Volume formula
Find Volume Formula
The cylinder volume formula, what each symbol means, and a worked example you can copy — plus a live calculator to check your own numbers.
The volume of a right circular cylinder is V = π r² h: the area of the circular base, π r², multiplied by the height. This page explains where that comes from, works through an example, and gives you a live tool so you can check any set of numbers against the find volume formula.
The formula looks abstract until you connect each symbol to something you can point at: r is how far it is from the middle of the end to the edge, h is how tall it stands, and pi is the fixed number that ties any circle's width to its area. Once those click, the equation is just base area, stretched upward.
How the volume is worked out
The volume of a cylinder is:
V = π r² hA 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.
How to work it out
- Measure across the circular end — the diameter or radius.
- If you measured the diameter, halve it to get the radius r.
- Square the radius and multiply by π to get the base area.
- Multiply the base area by the height h: V = π r² h.
- Convert the result into your preferred unit above.
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.
Once the result is in
To save you a second search, here are the related answers people most often want straight after this calculation:
What is the surface area, while I am here?
The total surface area of a closed cylinder is 2 pi r^2 + 2 pi r h — the two circular ends plus the curved side. It is a different quantity from volume, but it uses the very same two measurements.
Why is the radius squared?
Because the base is a circle, and a circle's area already needs r squared. Multiplying by the height then stretches that flat area into a solid, which is why the final unit is always cubic.
How does the diameter version work?
If you are given the diameter, use V = pi (d/2)^2 h, which is the same as pi d^2 h divided by 4. Halving the diameter first is usually the cleaner route, and it is what the calculator does automatically.
How do I rearrange it to find the height?
Divide the volume by the base area: h = V divided by (pi r^2). To find a radius from a known volume and height, use r = the square root of V divided by (pi h). The reverse-solver does both for you.
What to watch out for
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
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 cylinder volume gallons litres & liters. These related calculators pick up where this one leaves off:
Where people use this
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.
Good to know
What units can I use?
Is the volume of a cylinder squared or cubed?
Does this work for a tank or a pipe?
What is the cylinder volume formula?
V = π r² h. Using diameter, it becomes V = π (d/2)² h, which is the same as V = π d² h ÷ 4.