Solve a dimension
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 diameter of a 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.
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 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
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:
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.
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.
Where people go wrong
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.
Reading and converting your result
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.
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:
When this comes in handy
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
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.
Frequently asked questions
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.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.