Elliptical cylinder

Elliptical Cylinder Volume

An oval cross-section uses two semi-axes. Enter a, b and the height for the volume of an elliptical cylinder or oval tank.

Oval tanks and elliptical ducts need their own formula, and this elliptical cylinder volume provides it. Enter the two semi-axes and the height, and the oval base area is worked out and multiplied through for you.

The reason this shape earns a dedicated tool is that its two measurements are easy to get wrong. Confusing radius with diameter doubles your answer; mixing inches with centimetres throws it out completely. Keeping each measurement labelled, and letting the tool convert, removes both traps before they cost you.

The formula behind it

The volume of a elliptical cylinder is:

V = π a b h

A 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.

How to work it out

  1. Measure the two semi-axes a and b of the oval end.
  2. Measure the height (or length).
  3. The oval base area is π a b.
  4. Multiply by the height: V = π a b h.

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 if I have the diameter, not the radius?

Toggle the base input to diameter and the tool halves it for you. There is also a circumference option for when that is all you were able to measure.

How do I find a missing dimension?

If you know the volume you need and one measurement, the reverse-solver returns the height, radius or diameter that matches it.

Can I get the weight too?

Tick estimate weight, pick a material, and the calculator multiplies volume by density to show the mass in kilograms and pounds.

What will the volume be in gallons or litres?

You do not have to choose up front. The result lists litres, US gallons, Imperial gallons, cubic feet and more together, so you can switch the main unit whenever you like.

Common mistakes to avoid

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

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 oblique cylinder tank capacity. These related calculators pick up where this one leaves off:

Where people use this

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

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

Is the volume of a cylinder squared or cubed?
The result is in cubic units, because volume fills three dimensions. The radius is squared inside the formula only because it forms the flat circular base; multiplying by the height adds the third dimension.
Does this work for a tank or a pipe?
Yes. A solid tank uses the standard mode; for a pipe or tube use the hollow mode, which subtracts the bore. For a tank on its side, use the horizontal mode.
What is the formula for an elliptical cylinder?
V = π a b h, where a and b are the semi-axes (half the width and half the depth of the oval) and h is the height.
How is it different from a round cylinder?
A round cylinder is the special case where a = b = r. When the two semi-axes differ, the base is an oval and you multiply them together instead of squaring one radius.
What is the formula for the volume of a cylinder?
The volume is 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?
Either — just tell the calculator which you are entering. The radius is from the centre to the edge; the diameter is the full width across. The tool converts diameter to radius automatically.

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