Solve a dimension
Calculate Diameter of a 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 diameter of a cylinder rearranges V = π r² h for you and solves for the height, radius or diameter.
Working backwards is surprisingly common: you know the capacity you need and one dimension you are stuck with, and you have to find the rest. Rearranging the volume formula does the job, and it is far quicker than guessing dimensions and re-checking the volume each time.
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.
The maths in one line
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 10 cm (so a radius of 5 cm) and a height of 25 cm. The base area is π × 5² = 78.54 cm², and multiplying by the height gives a volume of about 1.96 litres (1,963 cm³ · 0.52 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.
Once the result is in
Most jobs need one or two more things once the volume lands. The common follow-ups, with the numbers you need, are below:
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.
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
Where people go wrong
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.
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 volume formula tank capacity cylinder volume. These related calculators pick up where this one leaves off:
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
Does this work for a tank or a pipe?
How do I find the height of a cylinder from its volume?
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?
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?
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.