Cylinder Volume Calculator

Instantly compute the volume of a right circular cylinder from radius or diameter and height. Designed for students, engineers, and makers, this tool supports metric and imperial units and reports results in cubic units, liters, and gallons with professional-grade precision.

Input

Choose input mode
Input Mode *

Results

Volume
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Volume (m³)
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Volume (liters)
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Volume (US gal)
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Volume (UK gal)
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Data Source and Methodology

Primary formula reference: Weisstein, Eric W. "Cylinder." MathWorld—A Wolfram Web Resource. Updated 2024. https://mathworld.wolfram.com/Cylinder.html.

Unit conversion constants follow the National Institute of Standards and Technology (NIST) Guide to the SI. https://www.nist.gov/pml/owm/si-units.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

For a right circular cylinder:

$$V = \pi r^2 h$$

If the diameter d is known:

$$r = \frac{d}{2} \quad \Rightarrow \quad V = \pi \left(\frac{d}{2}\right)^2 h = \frac{\pi d^2 h}{4}$$

Unit conversions (length to meters m):

$$\text{mm} \to \text{m}: \; \ell_{\text{m}} = \frac{\ell_{\text{mm}}}{1000}, \quad \text{cm} \to \text{m}: \; \ell_{\text{m}} = \frac{\ell_{\text{cm}}}{100}, \quad \text{in} \to \text{m}: \; \ell_{\text{m}} = \ell_{\text{in}} \times 0.0254$$

Volume conversions:

$$1\,\text{m}^3 = 1000\,\text{L} = 264.172\,\text{US gal} = 219.969\,\text{UK gal}$$

Glossary of Variables

  • r: Radius of the cylinder's circular base (half the diameter).
  • d: Diameter of the circular base (2 × r).
  • h: Height of the cylinder (distance between the bases along the axis).
  • V: Volume of the cylinder.
  • Length unit: Common unit used for r/d and h (mm, cm, m, in, ft).
  • Precision: Number of decimal places shown in the results.
  • Outputs: Volume in the cubic form of the chosen unit, cubic meters (m³), liters (L), US gallons (gal), UK gallons (gal).

How It Works: A Step‑by‑Step Example

Scenario: A cylinder with diameter d = 10 cm and height h = 30 cm. Find V.

  1. Compute the radius: r = d/2 = 10/2 = 5 cm.
  2. Apply the formula: V = π r² h = π × (5 cm)² × (30 cm) = π × 25 × 30 cm³.
  3. Multiply: 25 × 30 = 750; thus V = 750π cm³ ≈ 2356.19 cm³.
  4. Convert: 1,000 cm³ = 1 L, so 2356.19 cm³ ≈ 2.356 L.

Therefore, the cylinder’s volume is about 2356.19 cm³ (2.356 L).

Frequently Asked Questions (FAQ)

Can I switch between radius and diameter without re-entering values?

Yes. Toggle the input mode and the calculator will interpret your size value accordingly. Ensure the number you enter matches the selected mode.

What if my measurements are in different units?

Convert them to a common unit first. This tool uses one unit setting for all length inputs to reduce mistakes.

Is this formula valid for slanted (oblique) cylinders?

No. The formula V = π r² h applies to right circular cylinders. Oblique cylinders require additional geometry but have the same volume if base area and perpendicular height are unchanged.

Why do I see slight differences compared to other tools?

Differences usually come from rounding and the value of π used. This tool uses JavaScript’s Math.PI and your chosen display precision.

How can I use this for tank capacity?

Use the calculator to get the full capacity. If your tank isn’t full, capacity depends on fill height; use a partial cylinder or tank-specific calculator.

What’s the fastest way to get liters?

Enter your lengths in meters for direct m³ output; liters are then simply 1000 × m³. The tool displays liters automatically.

Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Team.
Last reviewed for accuracy on: .