What is the volume of a cylinder?
A cylinder is a 3D shape with two parallel circular ends and a curved side connecting them — think of a soda can, a wine bottle, or a barrel. The volume is the amount of space the cylinder encloses, measured in cubic units (cm³, m³, cubic inches, gallons, etc.).
The formula:
V = πr²h
(volume equals π times the radius squared times the height)
Geometrically: it's the area of the base circle (πr²) multiplied by the height. Same idea as a rectangular prism, where volume is base area × height — except the base is a circle instead of a rectangle.
How to use the calculator
Two inputs and three outputs:
- Radius (r) — distance from the center of the circular base to its edge.
- Height (h) — perpendicular distance between the two circular ends.
- The calculator returns the volume, the total surface area (top + bottom + side), and the lateral area (just the side, no caps).
Output updates as you type. Try the worked-example buttons (soda can, wine bottle, trash can, barrel) to load real-world cylinder dimensions.
Worked example: a soda can
Standard 12 fl oz / 355 mL soda cans are approximately 6.6 cm in diameter and 12.2 cm tall. So radius ≈ 3.3 cm.
- Volume: V = π × 3.3² × 12.2 = π × 10.89 × 12.2 ≈ 417 cm³
- The actual liquid is 355 mL (= 355 cm³); the rest is headspace and the can wall thickness
- Surface area: 2π × 3.3² + 2π × 3.3 × 12.2 ≈ 68.4 + 252.95 ≈ 321.35 cm²
- That's the metal area you'd need to make one can
Doubling the radius would 4× the volume (since r² grows quadratically). Doubling the height would 2× the volume. Cylinders get big fast when you scale the radius — useful intuition for tank sizing, food containers, or aquarium volumes.
Surface area: top, bottom, and side
A cylinder has three surfaces if you think of it like a can: top circle, bottom circle, and the side that wraps around. The math:
Top + bottom (2 circles): 2πr²
Side (lateral area): 2πrh
Total surface area: 2πr² + 2πrh
The lateral area formula is interesting. If you cut a cylinder's side and unrolled it flat, you'd get a rectangle. The width is the circumference of the base (2πr), and the height is the cylinder's height (h). So the area is width × height = 2πrh. Geometric intuition that makes a curved surface easier to compute.
Practical use: label area for packaging. If you're designing a label that wraps around a cylindrical can, the label dimensions are 2πr × h. So a 3.3 cm radius can needs a label about 20.7 cm wide × 12.2 cm tall.
Common cylinder volumes
| Object | Radius | Height | Volume |
|---|---|---|---|
| Standard soda can | 3.3 cm | 12.2 cm | ≈ 417 cm³ |
| Energy-drink can (slim) | 2.6 cm | 16.5 cm | ≈ 350 cm³ |
| Wine bottle (750 mL) | 3.5 cm | 30 cm | ≈ 1,154 cm³ (some headspace) |
| 2L soda bottle (cylindrical body) | 5.5 cm | 30 cm | ≈ 2,851 cm³ |
| Tennis-ball can (3 balls) | 3.5 cm | 20 cm | ≈ 770 cm³ |
| Coffee mug (cylindrical) | 4 cm | 10 cm | ≈ 503 cm³ (~ 17 oz) |
| 5-gallon bucket | 14.5 cm (top) | 37 cm | ≈ 24,400 cm³ ≈ 24.4 L |
| 55-gallon drum | 29.2 cm | 87 cm | ≈ 233,000 cm³ ≈ 233 L |
| Round above-ground pool | 183 cm (6 ft) | 122 cm (4 ft) | ≈ 12.85 m³ ≈ 12,850 L |
Tips and edge cases
Tip: if you have a diameter instead of a radius, divide by 2 first. So a 4-inch diameter pipe has radius 2 inches. Don't accidentally use the diameter as the radius — that mistake quadruples the volume since r² grows quadratically.
Watch out for unit consistency. If radius is in cm and height is in metres, the result is meaningless. Convert to a single unit before computing. Common pitfall in engineering and DIY projects — pipe diameter quoted in mm but length in m gives volume in mm² × m, which is not a real unit.
Volume in litres from cm³ measurements. 1 L = 1,000 cm³, so divide cm³ by 1,000. A cylinder calculated as 5,000 cm³ is 5 L. For US gallons: 1 US gallon = 3,785.41 cm³, so divide cm³ by 3,785.41.
Hollow cylinders (pipes) need a different formula. If you have an outer radius and inner radius, the volume of the cylinder wall is π(R² − r²)h. The volume of the hollow space (the bore) is πr²h. Subtraction handles it.
Tilted or oblique cylinders. Cavalieri's principle — same formula works. The volume of an oblique cylinder (one that leans like the Tower of Pisa) is still πr²h, where h is the PERPENDICULAR height from base to top, not the slanted side length.
Related calculators
- For circle-only math (no third dimension), use the Circumference of a Circle Calculator — gives circumference, area, and diameter from radius.
- For straight-line distance between points (a related geometry tool), the Distance Formula Calculator.
- For aspect-ratio / diagonal math (also Pythagorean), the Aspect Ratio Calculator.
- For statistical mean of measurements, the Average Calculator.
Frequently asked questions
What is the formula for the volume of a cylinder?
V = πr²h, where r is the radius and h is the height. Geometrically: it's the area of the circular base (πr²) multiplied by the height. So a cylinder with radius 5 and height 10 has volume π × 25 × 10 ≈ 785.4 cubic units.
How do I find the volume of a cylinder?
Multiply π × radius² × height. Step by step: square the radius first (e.g. 4² = 16), multiply by π (16 × π ≈ 50.27), then multiply by the height (50.27 × 12 ≈ 603.2). The order matters less than getting r² right — that's the most common mistake.
How big is a soda can in cubic centimetres?
Standard 12 fl oz (355 mL) soda cans have approximately 6.6 cm diameter (radius 3.3 cm) and 12.2 cm height. Volume = π × 3.3² × 12.2 ≈ 417 cm³. The actual content is 355 mL (= 355 cm³); the rest is headspace and can-wall thickness.
What's the surface area of a cylinder?
Total surface area = 2πr² + 2πrh. The 2πr² term is the top and bottom circles together; 2πrh is the side surface (which, when unrolled, is a rectangle of width 2πr and height h). For a cylinder with r = 5 and h = 10, total surface area ≈ 471.24.
What's the difference between volume and surface area?
Volume measures the 3D space inside (cubic units, like cm³). Surface area measures the 2D area on the outside (square units, like cm²). A cylinder with r = 5, h = 10 has volume ≈ 785.4 cm³ but surface area only ≈ 471.2 cm² — they're not the same number and have different physical meanings.
How do I find the height if I know the volume and radius?
Rearrange the formula: h = V / (πr²). So if you know a cylinder holds 1 litre (1,000 cm³) and has radius 5 cm, the height is 1,000 / (π × 25) ≈ 12.73 cm.
Is my input saved or sent anywhere?
No. The calculation runs entirely in your browser using JavaScript — nothing is sent to a server, logged, or stored.