Solve a dimension
Diameter of a Cylinder Calculator
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 diameter of a cylinder calculator 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.
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 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 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.
What people work out next
Most jobs need one or two more things once the volume lands. The common follow-ups, with the numbers you need, are below:
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.
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
Because volume units are where most errors creep in, the tool does the converting for you. Enter your measurements once and every common unit appears together, from millilitres up to cubic metres and across to US and Imperial gallons. Pick whichever the task calls for and lift the rest from the list; nothing needs a second calculation. The result also updates live as you change a measurement, so you can compare two sizes quickly without starting over.
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:
When this comes in handy
It comes in handy across quite different tasks:
- 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
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.Do I use radius or diameter?
What units can I use?
Is the volume of a cylinder squared or cubed?
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.