๐ฅซ Cylinder Volume Calculator
By Shihab Mia ยท Updated 2026-08-03
Enter a radius or diameter and a height to compute the volume and surface areas.
Cylinder volume equals pi times the radius squared times the height (V = pi r^2 h). This calculator finds cylinder volume from either a radius or a diameter, then adds the total surface area and lateral surface area as bonus results. Type in your numbers and every value updates instantly, with a copy button so you can paste the result straight into a report or homework answer.
What is the Cylinder Volume Calculator?
A cylinder is a solid with two identical, parallel circular ends connected by a curved side. Because the cross-section is a circle all the way up the shape, cylinder volume is simply the area of one circular base multiplied by the height between the two bases. The base area is pi r^2, so the full cylinder volume formula is V = pi r^2 * h, where r is the radius of the base and h is the perpendicular distance between the two circles. This is the same logic used to find the volume of any prism: area of the base, times the height.
Most real-world measurements give you a diameter rather than a radius, since diameter is what you get from measuring straight across a pipe, can, or tank with a tape measure or calipers. The relationship is simple: radius is half of diameter, or r = d / 2. This calculator accepts either value, so if you only have the diameter, select "Diameter" and the tool converts it to a radius internally before computing cylinder volume, so you never have to do that division by hand.
Beyond volume, this calculator also reports two surface area figures that are useful for material estimates. The lateral surface area, 2 pi r h, is the area of just the curved side, the part you would need to know if you were wrapping a label around a can or painting the outside of a pipe. The total surface area, 2 pi r (r + h), adds in the two flat circular ends (top and bottom), which matters if you are calculating how much sheet metal, plastic, or material is needed to build the whole enclosed cylinder rather than just its side.
Units matter for every one of these results. If your radius and height are both in centimeters, the resulting cylinder volume comes out in cubic centimeters, and both surface area values come out in square centimeters. Mixing units, such as a radius in inches and a height in feet, is one of the most common sources of error, so always convert both measurements to the same unit before calculating cylinder volume.
When to use it
- Finding the cylinder volume of a water tank, drum, or silo to plan storage capacity.
- Working out how much liquid a can, bottle, or pipe segment holds before it is filled.
- Checking homework or exam answers for the volume of a cylinder formula in a geometry class.
- Estimating material needed for a cylindrical container by comparing lateral and total surface area.
- Sizing a cylindrical planter, vase, or 3D-printed part where both radius and height are known.
- Converting a measured diameter (from calipers or a tape measure) straight into cylinder volume without doing the division by hand.
How to use the Cylinder Volume Calculator
- Choose whether you know the radius or the diameter of the circular base from the dropdown.
- Enter that value (radius or diameter) in the first field.
- Enter the height of the cylinder, the perpendicular distance between the two circular ends.
- Read the cylinder volume, total surface area, and lateral surface area, which update instantly, and use "Copy result" to grab the numbers.
Formula & method
Worked examples
Find the cylinder volume of a tank with radius 5 units and height 10 units.
- Identify r = 5 and h = 10.
- Apply the formula: V = pi * r^2 * h.
- Square the radius: r^2 = 5^2 = 25.
- Multiply: V = pi * 25 * 10 = pi * 250 = 785.398 cubic units.
- Total surface area (bonus): A = 2 * pi * 5 * (5 + 10) = 2 * pi * 5 * 15 = 471.239 square units.
Result: Cylinder volume = 785.398 cubic units; total surface area = 471.239 square units.
A can has a diameter of 8 cm and a height of 12 cm. Find its cylinder volume and surface areas.
- Convert diameter to radius: r = d / 2 = 8 / 2 = 4 cm.
- Square the radius: r^2 = 4^2 = 16.
- Apply the formula: V = pi * r^2 * h = pi * 16 * 12 = pi * 192 = 603.186 cubic centimeters.
- Lateral surface area: A = 2 * pi * r * h = 2 * pi * 4 * 12 = 301.593 square centimeters.
