Volume to Cylinder

Volume to Cylinder

A cylinder's volume is the space inside it, measured in cubic units. You get it by multiplying the area of the circular base (π × r²) by the height. This calculator handles solid, hollow, and oblique cylinders with full unit conversion — from millimeters to miles. Enter your radius and height below for an instant result.

r h
V = π · r² · h
R r h
V = π · h · (R² − r²)

Volume of a Cylinder Definition

The volume of a cylinder is the total amount of space enclosed within its circular bases and curved surface. In solid geometry, a cylinder is a three-dimensional geometric shape with two parallel, congruent circular bases connected by a curved surface at a fixed distance (the height). Volume is measured in cubic units — cubic centimeters (cm³), cubic meters (m³), liters, gallons, and so on.

To find the volume you need two measurements: the radius of the circular base and the height (the perpendicular distance between the two bases). Pi (π ≈ 3.14159) ties them together. The formula multiplies the area of the base by the height, giving you the total enclosed space.

Cylinders appear everywhere. Drinking glasses, cans, pipes, flower pots, tree trunks, plant stems, and even some bones are cylindrical. Engineers use cylinder volume to size tanks, design piping systems, and calculate swept volume in engines. Students encounter it in mensuration and calculus courses when studying integrals of circular cross-sections.

Interactive Cylinder Diagram
r h πr²

The cylinder's volume equals the base area (πr²) multiplied by the height (h).

How to Calculate Volume of a Cylinder

Calculating cylinder volume takes three steps:

1. Measure the radius (r) of the circular base. If you only have the diameter (d), divide it by 2: r = d / 2. 2. Measure the height (h) — the straight-line distance between the two bases. 3. Plug into the formula: V = π × r² × h.

Example: A can with radius 4 cm and height 12 cm → V = π × 16 × 12 = 603.19 cm³. That's about 0.6 liters.

The result is always in cubic units that match your input. If you measure in inches you get cubic inches; in meters, cubic meters. Use the converter above to switch between units.

Click a Cylinder Type
R r h Hollow Cylinder
R h Right Circular
Cylinder
R h Oblique
Cylinder
V = πr²h

The standard right circular cylinder — two parallel circular bases connected by a curved surface perpendicular to the bases.

Volume of Cylinder Formula

The standard formula is:

V = π × r² × h

where: • V = volume (cubic units) • π ≈ 3.14159 • r = radius of the circular base • h = height of the cylinder

Breaking it down: r² gives the area factor of the base. Multiplying by π converts that into the actual circular area. Multiplying by h extends that area through the full height of the cylinder.

You can also write it using the diameter: V = π × (d/2)² × h = (π × d² × h) / 4. Both forms are equivalent.

Formula Breakdown
V = π × r² × h
Hover over each part of the formula to see what it represents.

Volume of a Hollow Cylinder

A hollow cylinder (or cylindrical shell) has an outer radius R and an inner radius r, with material between them. Think of a drinking straw, a section of pipe, or a roll of toilet paper.

The formula is:

V = π × h × (R² − r²)

You subtract the inner cylinder's volume from the outer cylinder's volume. The result is the volume of the material itself, not the empty space inside.

Example: A pipe with outer radius 5 cm, inner radius 4 cm, length 100 cm → V = π × 100 × (25 − 16) = π × 900 ≈ 2,827.43 cm³.

Hollow Cylinder Cross-Section
R r

The shaded ring shows the material volume: V = πh(R² − r²)

Volume of an Oblique Cylinder

An oblique cylinder is tilted — its sides are not perpendicular to its bases. Despite the slant, the volume formula stays the same: V = π × r² × h, where h is the perpendicular height (not the slant length).

This follows from Cavalieri's principle: if two solids have the same cross-sectional area at every height, they have the same volume. Tilting a cylinder doesn't change its cross-sections — each slice is still a circle with the same radius.

You see oblique cylinders in leaning towers of stacked coins, tilted containers, and some architectural columns. When measuring, always use the vertical height, not the length along the slanted side.

Right vs Oblique Cylinder
h

Both have the same volume: V = πr²h (h = perpendicular height)

Volume: Cylinder vs Cone

A cone with the same base radius and height as a cylinder holds exactly one-third the volume:

V_cone = (1/3) × π × r² × h

So three identical cones fill one cylinder perfectly. You can prove this with calculus (integration of circular cross-sections that shrink linearly) or by a physical experiment with water and plasticine models.

This 1:3 ratio is one of the most useful relationships in solid geometry. It applies to any cone-cylinder pair sharing the same base and height, whether right or oblique.

