Cylinder Calculator
Calculate the volume, lateral surface area, total surface area, and base area of a cylinder from its radius and height.
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How to use this calculator
Cylinder volume is the base circle area times height. Lateral surface area is the rectangle formed by "unrolling" the curved wall: width = circumference = 2πr, height = h.
- 1
Enter the base radius r (half the diameter of the circular end).
- 2
Enter the height h (length of the cylinder from one circular end to the other).
- 3
Volume, surface areas, and base circumference are displayed immediately.
Frequently asked questions
Does the calculator ask for radius or diameter?
Radius. If you measured across the circle, halve the diameter first. Entering a diameter by mistake multiplies the base area by 4, the volume by 4 and the curved surface area by 2, so the results can look plausible while being wrong.
What units are the results in?
Whatever you entered, with no conversion. Volume is in cubic units and the areas in square units. With radius and height in centimetres the volume is in cm³; dividing by 1000 converts cm³ to litres, so the 461.81412 cm³ for a 3.5 cm radius and 12 cm height is about 0.4618 L. Radius and height must use the same unit.
What is the difference between lateral and total surface area?
Lateral surface area is the curved wall only, 2πrh, and equals the area of the rectangle you get by unrolling the side. Total surface area adds the two circular ends, giving 2πrh + 2πr². For r = 4 and h = 10 the lateral area is 251.327412 and the total is 351.858377. An open tin without a lid needs the lateral area plus one base.
What is the space diagonal?
It is the longest straight line that fits inside the cylinder, from the rim of one end to the opposite point on the rim of the other: √((2r)² + h²). For r = 4 and h = 10 it is 12.806248. It matters for questions such as whether a rod of given length fits inside a can.
What happens if I enter zero or a negative number?
The calculator returns an error asking for a positive radius and height. A cylinder with a zero dimension has no volume, and a negative length has no physical meaning.
Does it handle hollow cylinders or pipes?
Not directly. For a pipe, calculate the outer cylinder and the inner cylinder separately using the same height and subtract the volumes. Surface areas of hollow shapes also need the inner wall and the ring-shaped ends, which this tool does not combine.
How precise are the results and is π approximated?
The calculation uses the full double-precision value of π from the browser, and the displayed numbers are rounded to six decimal places. A cylinder with radius 10 and height 10 returns a volume of 3141.592654, which is 1000π.
Cylinder calculator — volume, surface area, base and diagonal from radius and height
Formulas used
The base is a circle of area πr². Volume is that area times the height. The curved wall, unrolled, is a rectangle whose width is the base circumference 2πr and whose height is h, so its area is 2πrh. Total surface area adds the two bases. The calculator also gives the base circumference and the space diagonal.
| Quantity | Formula | Result |
|---|---|---|
| Volume | πr²h | 502.654825 |
| Total surface area | 2πr(r + h) | 351.858377 |
| Lateral surface area | 2πrh | 251.327412 |
| Base area | πr² | 50.265482 |
| Base circumference | 2πr | 25.132741 |
| Space diagonal | √((2r)² + h²) | 12.806248 |
Worked example: a can in centimetres
A can with radius 3.5 cm and height 12 cm has a volume of 461.81412 cm³, a base area of 38.48451 cm² and a lateral area of 263.893783 cm². Its total surface area is 340.862803 cm², the amount of metal needed if you ignore seams and overlaps. Dividing the volume by 1000 gives roughly 0.46 litres.
Worked example: a clean result in terms of π
With radius 10 and height 10, the volume is 3141.592654, which is 1000π, and the total surface area is 1256.637061, which is 400π. Recognising multiples of π is a quick way to sanity-check an answer. The space diagonal is 22.36068, or 10√5. A smaller case, radius 0.5 and height 2, gives a volume of 1.570796 and a total surface area of 7.853982.
Using the numbers
Volume answers capacity questions: how much liquid a tank holds, how much concrete a round column needs, how much soil fills a planter. Surface area answers coverage questions such as paint, insulation wrap or label size. For a label that wraps around the side, the lateral area is the useful figure, and its width is the base circumference. Capacity is for the inside dimensions, so use internal radius and height if wall thickness matters.
Common mistakes
The most frequent errors are entering the diameter as the radius, mixing units such as a radius in centimetres with a height in metres, and forgetting that area values are squared units. Check the units of your inputs before reading the output, and remember the calculator performs no conversion on your behalf.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →