Comprehensive Calculator Guide
A cylinder's volume is π × radius² × height. A round water tank 1.2 m across (0.6 m radius) and 1.5 m tall holds about 1.7 m³, roughly 1,696 litres. Enter the radius and height in any unit to get the volume and surface area, and show the volume directly in litres.
The formula
A cylinder is a circle stretched along its height, so V = πr²h. For the tank: π × 60² × 150 = 1,696,460 cm³, which is about 1,696 litres. Pick units for each input and the result, and the calculator converts.
The classic mistake is using the diameter instead of the radius. Because the radius is squared, that makes the answer four times too big. If you only know the circumference, r = C ÷ 2π.
Surface area, tanks and pipes
Total surface area is 2πr(r + h): the curved side 2πrh plus both ends. For an open-top tank, subtract one end, πr². A pipe is a long cylinder: one with a 10 cm bore and 6 m length holds about 47 litres. A horizontal tank's full volume uses the same formula with its length as height, but a partly filled one needs a different calculation.
How to Use
- 01Enter the radius (half the diameter) and its unit.
- 02Enter the height or length and its unit.
- 03Choose the units you want for volume, such as litres, and for surface area.
- 04Read both results; they update as you type.
Formula Used
Volume = π × r² × h | Total surface area = 2π × r × (r + h)Practical Examples
Example 1: water tank
Radius 60 cm, height 150 cm: 1,696,460 cm³, about 1,696 litres.
Example 2: water pipe
Radius 5 cm, length 6 m: 47,124 cm³, about 47 litres.
Example 3: a can
Radius 3 cm, height 10 cm: 282.7 cm³, about 283 mL, with 245 cm² of surface.
Important Tips
- Measure the circumference and divide by 2π if you cannot reach across.
- Use inside dimensions for tank capacity.
Common Mistakes to Avoid
- Entering the diameter as the radius, which quadruples the volume.
- Using this formula for a partly filled horizontal tank.
Frequently Asked Questions
- How do I calculate a cylinder's volume?
- Multiply π by the radius squared and by the height: radius 10 cm and height 20 cm give 6,283 cm³.
- How do I get a round tank's capacity in litres?
- Divide the volume in cm³ by 1,000, or choose litres as the result unit.
- How do I find the radius from the circumference?
- Divide it by 2π, about 6.2832: 3.77 m gives 0.6 m.
- What is the lateral surface area?
- 2πrh, the curved side only. Add 2πr² for both ends.