Cylinder Volume Calculator (V = π·r²·h)
The Cylinder Volume Calculator computes the exact interior volume and total surface area of a right circular cylinder from two inputs: radius (r) and height (h). Volume is given by V = π·r²·h, while total surface area combines both circular bases and the lateral wall: A = 2π·r·(r + h). Enter radius and height in any consistent unit (cm, in, ft, m) and get instant results in both cubic units and liters.
The volume of a cylinder is V = π × r² × h, where r is the base radius and h is the height. For example, a cylinder with r = 5 cm and h = 10 cm has V = π × 25 × 10 ≈ 785.40 cm³ (0.785 liters). To get liters from cm³, divide by 1,000.
When to use this calculator
- Calculating the capacity of a cylindrical water tank (r = 0.5 m, h = 1.2 m → V ≈ 942 L) before purchasing.
- Determining how much concrete (in ft³) is needed to fill cylindrical foundation columns on a construction site.
- Finding the volume of a graduated cylinder or beaker in a chemistry lab to verify liquid measurements in mL.
- Estimating the volume of a tin can or food container for packaging and nutritional label calculations.
- Computing the surface area of a cylindrical pipe to determine how much paint or insulation material is required.
- Designing cylindrical fuel tanks for vehicles or aircraft, where volume directly relates to range and weight budgets.
Worked Example
- r = 5 cm, h = 10 cm
- V = π × (5)² × 10 = π × 25 × 10 = π × 250
- V ≈ 785.40 cm³ = 0.785 L
- Total Surface Area = 2π × 5 × (5 + 10) = 2π × 75 ≈ 471.24 cm²
How it works
2 min readHow Cylinder Volume Is Calculated
A right circular cylinder has two congruent circular bases connected by a curved lateral surface. All formulas use π ≈ 3.14159265358979.
Volume:
V = π · r² · h
Lateral Surface Area (curved wall only):
A_lateral = 2π · r · h
Base Area (one circle):
A_base = π · r²
Total Surface Area (both bases + lateral):
A_total = 2π · r² + 2π · r · h
= 2π · r · (r + h)Where:
r = radius of the circular base (= diameter ÷ 2)h = height (perpendicular distance between the two bases)π ≈ 3.14159265…Units must be consistent. If r is in cm and h is in cm, then V is in cm³ and A is in cm². To convert cm³ to liters, divide by 1,000.
---
Reference Table: Common Cylinder Dimensions
| Radius (r) | Height (h) | Volume (V) | Total Surface Area |
|---|---|---|---|
| 1 cm | 5 cm | 15.71 cm³ (0.016 L) | 37.70 cm² |
| 3 cm | 10 cm | 282.74 cm³ (0.283 L) | 244.35 cm² |
| 5 cm | 10 cm | 785.40 cm³ (0.785 L) | 471.24 cm² |
| 5 cm | 15 cm | 1,178.10 cm³ (1.178 L) | 628.32 cm² |
| 10 cm | 30 cm | 9,424.78 cm³ (9.42 L) | 2,513.27 cm² |
| 0.5 m | 1.2 m | 0.9425 m³ (942.5 L) | 5.341 m² |
| 2 in | 6 in | 75.40 in³ | 100.53 in² |
| 1 ft | 3 ft | 9.42 ft³ (70.5 gal) | 25.13 ft² |
| 6 in | 12 in | 1,357.17 in³ | 678.58 in² |
> Unit conversion: 1 cm³ = 1 mL exactly; 1 L = 1,000 cm³; 1 ft³ ≈ 7.4805 US gallons; 1 in³ ≈ 0.004329 US gallons.
---
Typical Real-World Cases
Case 1 — Standard 12 oz soda can
A typical aluminum can: internal diameter ≈ 2.6 in (r ≈ 1.3 in), height ≈ 4.8 in:
V = π × (1.3)² × 4.8 = π × 1.69 × 4.8 ≈ 25.48 in³ ≈ 418 mLSlightly more than the nominal 355 mL because of headspace and wall thickness—exactly the precision needed in container design.
Case 2 — Concrete column (construction)
Cylindrical foundation column: r = 0.25 m, h = 3 m:
V = π × (0.25)² × 3 = π × 0.1875 ≈ 0.589 m³At 2,400 kg/m³ concrete density → ≈ 1,413 kg per column.
