A closed cylinder
For radius 2 and height 5, volume is 20π, lateral area is 20π, and closed surface area is 28π. One base contributes 4π square units.
Cylinder Calculator inputs
Changing the unit relabels the numbers. Convert measurements to one common unit before entering them.
Height is perpendicular to the circular bases. The surface options distinguish a sealed solid, an open-top vessel, and its curved wall. Positive measurements must be from 0.000000001 to 1,000,000,000; derived defining lengths must also remain in this range.
Calculated measurements
Volume
141.3716694 units³
| Measurement | Value |
|---|---|
| Volume | 141.3716694 units³ |
| Closed surface (two bases) | 150.7964474 units² |
| Open-top surface (one base) | 122.5221135 units² |
| Lateral surface (no bases) | 94.24777961 units² |
| One base area | 28.27433388 units² |
| Radius | 3 units |
Formula: V = πr²h; lateral = 2πrh; closed = 2πrh + 2πr²
A right circular cylinder. For internal capacity, enter internal dimensions; material thickness is not modeled.
Results use full floating-point precision internally and display up to 10 significant digits. Angles are in degrees.
Calculations run locally in your browser. Measurement values are not sent to a calculation service. The downloadable text contains your selected inputs and computed results.
How to use the Cylinder Calculator
- 01
Choose radius, diameter, or volume as the known size measurement.
- 02
Enter perpendicular height and use the same unit throughout.
- 03
Read capacity as cubic units and each surface result as square units.
- 04
Choose the surface total that matches your shape, then copy or download all results.
Examples
An open-top vessel
With the same radius 2 and height 5, the geometric surface with one base is 24π. This excludes a lid and does not include wall thickness or a rolled rim.
Recover radius from capacity
For height 10 and volume 90π, radius is 3. Enter the volume as a decimal, approximately 282.7433388 cubic units.
Height must be perpendicular to the bases
The cylinder model uses equal, parallel circular bases with the side wall perpendicular to them. Measure height along the cylinder’s central axis. A leaning or oblique cylinder needs different surface treatment; a pipe with an elliptical section is also outside this circular model.
Volume and inverse radius
One circular base has area πr², so volume is πr²h. If volume and height are known, the calculator rearranges this to r = √(V/(πh)). The height must stay positive. A volume measured in liters cannot be inserted directly beside a height in centimeters without converting to compatible cubic units.
Choose the right surface total
Unrolling the curved wall gives a rectangle with sides 2πr and h, so lateral area is 2πrh. Add one base for an open-top vessel or two for a sealed cylinder. Reporting all three totals helps prevent adding a circular lid that is absent from the object being modeled.
Dimensions versus usable capacity
External radius and height describe an external geometric envelope. Internal dimensions are needed for an approximate internal capacity. Bottom thickness, freeboard, fittings, and wall thickness affect a real vessel; the tool does not estimate those. Surface output is ideal area rather than a fabrication pattern with overlaps or material waste.
What to know
- Right circular cylinders only; no hollow walls, oblique ends, fittings, or allowances.
- All raw positive inputs use a 10⁻⁹–10⁹ numeric bound; the derived radius uses that length bound.
Common questions
Which result should I use for a label?
The lateral surface is the ideal curved wall area. A wraparound label may need extra overlap, margins, or clearance.
Can this calculate a hollow pipe?
It calculates a solid cylinder. A pipe needs outer and inner radii; subtract the two cylinder volumes for material volume, using equal heights.
Does diameter mode change the height?
No. Only the circular size input is divided by two to obtain radius; height remains your perpendicular measurement.
Why are liters not listed?
The unit selector uses compatible linear units and their squares or cubes. Convert a volume to the chosen cubic unit before entry.