Cylinder Volume Without Height
Don't know the height? You can still find the volume if you have enough other information — like the surface area and radius, or the lateral surface area and radius. This calculator shows you which combinations work and solves for the missing height automatically.
Volume Without Height
Finding Height from Other Measurements
If you know the volume and radius: h = V / (πr²)
If you know the total surface area and radius: SA = 2πr² + 2πrh → h = (SA − 2πr²) / (2πr)
If you know the lateral surface area and radius: LSA = 2πrh → h = LSA / (2πr)
If you know the diagonal (slant) of the surface and the radius: The diagonal d across the surface satisfies d² = (2πr)² + h², so h = √(d² − 4π²r²).
Using the Lateral Surface Area
The lateral surface area is the area of the curved side — imagine unrolling the cylinder into a rectangle. Its dimensions are the circumference (2πr) by the height (h), so LSA = 2πrh.
If you have a label that wraps around a can, the label's area gives you the lateral surface area. Divide by 2πr to get the height, then calculate volume.
Example: A label is 25 cm × 10 cm = 250 cm². The can's circumference is 25 cm, so r = 25/(2π) = 3.98 cm. Height = 10 cm. V = π × 15.84 × 10 = 497.6 cm³.
When Height Is Truly Unknown
If you have only the radius and no other information, you cannot determine the volume. The volume depends on both r and h — knowing only one gives infinite possible volumes.
In practice, you can always measure the height somehow: with a ruler, a tape measure, by filling and measuring the liquid, or by weighing and dividing by density and base area.
If you know the volume of liquid that fills it, you already have the volume — no height needed.