Cylinder Volume Calculator

The cylinder volume formula for a right cylinder is:

The formula works by first calculating the area of the circular base (π × r²), then multiplying the base area by the cylinder's height. The result is the cylinder volume in cubic units.

When using diameter instead of radius, the cylinder volume formula becomes: V = π × (d/2)² × h, or equivalently V = (π × d² × h) / 4, where d is the diameter of the cylinder.

The cylinder volume diagram below shows all dimensions needed to calculate the volume of a cylinder. Hover over each labeled dimension to see its role in the cylinder volume formula.

To calculate the volume of a cylinder, follow these 3 steps:

1. Measure the radius of the cylinder. Measure the distance from the center of the circular base to its edge. The radius can be in any unit — centimeters (cm), meters (m), inches (in), or feet (ft). Use a ruler or measuring tape for physical cylinders.
2. Square the radius and multiply the result by Pi (π). This calculates the area of the circular base. For a cylinder with a radius of 5 cm: π × 5² = π × 25 = 78.54 cm².
3. Multiply the base area by the cylinder's height. The final result is the cylinder volume. For a cylinder with radius 5 cm and height 10 cm: 78.54 × 10 = 785.40 cm³ (0.785 liters or about 0.21 US gallons).

A hollow cylinder, also called a cylindrical shell, is a cylinder with a smaller cylinder removed from its center. Both cylinders share the same vertical axis. Drinking straws, water pipes, and toilet paper rolls are examples of hollow cylinders.

The volume of a hollow cylinder formula is:

Where R is the external radius, r is the internal radius, and h is the cylinder's height.

The same formula can use the external diameter (D) and internal diameter (d): V = π × h × [(D² − d²) / 4].

For a toilet paper roll with an external diameter of 11 cm (5.5 cm external radius), an internal diameter of 4 cm (2 cm internal radius), and a height of 9 cm: V = π × 9 × (5.5² − 2²) = π × 9 × (30.25 − 4) = π × 9 × 26.25 = 742.2 cm³. This volume represents the space occupied by the paper and cardboard.

An oblique cylinder (or slanted cylinder) is a cylinder where the sides are not perpendicular to the bases. The oblique cylinder leans to one side, unlike a standard right cylinder that stands straight.

The cylinder volume formula for an oblique cylinder is the same as for a right cylinder: V = π × r² × h. The key difference is that the height (h) must be the perpendicular height — the shortest distance between the two parallel bases — not the length of the slanted side.

This works because of Cavalieri's principle: two 3D solids with equal cross-sectional areas at every height have the same volume. Tilting a cylinder does not change the area of circular cross-sections at any height.

The volume of a slanted cylinder uses the slant angle and the side length instead of the perpendicular height. This approach is practical when the perpendicular height is difficult to measure directly.

The slanted cylinder volume formula is:

Where r is the radius of the cylinder, L is the side length (slant length), and θ is the slant angle between the side and the base.

To calculate the volume of a slanted cylinder, follow these 6 steps:

1. Find the radius, side length, and slant angle of the cylinder.
2. Square the radius.
3. Multiply the result by Pi (π).
4. Take the sin of the angle.
5. Multiply the sin by the side length.
6. Multiply the results from steps 3 and 5 together. The result is the slanted cylinder volume.

An elliptical cylinder has an ellipse as its base instead of a circle. An ellipse has two radii: the major axis (largest radius, often labeled a) and the minor axis (smallest radius, often labeled b).

The elliptical cylinder volume formula is:

Where a is the major axis (largest radius), b is the minor axis (smallest radius), and h is the cylinder's height.

When a = b, the ellipse becomes a circle and the formula reduces to the standard cylinder volume formula: V = π × r² × h.

An oval cylinder has an oval (ellipse) as its base rather than a circle. The terms "oval cylinder" and "elliptical cylinder" describe the same 3D solid — a cylinder with an elliptical cross-section.

To find the volume of an oval cylinder, follow these 4 steps:

1. Multiply the smallest radius of the oval (minor axis) by the largest radius (major axis).
2. Multiply the product by Pi (π). This gives the area of the elliptical base.
3. Multiply the base area by the cylinder's height.
4. The result is the volume of the oval cylinder.

For an oval cylinder with a major axis of 8 cm, a minor axis of 5 cm, and a height of 12 cm: V = π × 8 × 5 × 12 = π × 480 = 1,507.96 cm³ (1.508 liters or about 0.398 US gallons).

A right cylinder is a cylinder where the sides are perpendicular (at a 90° angle) to the circular bases. The term "right" means the axis connecting the centers of the two bases is at a right angle to the bases. Most cylinders encountered in everyday life — cans, bottles, pipes — are right cylinders.

The volume of a right cylinder uses the standard cylinder volume formula: V = π × r² × h, where r is the radius of the cylinder and h is the cylinder's height.

The difference between a right cylinder and an oblique cylinder is the orientation of the axis. A right cylinder stands straight, while an oblique cylinder tilts. Both have the same volume when the perpendicular height and radius are equal.

A sphere inscribed inside a cylinder (touching both bases and the side) has a specific volume relationship to that cylinder. The sphere volume equals two-thirds (⅔) of the cylinder volume.

The formulas are:

• Cylinder volume = π × r² × h = π × r² × 2r = 2πr³
• Sphere volume = (4/3) × π × r³ = (4/3)πr³
• Ratio: Sphere / Cylinder = (4/3)πr³ / 2πr³ = 2/3

For a cylinder with radius 5 cm and height 10 cm (2r): cylinder volume = 2π × 125 = 785.40 cm³. The inscribed sphere volume = (4/3) × π × 125 = 523.60 cm³, which is exactly ⅔ of 785.40.

A cone with the same radius and height as a cylinder has exactly one-third (⅓) the volume. This relationship is a fundamental property of 3D solids.

The formulas show the relationship:

• Cylinder volume = π × r² × h
• Cone volume = (1/3) × π × r² × h
• Ratio: Cone / Cylinder = 1/3

3 cones with identical radius and height fill exactly 1 cylinder. This can be demonstrated by filling a cone with water three times and pouring the water into a cylinder of the same dimensions — the cylinder fills completely.