Cylinder Volume Calculator
Calculate the volume, height, or radius of a solid or hollow cylinder. Enter its dimensions or known volume, choose a length unit, and see surface areas and volume conversions.
Find Cylinder Volume, Dimensions, and Surface Area
Cylinder Volume Formula
Where:
- \(V\) — cylinder volume, in cubic units
- \(r\) — radius of a solid cylinder, or inner radius of a hollow cylinder
- \(R\) — outer radius of a hollow cylinder
- \(h\) — cylinder height
- \(A_{\mathrm{l}}\) — lateral surface area, in square units
- \(A_{\mathrm{t}}\) — total surface area, in square units
Volume is the area of the circular or ring-shaped cross-section multiplied by height. For a hollow cylinder, the result is the volume of material between its inner and outer surfaces—not the volume of the empty space inside.
Cylinder Volume – Calculation Example
Example: using the default settings, find the volume of a solid cylinder with a radius of 5 cm and a height of 12 cm.
\[V=\pi r^{2}h=\pi(5\ \mathrm{cm})^{2}(12\ \mathrm{cm})=300\pi\ \mathrm{cm}^{3}\approx942.477796\ \mathrm{cm}^{3}\]
The curved surface area is \(2\pi(5)(12)=120\pi\approx376.991118\ \mathrm{cm}^{2}\). Including both circular ends gives a total surface area of \(170\pi\approx534.070751\ \mathrm{cm}^{2}\).
Result: the volume is approximately 942.478 cm³, or 0.942478 L.
How to use the calculator
- Under Calculate, choose Volume, Height from volume, or Radius from volume and height. The calculator shows the fields needed for that choice.
- Choose Cylinder type: Solid cylinder for a full circular cross-section, or Hollow cylinder (pipe or tube) for a ring-shaped cross-section.
- For a solid cylinder when calculating volume or height, use Solid cylinder measurement to choose Radius or Diameter, then enter Radius (r) or Diameter (d). For a hollow cylinder, enter Outer diameter (D) and Inner diameter (d) when those fields appear. The outer diameter must exceed the inner diameter.
- Enter Height (h) when calculating volume or radius. Enter Known volume (V) when calculating height or radius. To find a tube’s outer radius, also enter its Inner diameter (d).
- Choose Length unit. All entered lengths use that unit, while Known volume (V) uses the corresponding cubic unit—for example, cm and cm³. Read the calculated dimension, volume, surface areas, and conversions in Cylinder Results.
What cylinder volume tells you
Cylinder volume measures three-dimensional space. For a solid cylinder, imagine identical circular cross-sections stacked along its height: each has area \(\pi r^{2}\), so multiplying by height gives \(\pi r^{2}h\). Diameter spans the full width of the circle and is twice the radius. If you measured a diameter, the calculator halves it before using the radius in the formula.
A hollow cylinder has material around an empty center. Its cross-section is a ring, so subtract the inner circle’s area from the outer circle’s area before multiplying by height. This distinction matters when estimating the amount of material in a pipe or tube. If you instead need the space inside the tube, calculate \(\pi r^{2}h\) using its inner radius and the relevant interior length; the displayed hollow-cylinder volume does not represent that capacity.
You can also work backward from a known volume. Select Height from volume to find the height needed for a specified cross-section, or Radius from volume and height to find a solid cylinder’s radius or a tube’s outer radius. The result also includes volume in liters, US gallons, cubic feet, and cubic meters, regardless of the length unit selected. Its primary volume result remains in the cubic form of your chosen unit.
Surface area and measurement tips
Lateral surface area is the area along the curved side. For a solid cylinder, it includes the outer curved surface only. For a hollow cylinder, it includes both the outer and inner curved surfaces. Total surface area adds the two circular ends of a solid cylinder or the two ring-shaped end faces of a tube. These are geometric areas; whether a physical object has exposed, covered, or joined faces may change the area you actually need. For a calculation focused on surface measurements, see the Cylinder Surface Area Calculator.
Use positive measurements and keep every length in the same unit. For example, convert millimeters to centimeters before entering dimensions alongside a height in centimeters. Measurements should describe a straight cylinder with constant circular cross-sections; a tapered container is better modeled with the Cone Volume and Surface Area Calculator. For a spherical shape, use the Sphere Volume and Surface Area Calculator instead.
Frequently Asked Questions
How do I calculate cylinder volume by hand if I know the diameter?
Square the diameter, multiply by the height and by \(\pi\), then divide by 4: \(V=\pi d^{2}h/4\). For a cylinder 8 cm across and 10 cm tall, \(V=\pi(8)^{2}(10)/4=160\pi\approx502.65\) cm³. Use the same length unit for both measurements; the answer will be in cubic units.
How do I calculate the volume of material in a pipe from its wall thickness?
Subtract twice the wall thickness from the outer diameter to get the inner diameter. Then use both diameters to calculate the ring-shaped cross-section. For example, a pipe with a 10 cm outer diameter and 1 cm walls has an 8 cm inner diameter. Wall thickness must be less than half the outer diameter; otherwise, there is no open center.
How do I convert cylinder volume to liters or US gallons?
First calculate the volume in cubic units, then apply the appropriate conversion: 1,000 cm³ equals 1 L, and 1 US gallon equals 3.785411784 L. If your measurements are in inches, 1 in³ equals 0.016387064 L. Convert the finished volume rather than treating a centimeter-to-meter conversion as though it also converts cubic centimeters to cubic meters.
What happens to cylinder volume if I double the radius, diameter, or height?
Doubling the radius or diameter while keeping height fixed makes the volume four times as large. Doubling only the height makes it twice as large. If you double every length, the volume becomes eight times as large. This is why a small error in measuring a cylinder’s width can affect the result more than the same percentage error in its height.
Is the height of a tilted or horizontal cylinder measured vertically?
No. For a straight cylinder, measure height along its central axis, from one circular end to the other, regardless of how the object is positioned. A horizontal tank’s height in the volume formula is therefore its end-to-end length, not its distance above the ground. If you need the volume at a particular fill depth, you need a partially filled cylinder calculation instead.
Does cylinder surface area include an open top or the inside of a container?
The appropriate area depends on which surfaces you need to cover. For an open-top solid-walled container, subtract one circular end from the total surface area if you are counting its outside only. If you are painting the inside too, add the interior surfaces separately. The calculator’s geometric total includes both ends, so it may not equal the area requiring paint or other material.
Is there a normal or good volume for a cylinder?
No single volume is normal: it depends on the cylinder’s intended capacity and dimensions. When comparing designs, specify the requirement first, such as liters of storage or cubic centimeters of material. Two cylinders can have the same volume but very different diameters, heights, and surface areas, which may matter for available space, packaging, or material use.