Introduction
A cylinder is a 3D shape with two flat, circular ends and one curved side. Think of a soup can or a drinking glass — those are cylinders! The volume of a cylinder tells you how much space is inside it, or how much it can hold. To find the volume, you multiply the area of the circular base by the height of the cylinder. The formula is V = π × r² × h, where r is the radius (the distance from the center of the circle to its edge) and h is the height. This Cylinder Volume Calculator does the math for you — just enter the radius and height, and it will give you the answer right away.
How to Use Our Cylinder Volume Calculator
Enter the radius and height of your cylinder, and this calculator will give you the volume.
Radius: Type in the radius of your cylinder. The radius is the distance from the center of the circular base to its edge. You can enter this in any unit, such as inches, centimeters, or meters.
Height: Type in the height of your cylinder. The height is the straight distance from one flat base to the other. Use the same unit you used for the radius.
What Is Cylinder Volume?
The volume of a cylinder is the amount of space inside it. Think of a cylinder as a can of soup or a paper towel roll — it has a circular base and a certain height. To find how much space is inside, you use a simple formula that connects the size of the circle on top (or bottom) with how tall the cylinder is.
The Basic Formula
For a standard right cylinder (one that stands straight up), the volume formula is:
V = π × r² × h
Here, V is the volume, r is the radius of the circular base (the distance from the center to the edge), and h is the height. The symbol π (pi) is approximately 3.14159. If you know the diameter instead of the radius, just divide the diameter by 2 to get the radius.
Types of Cylinders
Not all cylinders look the same. There are three common types:
- Right Cylinder: The most common type. The sides go straight up at a 90-degree angle from the base. This is the shape of most cans and drinking glasses.
- Oblique Cylinder: This cylinder leans to one side, like a tilted can. Its volume formula is V = π × r² × s × sin(θ), where s is the length of the slanted side and θ is the angle between the side and the base. The part s × sin(θ) gives you the effective vertical height.
- Hollow Cylinder: This is a cylinder with a hole through the middle, like a pipe or a toilet paper roll. Its volume formula is V = π × h × (R² − r²), where R is the outer radius and r is the inner radius. You are basically subtracting the empty space from the full cylinder.
Related Measurements
When you calculate a cylinder's volume, there are other useful measurements you can find at the same time:
- Base Area: The area of one circular end, calculated as π × r². If you need to calculate the area of a circle on its own, try our Circle Area Calculator.
- Lateral Surface Area: The area of the curved side that wraps around the cylinder, calculated as 2 × π × r × h for a right cylinder.
- Total Surface Area: The lateral area plus the area of both circular ends: 2 × π × r × h + 2 × π × r². For projects like painting a cylindrical column, our Paint Calculator can help estimate how much paint you'll need for the surface area.
Solving for Missing Dimensions
The volume formula works in reverse too. If you already know the volume, you can solve for a missing measurement. For example, if you know the volume and the height, you can find the radius by rearranging the formula to r = √(V / (π × h)). If you know the volume and the radius, you can find the height with h = V / (π × r²). This is helpful in real-world problems where you need to design a container to hold a specific amount.
Practical Uses
Cylinder volume comes up often in everyday life and many jobs. Engineers use it to figure out how much water a pipe can carry. Builders use it to calculate how much concrete goes into a round column. Scientists use it to measure liquid in test tubes and beakers. Even cooking involves cylinder volume — when you fill a round baking pan, you are working with a cylinder. For related 3D volume calculations, you may also find our Sphere Volume Calculator useful. If you're working with triangular shapes instead, check out our Triangle Area Calculator or Right Triangle Calculator. For construction projects involving area measurements, our Square Footage Calculator is another handy tool. Understanding this formula gives you a useful tool for solving many real-world problems.