How to calculate cylinder volume in liters
Use radius, height and π to estimate cylindrical tanks and containers.
What the calculation represents
Round drums and vertical tanks use the inside radius and liquid height. Keeping inch measurements is fine when the final cubic-inch value is converted rather than treated as liters.
- Reference formula
V = π × r² × h- Unit reference
- 1 L = 1,000 cm³ · 1 m³ = 1,000 L · 1 US gal = 231 in³ = 3.785411784 L
A practical workflow
- Measure the maximum and minimum inside diameters on perpendicular axes. If they are nearly equal, halve their average; if not, model the cross-section as an ellipse using π × (d₁/2) × (d₂/2).
- Measure vertical liquid height from the usable bottom to the operating fill line, excluding a neck or lid space.
- Square the radius and multiply by π and height while retaining full calculator precision.
- Convert cubic inches with 231 in³ per US gallon, or convert the metric result to liters, before applying headspace.
Worked example
An 18-inch inside diameter and a 30-inch fill height give a 9-inch radius. The resulting 7,634 in³ is approximately 125.1 liters.
Reading the answer correctly
A domed base, rounded shoulders or a fill line below the lid means the usable capacity is lower than a perfect cylinder.
Radius is squared, so diameter error has twice the approximate percentage effect on cross-sectional area. A careful diameter measurement usually improves the answer more than extra decimal places.
Checks before relying on the number
- The value squared in the formula is radius rather than the full diameter.
- Diameter and fill height are inside measurements expressed in a consistent unit.
- The formula describes an upright cylinder; a partly filled horizontal tank needs circular-segment geometry.
- An oval section retains both diameters instead of forcing one circular radius; domed ends and baffles are handled separately.
Sources and references
These references support the units, method, or limitations explained in this guide.
- NIST — SI units of volume
Official reference for the liter, cubic meter, and metric relationships used in the calculations.
Keep the measured diameter, derived radius and liquid height together, then label the final figure as gross or working capacity.
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