Cylinder Volume Formula Using Diameter

How the volume is worked out

The volume of a cylinder is:

A worked example

Worked example. Take a cylinder with a diameter of 20 cm (so a radius of 10 cm) and a height of 40 cm. The base area is π × 10² = 314.16 cm², and multiplying by the height gives a volume of about 12.57 litres (12,566 cm³ · 3.32 US gallons).

Conversions use standard factors: 1 US gallon = 231 in³, 1 Imperial gallon = 4.54609 L, 1 litre = 1000 cm³.

How the calculation works

1. Measure across the circular end — the diameter or radius.
2. If you measured the diameter, halve it to get the radius r.
3. Square the radius and multiply by π to get the base area.
4. Multiply the base area by the height h: V = π r² h.
5. Convert the result into your preferred unit above.

Getting an accurate measurement

If you can only reach the top, measure the diameter across the opening and halve it. Keep every measurement in the same system, and let the tool convert between units for you.

Once the result is in

To save you a second search, here are the related answers people most often want straight after this calculation:

How do I rearrange it to find the height?

Divide the volume by the base area: h = V divided by (pi r^2). To find a radius from a known volume and height, use r = the square root of V divided by (pi h). The reverse-solver does both for you.

What is the surface area, while I am here?

The total surface area of a closed cylinder is 2 pi r^2 + 2 pi r h — the two circular ends plus the curved side. It is a different quantity from volume, but it uses the very same two measurements.

Why is the radius squared?

Because the base is a circle, and a circle's area already needs r squared. Multiplying by the height then stretches that flat area into a solid, which is why the final unit is always cubic.

How does the diameter version work?

If you are given the diameter, use V = pi (d/2)^2 h, which is the same as pi d^2 h divided by 4. Halving the diameter first is usually the cleaner route, and it is what the calculator does automatically.

Common mistakes to avoid

The commonest slip is using the diameter where the formula wants the radius, which on its own quadruples the base area. Close behind is mixing units, such as a radius in centimetres with a height in metres. Keep every length in the same unit, or let the tool convert, and double-check whether you measured to the centre or across the whole width. When a figure looks surprising, that width measurement is almost always where the problem is hiding, so re-read it first.

One result, every unit

Showing every unit at once is about speed and safety: you see the answer in litres, gallons and cubic feet side by side, so there is no chance of applying the wrong conversion factor. Change the output unit at the top to make any of them the headline figure, switch the precision to exact if you want the value in terms of pi, and use copy-result to paste a tidy summary wherever you need it.

Keep going

Once you have your answer you may also want to work in cylinder volume gallons litres & liters. These related calculators pick up where this one leaves off:

Where people use this

A few of the jobs it gets used for:

• Checking a geometry homework answer
• Sizing a barrel, drum or planter
• Estimating pipe or duct volume
• Planning a DIY water feature

To sum up, the whole job is two measurements and one formula. Enter them above, pick your unit, and you have an accurate figure plus every equivalent unit beside it. Keep a copy with the copy-result button, save the shareable link if someone else needs the same numbers, and use the history panel to compare a few options without starting from scratch.

Questions people ask