- Total surface area: A = 2 * pi * r * (r + h) = 2 * pi * 4 * 16 = 402.124 square centimeters.
Result: Cylinder volume = 603.186 cm^3; lateral area = 301.593 cm^2; total area = 402.124 cm^2.
Cylinder volume for common radius and height combinations
| Radius | Height | Cylinder volume |
|---|---|---|
| 1 | 1 | 3.142 |
| 2 | 5 | 62.832 |
| 3 | 6 | 169.646 |
| 5 | 10 | 785.398 |
| 10 | 20 | 6,283.185 |
How doubling radius versus height changes cylinder volume (base case: r = 5, h = 10, V = 785.398)
| Change made | New radius | New height | New volume | Multiplier |
|---|---|---|---|---|
| None (base case) | 5 | 10 | 785.398 | 1x |
| Double the height only | 5 | 20 | 1,570.796 | 2x |
| Double the radius only | 10 | 10 | 3,141.593 | 4x |
| Double both radius and height | 10 | 20 | 6,283.185 | 8x |
Common mistakes to avoid
- Using the diameter as if it were the radius. The cylinder volume formula needs the radius, not the diameter. If you measured across the whole circle (the diameter), divide by 2 before squaring, or simply select "Diameter" in this calculator so the conversion happens automatically.
- Forgetting to square the radius. Cylinder volume uses r^2, not r. Multiplying pi * r * h without squaring the radius understates the volume for anything larger than a unit radius, and the error grows fast since it is a squared term.
- Mixing units between radius and height. If the radius is in inches but the height is in feet, the result is meaningless until both are converted to the same unit. Always match units before computing cylinder volume, and check the unit label on your final answer.
- Confusing lateral surface area with total surface area. Lateral surface area (2*pi*r*h) covers only the curved side. Total surface area (2*pi*r*(r+h)) also includes the two circular ends. Use lateral area for labels wrapped around a can; use total area for the material to build the whole container.
Glossary
- Cylinder
- A three-dimensional solid with two parallel, congruent circular bases connected by a curved lateral surface.
- Radius (r)
- The distance from the center of a circular base to its edge. Half of the diameter.
- Diameter (d)
- The distance straight across a circular base through its center. Equal to twice the radius (d = 2r).
- Height (h)
- The perpendicular distance between the two circular bases of the cylinder.
- Lateral surface area
- The area of the curved side of a cylinder only, excluding the top and bottom circles. Formula: 2*pi*r*h.
- Total surface area
- The full outer area of a cylinder, including the curved side plus both circular ends. Formula: 2*pi*r*(r+h).
Frequently asked questions
What is the formula for cylinder volume?
Cylinder volume is V = pi * r^2 * h, where r is the radius of the circular base and h is the height. Multiply the base area (pi * r^2) by the height to get the volume.
How do I find cylinder volume from the diameter instead of the radius?
First divide the diameter by 2 to get the radius (r = d / 2), then use the standard formula V = pi * r^2 * h. This calculator does that conversion for you when you select "Diameter" as the known value.
What units does the cylinder volume come out in?
The volume is in cubic units matching whatever unit you entered for radius and height. Centimeters in gives cubic centimeters out; inches in gives cubic inches out. Always use the same unit for both radius and height.
How is cylinder volume different from cylinder surface area?
Volume measures how much space is inside the cylinder (cubic units), while surface area measures how much material covers its outside (square units). This calculator reports volume plus both lateral surface area (curved side only) and total surface area (curved side plus both ends).
How much does cylinder volume change if I double the radius?
Doubling the radius quadruples the cylinder volume, because radius is squared in the formula. Doubling the height only doubles the volume, since height is not squared. Doubling both dimensions multiplies volume by 8.
How do I convert cylinder volume to liters or gallons?
If the volume is in cubic centimeters, divide by 1,000 to get liters. If it is in cubic inches, divide by 231 to get US gallons. Compute the cylinder volume first in consistent units, then apply the conversion factor for the unit you need.