Vessel Capacity Calculator
Interior volume of a straight or tapered pot in millilitres and fluid ounces, with the average-diameter shortcut measured against the real thing.
Measure to the fill line rather than the rim — nobody fills a mug to the brim, and a glaze line or a curve near the top will move the answer. A curved profile is not a straight taper either; for those, measuring water in is the honest method. Nothing is uploaded.
The average-diameter shortcut always understates
A tapered vessel is a cone frustum, and its volume carries a cross term the average-diameter cylinder drops. Working the algebra through, the difference is exactly πh(r₁−r₂)²⁄12 — a square, so it is never negative. The shortcut cannot overstate a volume; it can only understate it, and it is exact only when there is no taper at all.
| Vessel | Frustum | Average-diameter | Understated by | Holds |
|---|---|---|---|---|
| Mug, nearly straight | 574.9 mL | 572.6 mL | 2.36 mL | 19.4 fl oz |
| Tumbler, flared | 659.7 mL | 636.2 mL | 23.56 mL | 22.3 fl oz |
| Cylinder, no taper | 785.4 mL | 785.4 mL | exact | 26.6 fl oz |
| Bowl, strong flare | 914.2 mL | 850.6 mL | 63.62 mL | 30.9 fl oz |
Which gives a usable rule: for a nearly straight mug the shortcut is worth a couple of millilitres and you can ignore it. For the flared bowl it is 63.6 mL — 2.2 fluid ounces on a piece that holds 30.9. The gap grows with the square of the taper, so doubling the flare quadruples the error.
Wall thickness is not a small correction
Wall thickness comes off both sides of a diameter, so a 10 cm mug thrown at
8 mm walls has a 8.4 cm bore — a
16% cut in diameter. But volume goes with the square of
the radius, so that is not a 16% correction to the capacity. It is
29%: 707 mL measured
outside against 499 mL of usable space.
This is why a mug that looks generous on the shelf can hold less than a thinner-walled one
the same size, and why measuring a finished pot from the outside will always flatter it. If
you have the pot in your hands, the honest method is to weigh the water it takes: a millilitre
is a gram, so the scale gives you the answer with no geometry at all.
How to use
- Measure the interior diameters at the bottom and the fill line.
- Measure the height to the fill line.
- Add a wall thickness if you measured the outside.
- Read the capacity in millilitres and ounces.
Frequently asked questions
Can I just use the average diameter?
It always understates, and by a known amount. A tapered vessel is a cone frustum whose volume carries a cross term the average-diameter cylinder drops, and the difference works out to exactly pi times height times the squared difference in radii, over twelve. Being a square, it can never go the other way.
How much does that actually matter?
Depends on the flare. On a nearly straight mug it is a couple of millilitres and you can ignore it. On a bowl running 5 cm at the foot to 14 cm at the rim, it is 63.6 mL — over two fluid ounces on a piece that holds thirty-one. The gap grows with the square of the taper, so doubling the flare quadruples the error.
Do I measure inside or outside?
Inside, and it matters more than it sounds. Wall thickness comes off both sides of a diameter, so 8 mm walls take 16 mm off a 10 cm mug — and since volume goes with the square of the radius, that removes about 30% of the capacity rather than 16%.
Where should I measure the height to?
The fill line, not the rim. Nobody fills a mug to the brim, and a glaze line or a curve near the top will move the answer more than the arithmetic will.
What about a curved profile?
This models a straight taper between two diameters. A belly or a strong curve is neither, and for those the honest method is water: fill the pot from a measuring jug, or weigh the water it takes, since a millilitre is a gram.
Why does my mug hold less than one the same size?
Usually wall thickness. A heavily-walled mug looks generous on the shelf and holds noticeably less than a thinner one of the same outside dimensions, because the bore is what counts and it shrinks twice as fast as the wall grows.
What is a standard mug size?
Commonly 10 to 12 fluid ounces for everyday use and 14 to 16 for a large one, but it is worth deciding from the vessel rather than the label — measure a mug you already like and work back to the dimensions.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.