three dimensional space. The answer is written in cubic units, such as cubic inches, cubic feet, cubic meters or cubic centimeters.
A cubic unit is a cube that is 1 unit wide, 1 unit long and 1 unit tall.
Volume is different from area. Area covers a surface. Volume fills space inside a solid or container.
Shape volume formulas
A rectangular box uses volume = length x width x height. A cylinder uses volume = pi x radius squared x height.
A cone uses volume = pi x radius squared x height / 3. A sphere uses volume = 4 / 3 x pi x radius cubed.
For pyramids and cones, the division by 3 comes from comparing them with prisms or cylinders that have the same base area and height.
Cylinder volume example
A box that is 10 inches long, 6 inches wide and 4 inches tall has volume 10 x 6 x 4, or 240 cubic inches.
A cylinder with radius 3 cm and height 8 cm has volume pi x 3^2 x 8. That is about 226.19 cubic centimeters.
A cone with the same radius and height would be one third of that cylinder volume, or about 75.4 cubic centimeters.
Missing cubic units
The most common mistake is using diameter where the formula needs radius. If a cylinder is 10 inches across, the radius is 5 inches.
Another mistake is forgetting cubic units. If the inputs are centimeters, the volume is cubic centimeters.
Also make sure height is perpendicular to the base. Slanted height is not the same as vertical height for cones and pyramids.
For containers, do not assume geometric volume equals usable volume. Lids, walls, fill lines and shape details can reduce practical capacity.
Volume Calculator FAQ
How is volume different from area?
Area measures a flat surface. Volume measures space inside a three dimensional shape.
A floor has area. A box has volume.
Area uses square units, while volume uses cubic units.
Why is cone volume divided by 3?
A cone has one third the volume of a cylinder with the same base radius and height.
That is why the formula is pi x radius squared x height divided by 3.
The same one third idea appears with pyramids compared with prisms that share the same base area and height.
Do I use radius or diameter for cylinder volume?
Cylinder volume uses radius. If you know the diameter, divide it by 2 first.
For a diameter of 12 inches, the radius is 6 inches.
Using diameter as radius makes the circular base area four times too large, so the volume becomes four times too large.
What units should volume be in?
Use cubic units based on the input length unit. Inches give cubic inches. Feet give cubic feet. Meters give cubic meters.
If you need liters or gallons, convert from cubic units into volume capacity units after calculating.
For containers, check whether the question asks for geometric volume or usable capacity.
How can I check a volume answer?
First check the formula for the selected shape. Then check whether radius, diameter and height were entered correctly.
Finally, check the unit. A volume result should be cubic, not square.
For simple shapes, estimate with a box around the object. The calculated volume should usually be in a reasonable range.
If the exact shape is rounded, compare it with a nearby box or cylinder to catch obvious scale mistakes.