Volume formula
Volume Calculation Formula for Cylinder
The cylinder volume formula, what each symbol means, and a worked example you can copy — plus a live calculator to check your own numbers.
There is really only one formula to remember, and this page makes the volume calculation formula for cylinder stick. You will see the equation, what each letter stands for, the diameter version, and a worked example — then a calculator to try it yourself.
What makes this worth truly understanding, rather than just plugging into, is that every related shape is a small variation on it — halve it, subtract an inner tube, swap the circle for an oval — so learning the one formula quietly unlocks all of them.
Using the calculator
- 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.
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 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.
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:
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.
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
Getting it right
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.
Reading and converting your result
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.
Related things you might need
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:
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
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.