Cylinder Volume Calculator
Calculate the volume of a cylinder quickly and accurately. Enter the radius, diameter, or height and get instant results in multiple units. Perfect for students, engineers, and DIY projects.
What Is a Cylinder?
A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface. The bases are congruent circles, and the axis of the cylinder is the line segment joining the centers of the two bases. A cylinder is one of the most common shapes in everyday life — from cans and pipes to columns and storage tanks.
The volume of a cylinder is the amount of space it occupies. It is calculated by multiplying the area of the base (a circle) by the height of the cylinder.
How Does the Cylinder Volume Calculator Work?
The calculator uses the standard geometric formula for the volume of a cylinder:
V = π × r² × h
Where:
V = Volume of the cylinder
π (Pi) ≈ 3.14159
r = Radius of the circular base
h = Height of the cylinder
Alternative formula using diameter: V = π × (d/2)² × h
Simply enter the radius (or diameter) and height of the cylinder, and the calculator will instantly compute the volume, base area, and show you the formula used.
Why Use This Cylinder Volume Calculator?
- Fast & Accurate: Get precise results with zero math errors.
- Multiple Units: Supports metric and imperial units, plus liters and gallons.
- Formula Display: See the formula used and the step-by-step calculation.
- Free & Private: No registration, no data storage.
- Mobile-Friendly: Works on any device.
Real-World Applications of Cylinder Volume
- Engineering & Construction: Calculating the volume of concrete needed for cylindrical columns or pipes.
- Manufacturing: Determining the capacity of tanks, drums, and containers.
- Food & Beverage: Measuring the volume of cans, bottles, and other cylindrical packaging.
- Science & Chemistry: Calculating the volume of liquids in graduated cylinders and beakers.
- Everyday Life: Estimating the amount of water in a cylindrical pool or the storage capacity of a silo.
❓ Cylinder Volume FAQ
What is the formula for the volume of a cylinder?
The formula is V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.[reference:0]
How do I calculate the volume of a cylinder using diameter?
If you know the diameter (d), use the formula V = π × (d/2)² × h, or V = (πd²h)/4.[reference:1]
What is the difference between a cylinder and a prism?
A prism has polygonal bases (e.g., triangles, rectangles), while a cylinder has circular bases. Both have the same volume formula: base area × height.
What is a right circular cylinder?
A right circular cylinder has circular bases that are perpendicular to the axis (the line connecting the centers of the bases). The sides are straight and perpendicular to the bases.
What is an oblique cylinder?
An oblique cylinder has bases that are not aligned directly above each other. The sides lean at an angle, and the axis is not perpendicular to the bases.
What is a hollow cylinder?
A hollow cylinder is a cylinder with a cylindrical hole in the middle. The volume of a hollow cylinder is V = πh(R² − r²), where R is the outer radius and r is the inner radius.
How do I find the height of a cylinder if I know the volume and radius?
Rearrange the formula: h = V / (πr²). Simply divide the volume by the area of the base.
How do I find the radius of a cylinder if I know the volume and height?
Rearrange the formula: r = √(V / (πh)). Take the square root of the volume divided by π times the height.
What is the surface area of a cylinder?
The total surface area of a cylinder is A = 2πr² + 2πrh, which includes the area of the two circular bases and the lateral (curved) surface.
What is the lateral surface area of a cylinder?
The lateral surface area (or curved surface area) is the area of the curved side only: AL = 2πrh.
How do I convert cylinder volume to liters?
1 cubic centimeter (cm³) = 0.001 liters. 1 cubic meter (m³) = 1000 liters. Our calculator can display results in liters automatically.
How do I convert cylinder volume to gallons?
1 US gallon = 231 cubic inches. 1 US gallon ≈ 3.785 liters. Our calculator includes gallons as an output option.
What is the volume of a cylinder with radius 5 and height 10?
Using V = πr²h = π × 5² × 10 = π × 25 × 10 = 250π ≈ 785.40 cubic units.
How does the volume change if I double the radius?
Volume is proportional to the square of the radius. Doubling the radius increases the volume by a factor of 4 (2²).
How does the volume change if I double the height?
Volume is directly proportional to the height. Doubling the height doubles the volume.
What is the volume of a cylinder in terms of diameter?
V = (πd²h)/4, where d is the diameter of the base.
Can I use this calculator for a cylinder with different units?
Yes. You can enter dimensions in inches, feet, centimeters, or meters. The calculator will display the volume in the corresponding cubic units, liters, or gallons.
What is the difference between volume and capacity?
Volume is the amount of space a solid object occupies. Capacity is the amount of liquid or gas a container can hold. For a cylinder, the volume and capacity are numerically equal when measured in the same units.
What is π (Pi) in volume calculations?
π (Pi) is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter.[reference:2]
How do I calculate the volume of a cylinder in cubic feet?
Enter the radius and height in feet, and the calculator will display the result in cubic feet. You can also convert from other units using the unit system selector.