Solve a dimension

Calculate Height of Cylinder

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 calculate height of cylinder 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.

How to work it out

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.

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 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).

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.

Follow-on questions, answered

The figure above is usually the start, not the finish. These are the questions that tend to come next, answered here so you do not have to run another search:

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.

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.

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

Common mistakes to avoid

Two things trip people up: squaring the wrong number, and forgetting that the answer is cubic. If a result looks four times too big or too small, you have probably swapped radius and diameter somewhere, so it is always worth re-reading the measurement you are least sure of. It also helps to glance at the equivalent units; if the litre and gallon figures are both off by the same factor, the input is the culprit, not the maths.

Getting the number in the unit you need

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.

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

The bottom line: with the radius or diameter and the height, the volume follows immediately, and the breakdown lets you hand the same number to anyone in the unit they prefer. Measure inside dimensions for anything that holds liquid, leave a little headspace at the top of a real container, and treat the geometric figure as a clean maximum rather than the final word on usable capacity.

Questions people ask

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.

What is the formula for the volume of a cylinder?

The volume is V = π r² h — the area of the circular base (π r²) multiplied by the height (h). If you have the diameter instead of the radius, halve it first: r = d ÷ 2.