Case 3 — Circular above-ground pool
Diameter = 12 ft (r = 6 ft), water height = 4 ft:
V = π × 6² × 4 = π × 144 ≈ 452.39 ft³ ≈ 3,384 US gallons---
Common Mistakes to Avoid
1. Using diameter instead of radius. If you measure a pipe's outer width of 6 cm, the radius is 3 cm. Using diameter doubles r, which quadruples volume (since V ∝ r²).
2. Mixing units. Combining inches for radius and feet for height gives wrong results. Convert everything to the same unit first.
3. Forgetting both bases in surface area. Lateral area (2π·r·h) covers only the curved wall. For a closed tank, add 2·π·r² for the top and bottom.
4. Confusing geometric volume with fill capacity. For tanks with thick walls, use internal radius for fill capacity.
Frequently asked questions
What is the formula for the volume of a cylinder?
The volume of a right circular cylinder is V = π · r² · h, where r is the base radius and h is the height. For example, a cylinder with r = 5 cm and h = 10 cm has V = π × 25 × 10 ≈ 785.40 cm³ (0.785 L). The formula works in any consistent unit: inches, feet, meters.
How do I convert cylinder volume from cm³ to liters or gallons?
1 liter = 1,000 cm³ exactly, so divide by 1,000 to get liters. For US gallons: 1 US gallon = 3,785.41 cm³, so divide by 3,785.41. Example: 9,424.78 cm³ ÷ 1,000 = 9.42 L = 9,424.78 ÷ 3,785.41 ≈ 2.49 US gallons.
What is the total surface area of a cylinder and when do I need it?
Total surface area is A = 2π·r·(r + h) — two circular bases plus the curved lateral wall. You need it when estimating paint, insulation, or material costs. For r = 3 cm, h = 10 cm: A = 2π × 3 × 13 ≈ 244.35 cm². For just the curved wall (like a label), use the lateral area: 2π·r·h.
How do I find the radius if I only know the diameter?
Divide the diameter by 2: r = d ÷ 2. If you know the circumference (C): r = C ÷ (2π). Example: a pipe with circumference 31.42 cm → r = 31.42 ÷ (2 × 3.14159) ≈ 5.00 cm. Always measure the widest point and halve it to get the true radius.
Does the formula change for a hollow cylinder (pipe or tube)?
Yes. For a hollow cylinder with outer radius R and inner radius r, the wall material volume is V = π·h·(R² − r²). The interior volume (what the pipe carries) is π·r²·h using the inner radius only. Example: steel pipe with R = 2 in, r = 1.75 in, h = 10 in → wall volume = π × 10 × (4 − 3.0625) ≈ 29.45 in³.
Why does doubling the radius increase volume more than doubling the height?
Because volume scales with r² but linearly with h. Doubling r multiplies volume by 4 (since (2r)² = 4r²), while doubling h only doubles the volume. Example: r=2, h=5 → V≈62.83. Double r: r=4, h=5 → V≈251.33 (×4). Double h: r=2, h=10 → V≈125.66 (×2). This is why pipe bore matters so much for flow capacity.
Can this calculator be used for oblique (tilted) cylinders?
Yes — Cavalieri's Principle states that an oblique cylinder has the same volume as a right cylinder with identical base radius and the same perpendicular height. Use h as the true (perpendicular) height, not the slant length. Surface area calculations differ for oblique cylinders and are more complex.
What unit should I enter — cm, inches, or meters?
Any unit works as long as radius and height are in the same unit. The result will be in cubic units of what you entered: cm→cm³, in→in³, m→m³. To convert: 1 m³ = 1,000,000 cm³ = 1,000 L; 1 ft³ ≈ 28,317 cm³ ≈ 7.48 US gallons. Convert one measurement if they come in mixed units before calculating.
How do I calculate the volume of a cylinder in liters for a water tank?
Enter radius and height both in centimeters. The calculator shows volume in cm³ and liters (1 L = 1,000 cm³) directly. Example: a water tank with r = 30 cm and h = 80 cm → V = π × 900 × 80 ≈ 226,195 cm³ = 226.2 L. For meters: r = 0.30 m, h = 0.80 m → V ≈ 0.226 m³ = 226 L — same result.