NOTE: see
v2.0 of this post. (25.04.2017)
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It's a common question so I thought I'd write a post about it.
The highest capacity cups are the large Fleurcup, Yuuki and the XL Meluna. They all hold about 30 ml (to the holes) and different sources have different info on which one holds most.
Nowadays there are a few more high capacity cups. If your flow is extremely heavy (changing disposables every 1-2 hours), I recommend you to try out one of these ones. It seems like many of those with a heavy flow end up trying more than one before finding the one that they can wear longest. Please note: if you have a fairly heavy flow but not "gushing", there's a variety of other cups that might also fit you very well and still hold enough.
The info on stiffness is as per
this chart. See also: the pros and cons of soft/stiff cups (in the comments over there),
a poll on stiffness and leaks,
advice on making soft cups pop open,
a guide to understanding the cervix.
XL Meluna
Dimensions: 47x56, total length up to 71 mm
Stiffness: three options
Advantages/disadvantages: as with any cup, most features are advantages for some and disadvantages for others. It's one of the longest cups and it comes with a variety of stems - all of which are pretty short, 15 mm or less. You *probably* shouldn't get this one if you can reach your cervix fairly easily.
(see photos here) Femmycycle
Dimensions: 40x50, total length 68 mm
Stiffness: pretty soft (1.7). The company claims that due to the softness it is less durable than other cups and should be replaced every year
Advantages/disadvantages: It's a unique cup with an anti-spill design. It's certainly worth a try if you are struggling to find a cup that would match your heavy flow. It is soft and has a ring stem, larger than the one Meluna offers. You *probably* shouldn't get this one if you can reach your cervix fairly easily, especially if you haven't tried a cup yet.
(see photos here) Large Yuuki
Dimensions: 46x56, total length 74 mm
Stiffness: stiff (rated as 8.5). Used to be very soft and you can probably still find an old one but obviously it'll be more and more difficult as time passes.
Advantages/disadvantages: It's also one of the longest cups. It has a tube stem which is longer than the stem of the XL Meluna. Again, it might not be the best choice if you have a low cervix. Get this one if you want a long, stiff cup.
(see photos here) Large Fleurcup
Dimensions: 46x52, total length 70 mm
Stiffness: soft (rated as 2). Used to be stiffer, you might still be able to find an older one.
Advantages/disadvantages: If you can reach your cervix easily or fairly easily, this is the best choice. Note that your cup doesn't have to be shorter than the distance to your cervix - if you have a very heavy flow and a low cervix, better try this one instead of getting one of the highest capacity small sizes (narrow cups might sit lower too). Of course you can also get it if you have a high cervix - especially if you think the stem will be convenient for you.
A possible disadvantage is that if your cervix sits in the cup, the capacity might be reduced less with a longer cup - if you can accomodate one.
(see photos here) NOTE: if your cup starts leaking when it's half-full, the best options are a large Fleurcup, an XL Meluna or a Femmycycle cup.
If you can't reach your cervix, choose the stiffness and see the photos to decide which stem you like most (and consider the unique Femmycycle cup). If you can reach your cervix fairly easily, get a large Fleurcup. (again, this is for the folks with an extremely heavy flow! if yours is "just" heavy, consider other options too)
Also please note that I haven't used any of these cups myself. If you have any questions about a specific cup, ask them in the community itself.
This post will be updated if changes are made to one of these cups or if another high capacity cup appears on the market.
DONE Please note: if you want to suggest a cup, find out whether it holds around 30 ml to the holes and/or post links to any specific entries/comments from folks with an extremely heavy flow.