This calculator computes the full geometry of a right circular cylinder from its radius and height. Enter those two values and it returns the volume, total surface area, and the lateral (curved) and base areas. It is useful for sizing tanks, pipes, cans and any cylindrical container — keep your units consistent and read all results instantly.
How it works
From the radius (r) and height (h), the tool applies the standard cylinder formulas using full-precision π:
| Quantity | Formula |
|---|---|
| Volume | π · r² · h |
| Base area (one end) | π · r² |
| Lateral surface area | 2 · π · r · h |
| Total surface area | 2 · π · r · h + 2 · π · r² = 2 · π · r · (r + h) |
The lateral area is the curved wall; the total area adds both circular ends.
Example
A cylinder with radius 3 and height 10:
volume = π · 3² · 10 = 90π ≈ 282.743 lateral area = 2π · 3 · 10 = 60π ≈ 188.496 total area = 60π + 18π = 78π ≈ 245.044
So this cylinder holds about 282.74 cubic units and has a total surface area of about 245.04 square units.
When to use which result
Volume is what you need when sizing a tank (how much liquid does it hold?), calculating material fill for a cylindrical casting, or working out the capacity of a pipe section. Keep units consistent: if radius is in centimetres and height is in centimetres, the volume is in cubic centimetres.
Lateral surface area is the curved wall only — the outside of a can without the lid and base. Use it when calculating paint coverage for a round column, the surface area of a pipe for insulation, or the label area on a cylindrical container.
Total surface area adds both flat circular ends to the lateral area. This is what you need for wrapping, coating, or painting the entire outer surface, including the top and bottom — for example, estimating how much material to fabricate a closed cylindrical vessel.
Practical notes on units
The calculator uses whatever units you enter for radius and height. For real-world problems, make sure both inputs use the same unit before you start. Common conversions:
- 1 metre = 100 cm = 1,000 mm
- To convert cubic centimetres to litres, divide by 1,000
- To convert cubic metres to litres, multiply by 1,000
For a cylindrical water tank where radius is 0.5 m and height is 1.2 m, for example, the volume is π × 0.5² × 1.2 ≈ 0.942 m³, which equals about 942 litres. Enter the numbers directly and the tool returns the result instantly.