Cylinder Volume Calculator

Cylinder Volume Calculator

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Cylinder volume is calculated using V = pi r squared h. For a cylinder with radius 10 cm and height 25 cm, the volume is pi times 100 times 25, which equals 7,853.98 cm3 or 7.854 litres. This formula applies to solid round pipes, tanks, and containers. Select your cylinder type and enter your dimensions below.

Calculator

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

Cylinder volume is the total amount of space enclosed within a cylinder: a 3D solid with two parallel circular bases connected by a curved surface. Sometimes called circular volume because of its round base, cylinder volume is measured in cubic units such as cubic centimeters (cm³), cubic meters (m³), cubic inches (cu in), or liters (l).

Cylinder Volume Formula

The cylinder volume formula for a right cylinder is:

V = π × r² × h
π (Pi) = 3.14159…: the ratio of a circle's circumference to its diameter
r = radius of the cylinder: the distance from the center of the circular base to the edge
h = cylinder's height: the perpendicular distance between the two circular bases

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, you can calculate the volume of a cylinder with diameter directly. 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. This form is useful whenever you know the cylinder volume diameter and height but not the radius.

Cylinder Volume Diagram

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.

r (radius) h (height) d (diameter = 2r)

Hover over a dimension to learn more

How to Calculate Volume of a Cylinder

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).

Interactive Step Calculator

cm
cm
r = 5 h = 10
Step 1: r = 5 cm
Step 2: π × 5² = π × 25 = 78.54 cm²
Step 3: 78.54 × 10 = 785.40 cm³

Cylinder types and specific calculations

Choose a dedicated calculator for your specific cylinder geometry, measurement constraints, or material properties:

🔲 Hollow Cylinder Calculator Calculate the solid material volume of pipes, tubes, and cylindrical shells by subtracting inner cavity from outer volume. 📐 Oblique Cylinder Calculator Find the volume of leaning cylinders and slanted pipes using perpendicular height or slant angle. 📊 Cylinder Geometry Calculator Explore elliptical cylinders, oval cross-sections, lateral area, total surface area, and surface-to-volume ratios. 🔘 Using Radius Calculator Calculate standard right cylinder volume directly from circular base radius and height. 🔺 Cylinder vs Cone and Sphere Review the exact 3:1 ratio with cones and 3:2 ratio with inscribed spheres. 🛢️ Tank Volume Calculator Compute liquid storage capacities and fill levels for vertical and horizontal cylindrical vessels. ⚖️ Cylinder Weight Calculator Estimate total cylinder mass and weight across materials like steel, concrete, aluminum, and water.

Calculator Tools

Explore our 39 specialized cylinder calculators: each tailored for a specific calculation need.

⌀ Using Diameter 🔘 Using Radius ⭕ Using Circumference 📏 Without Height 🔲 Hollow Cylinder 🛢️ Cylinder Tank ⚙️ Hydraulic Cylinder 📊 Geometry Calculator 📐 Oblique Cylinder 🔺 Cylinder vs Cone ⚖️ Weight Calculator 💧 Liters 🪣 Gallons 📦 Cubic Feet 📦 Cubic Inches 📦 Cubic Meters 🧪 Milliliters 🧫 Cubic Centimeters 🥤 Fluid Ounces 🫙 Quarts 🛢️ Barrels 🏗️ Cubic Yards 📏 Metric 🔬 Millimeters 📏 Centimeters 📐 Meters 📏 Inches 📐 Feet 🔄 Liters → Gallons 🔄 Gallons → Liters 🔄 Inches → Liters 🔄 Inches → Gallons 🔄 mm → Liters 🔄 cm → Liters 🔍 Without Radius ⬆️ Vertical Cylinder ➡️ Horizontal Cylinder 🏎️ Engine Cylinder

Learn the core cylinder concepts before or after using the calculator. These guides expand on the interactive explanations on the homepage and connect directly to the most relevant measurement tools.

Geometry

Cylinder Volume Formula: Derivation, Proof, and Why It Works

See where V = pi x r^2 x h comes from with interactive visuals, proof ideas, and links to the right calculators.

Read More →

Geometry

Parts of a Cylinder: Bases, Height, Radius & Lateral Surface

See how each cylinder part connects to base area, lateral area, and volume with interactive diagrams and direct calculator links.

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Geometry

What Is a Cylinder? Definition, Properties, and Real-Life Examples

Get the broader geometry foundation, including faces, edges, properties, cylinder types, formulas, and everyday examples.

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Geometry

Surface Area, Lateral Area, and Volume Formulas

Compare cylinder formulas with other 3D shapes and review TSA, CSA, lateral area, and volume in one place.

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FAQs

How to find the volume of a cylinder?
To find the volume of a cylinder: (1) Measure the radius of the circular base. (2) Square the radius and multiply by Pi (3.14159) to get the base area. (3) Multiply the base area by the height. The formula is V = π × r² × h. Use our cylinder volume calculator at the top of this page for instant results with automatic unit conversion.
Why is the volume of a cylinder pi r squared h?
The volume of a cylinder equals πr²h because of 2 geometric facts: (1) The area of a circle is πr². (2) A cylinder is formed by stacking identical circles (cross-sections) along a height h. The volume of any prism-like shape equals the base area multiplied by the height. Since the cylinder's base is a circle with area πr², and the cylinder's height is h, the total volume is πr² × h.
What is a hollow cylinder?
A hollow cylinder, also known as a cylindrical shell or pipe, is a cylinder with a smaller cylinder removed from its center along the same axis. Its material volume equals the total outer volume minus the inner cavity volume: V = π × h × (R² − r²), where R is the external radius, r is the internal radius, and h is the height.
How do I convert between radius and diameter?
The diameter of a circle is twice the radius (d = 2r), and the radius is half the diameter (r = d / 2). If you know the diameter, divide it by 2 to get the radius before calculating, or use the direct formula V = (π × d² × h) / 4.
Can I use different units for radius and height?
Yes. Our online calculator converts mixed units automatically. If calculating manually, convert the radius and height into the same measurement unit (such as centimeters or inches) before applying the volume formula.
What units does this calculator support?
The calculator supports metric units (millimeters, centimeters, meters, kilometers) and imperial units (inches, feet, yards, miles). Output volume can be displayed in cm³, m³, litres, millilitres, cubic inches, cubic feet, US gallons, UK gallons, fluid ounces, and barrels.
How much volume can a cylinder hold?
The volume a cylinder can hold equals its internal capacity: V = π × r² × h. A standard coffee mug (radius 4 cm, height 9.5 cm) holds about 478 cm³ or 0.478 liters (16.2 US fluid ounces). A 2-liter soda bottle has a radius of roughly 5.2 cm and height 23.5 cm, holding about 2,000 cm³ (2 liters or 0.528 US gallons).
Is this calculator free to use?
Yes. The Cylinder Volume Calculator is 100% free with no registration required, no usage limits, and instant calculations executed directly in your web browser.