How to use the cylinder calculator
- Enter the Radius of the circular end.
- Enter the Height, the distance between the two ends.
- Read Volume (πr²h), then Base area (πr²), Lateral surface (2πrh) and Total surface (2πr(r + h)).
What it does and when to use it
Cylinders are everywhere: water tanks, cans, pipes, candles, round cake tins, drums and columns. The volume tells you how much a tank or tin holds. The lateral surface tells you how big a label, wrap or insulation sheet must be. The total surface is what you would paint or cover on a closed container. The base area is handy for working out how much floor a tank takes up or how deep water will be for a given volume.
For a part with a pointed top, the cone calculator works the same way. The volume calculator can show litres directly, and the surface area calculator covers other solids.
How it works
With radius r and height h:
- Base area: πr²
- Volume: V = πr²h (the base area stacked h high)
- Lateral surface: 2πrh (unroll the side and it becomes a rectangle 2πr long and h high)
- Total surface: 2πr² + 2πrh = 2πr(r + h)
Worked examples
A cake tin, step by step. Radius 5 cm, height 20 cm.
- Base area: π × 5² = 25π = 78.53981634 cm².
- Volume: base area × height = 78.53981634 × 20 = 1,570.796327 cm³.
- Side: 2 × π × 5 × 20 = 628.3185307 cm².
- Total surface: 2 × 78.53981634 + 628.3185307 = 785.3981634 cm².
The tool shows Volume (πr²h): 1,570.796327, about 1.57 litres, and Lateral surface (2πrh): 628.3185307 for a band of baking paper around the inside.
A small tank in metres. Radius 0.5 m and height 2 m give a volume of 1.570796327 m³ (about 1,571 litres) and Total surface (2πr(r + h)): 7.853981634 m² to paint, top and bottom included.
Limits and tips
- Radius and height must be greater than zero.
- There is no unit menu. Keep both inputs in the same unit; areas come out squared and volume cubed.
- Wall thickness is ignored. For the inside capacity of a thick-walled container, measure the inner radius and depth.
- Runs in your browser.
Frequently asked questions
How do I turn the volume into litres?
Which surface figure do I need for a label or a pipe?
Does it work for a cylinder lying on its side?
What if I know the diameter?
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