3 Cones = 1 Cylinder
Cylinder
πr²h
Cone
⅓πr²h
1

Slide to fill the cylinder with cones. It takes exactly 3 cones to match the cylinder's volume.

Cylinder vs Sphere Volume

A sphere's volume depends only on its radius:

V_sphere = (4/3) × π × r³

Compare that with a cylinder of the same radius and height equal to the sphere's diameter (h = 2r):

V_cylinder = π × r² × 2r = 2π × r³

The ratio is V_sphere / V_cylinder = (4/3) / 2 = 2/3. The sphere fills two-thirds of the cylinder that just contains it. Archimedes discovered this relationship and considered it his greatest achievement.

This comparison appears in packaging, ball bearings, and tank design — anywhere you choose between cylindrical and spherical containers for the same contents.

Volume Comparison
Cylinder (h=2r)
1570.80
Sphere
523.60

The sphere fills exactly ⅔ of the cylinder that contains it — Archimedes' discovery.

Frequently Asked Questions

Where can you find cylinders in nature?
Tree trunks, plant stems, bones, and flagella are all roughly cylindrical. Stalactites and some crystal formations also grow in cylindrical shapes. Even a spider's silk thread is a tiny cylinder.
How do I draw a cylinder?
Draw two parallel ovals (ellipses) for the top and bottom bases. Connect them with two straight vertical lines on the left and right sides. Make the back edge of the bottom oval dashed to show depth. Add light shading on one side to create a 3D effect.
How do you calculate the weight of a cylinder?
First calculate the volume using V = π × r² × h. Then multiply by the material's density: Weight = Volume × Density. For example, a steel cylinder (density ≈ 7,850 kg/m³) with r = 0.05 m and h = 0.2 m weighs about π × 0.0025 × 0.2 × 7850 ≈ 12.3 kg.
How do you calculate the surface area to volume ratio of a cylinder?
Surface area = 2πr² + 2πrh. Volume = πr²h. The ratio is SA/V = (2πr² + 2πrh) / (πr²h) = 2/h + 2/r. As a cylinder gets larger, this ratio decreases — which is why large tanks lose heat more slowly than small ones.
How do you find the height of a cylinder?
Rearrange the volume formula: h = V / (π × r²). If you know the volume and the radius, divide the volume by (π times the radius squared) to get the height.
How do I find the radius of a cylinder?
Rearrange the formula: r = √(V / (π × h)). Divide the volume by (π times the height), then take the square root of the result.
How do you find the volume of an oval cylinder?
An oval (elliptical) cylinder has an elliptical base instead of a circular one. Its volume is V = π × a × b × h, where a and b are the semi-major and semi-minor axes of the ellipse and h is the height.
How do you find the volume of a slanted cylinder?
A slanted (oblique) cylinder has the same volume as a right cylinder with the same base and perpendicular height. Use V = π × r² × h, where h is the vertical height — not the slant length.
How do you calculate the swept volume of a cylinder?
Swept volume is the volume displaced by a piston moving from bottom dead center to top dead center in an engine cylinder. It equals V = π × r² × stroke, where the stroke is the distance the piston travels.
Why is the volume of a cylinder πr²h?
The base is a circle with area πr². The cylinder is formed by stacking that circle straight up through the height h. Volume = base area × height = πr² × h. This logic works because every horizontal cross-section is an identical circle.
Why is the volume of a cone one-third of a cylinder?
A cone tapers from a full circular base to a point. Its cross-sectional area shrinks proportionally with height. When you integrate those shrinking circles from base to tip, the total volume comes out to exactly (1/3) × πr²h — one-third of the cylinder with the same base and height.
How do you express cylinder volume in cubic inches?
Measure the radius and height in inches, then apply V = π × r² × h. The result is in cubic inches (in³). To convert from cubic centimeters, divide by 16.387. To convert from liters, multiply by 61.024.
How do you calculate cylinder volume in litres?
Calculate the volume in cubic centimeters (measure in cm), then divide by 1,000 to get liters. 1 liter = 1,000 cm³. For example, a cylinder with r = 5 cm and h = 20 cm has V = π × 25 × 20 = 1,570.8 cm³ ≈ 1.57 liters.
How much volume can a cylinder hold?
A cylinder can hold any volume — it depends on the radius and height. A small drinking glass (r ≈ 3.5 cm, h ≈ 12 cm) holds about 462 cm³ (0.46 L). A standard 55-gallon drum (r ≈ 29 cm, h ≈ 85 cm) holds about 208 liters.