Volume Equation for Cylinder

The formula behind it

The volume of a cylinder is:

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).

Conversions use standard factors: 1 US gallon = 231 in³, 1 Imperial gallon = 4.54609 L, 1 litre = 1000 cm³.

Using the calculator

1. Measure across the circular end — the diameter or radius.
2. If you measured the diameter, halve it to get the radius r.
3. Square the radius and multiply by π to get the base area.
4. Multiply the base area by the height h: V = π r² h.
5. 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

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 mistakes to avoid

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.

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:

Common uses

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

In short: measure the width and the height, keep them in the same unit, and the tool turns them into a volume you can read in litres, gallons, cubic feet or anything else, with the working shown so you can trust it. If a result ever looks off, re-enter the measurement you are least sure of, or switch to the diameter input and let the tool halve it for you, which catches the most common error before it matters.

Good to know