Solve a dimension

Cylinder Diameter

Work backwards: enter the volume you need plus one dimension, and solve for the missing height, radius or diameter.

Sometimes you know the volume you need and have to find a dimension to match — the height of a tank to hold so many litres, say. This cylinder diameter rearranges V = π r² h for you and solves for the height, radius or diameter.

Design problems usually arrive back-to-front — the required volume is fixed, the space is constrained, and the missing measurement is what you actually need. Solving the formula for that unknown turns a trial-and-error job into a single step.

The formula behind it

The volume of a cylinder is:

h = V / (π r²) · r = √(V / π h)

A worked example

Worked example. Take a cylinder with a diameter of 15 cm (so a radius of 7.5 cm) and a height of 30 cm. The base area is π × 7.5² = 176.71 cm², and multiplying by the height gives a volume of about 5.30 litres (5,301 cm³ · 1.40 US gallons).

For anything that holds liquid, measure the inside of the cylinder — the wall takes up space that the contents cannot.

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

How the calculation works

Choose which dimension you need — height, radius or diameter.
Enter the target volume you want the cylinder to hold.
Enter the one dimension you already know.
The tool rearranges V = π r² h and solves for the rest.

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.

What people work out next

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

Which dimension can I solve for?

Height, radius or diameter. Pick one, enter the target volume and the dimension you already know, and the tool rearranges V = pi r squared h for the rest.

How tall must a tank be to hold a set amount?

Choose height, enter the volume in gallons or litres and the radius, and the answer is the height needed to reach that capacity.

How wide must it be for a fixed height?

Choose radius or diameter, enter the volume and the height, and the tool returns the width required to hold it.

Does it work in any unit?

Yes. Enter the target volume in gallons, litres or cubic feet and the known dimension in any length unit, and the solved dimension comes back in the length unit you pick.

Getting it right

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

One number, many units. Whatever you enter, the result lists the same volume as litres, US gallons, Imperial gallons, millilitres, cubic centimetres, cubic inches, cubic feet, cubic yards and cubic metres at the same time. You almost never have to convert by hand: read the figure in the unit your job uses and copy any of the others straight from the breakdown. If you need a shareable version, the copy-link button preserves your exact inputs so a colleague opens the page with the same calculation already filled in.

What to work out next

Once you have your answer you may also want to work in volume formula tank capacity cylinder volume. These related calculators pick up where this one leaves off:

Diameter of a Cylinder Diameter of a Cylinder Calculator Height of Cylinder Calculator Cylinder Height Calculator Height of a Cylinder Calculator Calculate Diameter of a Cylinder

Common uses

People reach for this in a range of situations:

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.

Frequently asked questions

Do I use radius or diameter?

Either — just tell the calculator which you are entering. The radius is from the centre to the edge; the diameter is the full width across. The tool converts diameter to radius automatically.

What units can I use?

Any of millimetres, centimetres, metres, inches, feet or yards for the measurements, and you can read the result in litres, gallons, cubic feet, cubic inches and more.

Is the volume of a cylinder squared or cubed?

The result is in cubic units, because volume fills three dimensions. The radius is squared inside the formula only because it forms the flat circular base; multiplying by the height adds the third dimension.

Does this work for a tank or a pipe?

Yes. A solid tank uses the standard mode; for a pipe or tube use the hollow mode, which subtracts the bore. For a tank on its side, use the horizontal mode.

How do I find the height of a cylinder from its volume?

Rearrange the formula: h = V ÷ (π r²). Enter the target volume and the radius above, and the height is solved for you.

How do I find the radius from volume and height?

Use r = √(V ÷ (π h)). The tool can also return the diameter, which is simply twice the radius.