Accurate geometry • transparent method
See cylinder volume, not just the answer.
Calculate solid, hollow and oblique cylinders with independent units, immediate validation, and graphs that explain how each dimension changes the result.
Live calculator
Cylinder volume
Enter radius or diameter. Every field can use its own unit.
V = πr²h
Enter a positive radius or diameter and height.
Volume growth by radius
Height held constant1 • Definition
What cylinder volume means
Volume measures the three-dimensional space inside a cylinder’s boundary. A circular base contributes area, πr², and the perpendicular distance between the two parallel bases extends that area through height h.
That makes the formula more than a rule to memorize: it is simply constant cross-sectional area × distance. Use internal dimensions for capacity and outside dimensions for the envelope occupied by a solid object.
2 • Method
Three steps, three cylinder types
Select a shape to connect its diagram, formula and measurement rule. Every control changes real explanatory content.
Find radius and perpendicular height.
Convert all physical lengths to a consistent unit before squaring.
Use V = πr²h and report a cubic unit.
3 • Formula
Explore each term
Focus, hover or tap a term to see its role. The formula is deliberately broken into parts so the exponent and units stay visible.
Choose a formula term to read its meaning.
4 • Hollow cylinders
Subtract the inner void
A pipe or sleeve contains an outer cylinder and a missing inner cylinder. Their shared length means only the annular cross-sectional area changes.
Vmaterial = π(R² − r²)h
Here R is outer radius and r is inner radius. The result is wall material, not internal capacity. At R = 5 cm, r = 4 cm and h = 100 cm, material volume is 2,827.433388 cm³.
5 • Oblique cylinders
Tilting does not change volume
Cavalieri’s principle compares equal cross-sections at every perpendicular height. Sliding those circular layers sideways changes the silhouette, but not their area or total volume.
For the upright form, height follows the central axis and is perpendicular to the bases.
6 • Cone relationship
One cylinder holds three cones
For a cone and cylinder with identical base radius and height, the cone occupies one third of the cylinder. Move the slider to pour zero through three cone-volumes into the cylinder.
1.0 cone fills 33.3% of the cylinder.
7 • Sphere relationship
A sphere fills two thirds of its enclosing cylinder
The enclosing cylinder has the same radius and height 2r. Edit radius to verify the ratio at any scale.
Cylinder (h = 2r): 785.40
Sphere: 523.60
Sphere ÷ cylinder: 2/3
23 focused calculators and guides
Choose the measurements you actually have
Each page answers a distinct cylinder question, includes a checked example, limitations and relevant FAQs.
Clear answers
Frequently asked questions
What is the formula for cylinder volume?
For a solid circular cylinder, V = πr²h, where r is base radius and h is the perpendicular distance between the parallel bases.
Can I use diameter instead of radius?
Yes. Since r = d/2, the equivalent formula is V = πd²h/4. The main calculator links radius and diameter automatically.
Which height should an oblique cylinder use?
Use perpendicular height, not the sloping edge. Equal cross-sectional slices make its volume match a right cylinder with the same base and perpendicular height.
How is hollow-cylinder volume different?
Material volume subtracts the inner cylinder from the outer one: π(R² − r²)h. It is not the same as the capacity of the inner void.
Why are my units cubed?
Volume combines three length dimensions. If measurements are in centimetres, the result is cubic centimetres; this calculator can then convert it to litres, gallons and other volume units.
Does changing a unit change the physical size?
No. The main calculator converts the displayed value so the same physical dimension is preserved.
How accurate is the calculator?
The formulas use Math.PI and keep full floating-point precision internally. Real accuracy is limited by the measurements and how closely the object matches an ideal cylinder.
Is 1,000 cm³ exactly one litre?
Yes. 1,000 cubic centimetres equal one cubic decimetre, which is exactly one litre.
Are US and imperial gallons the same?
No. One US liquid gallon is 3.785411784 L; one imperial gallon is 4.54609 L. Both outputs are explicitly labelled.
How do I calculate a partly filled horizontal tank?
Use the circular-segment formula with internal radius, tank length and vertical liquid depth. The horizontal calculator includes the nonlinear fill graph.
Can surface area alone determine volume?
No. You also need an independent radius or height because many cylinders can share a surface area but have different volumes.
What happens if the inner radius equals the outer radius?
The material volume becomes zero. A larger inner radius is impossible and is rejected by the calculator.
Does the graph change the answer?
No. It visualizes how volume responds when one dimension varies while the others are held fixed.
Can I rely on this for engineering or safety decisions?
Use it as an educational and estimation tool. Verify dimensions, tolerances, vessel geometry and applicable standards with qualified sources for critical work.
Methodology
Transparent by design
All length inputs are converted to metres, formulas run at full JavaScript floating-point precision, and only the display is rounded. No measurement is invented when the given data are insufficient. Content and examples were reviewed on 2026-11-05; critical applications still require independent verification.
Read our methodology