If you choose to carry a cordelette, the first questions are: what diameter, and how long?
For snow climbing or glacier travel, consider 4 meters of 6 mm cord.
For rock climbing, consider 5 to 7 meters of 7 mm cord.
6 mm cord is dramatically less strong than 7 mm. But, on snow or lower angle alpine ice, you can build anchors usually pretty much wherever you want to, and usually the impact of a fall is going to be fairly low. Because of this, you can probably use a shorter, smaller diameter cord.
On rock, it’s the opposite. You’re going to have potentially higher impacts on the anchor, and your placements have to align with what the rock offers you and the gear you have left, which means they may be farther apart. Both of these point to using a longer, larger diameter cord.
Cord strength (a kilonewton is a metric unit of force, equal to about 220 pounds)
5mm - 5.5 kN
6mm - 7.5 Kn
7mm - 13 kN
Look at that jump in strength going from 6mm to 7mm! For me, that’s a pretty compelling reason to use 7 mm cord for rock climbing. But hey, don't take my word for it, keep on reading for more expert opinion.
Try tying it “bunny ears” style, with a small figure 8 or overhand loop in each end, rather than the standard configuration of one big loop. Because the bunny ears style gives you a wider reach, you may find you can get away with a shorter length cordelette. But try climbing on the slightly longer cord for a while and see what you like. (You can always cut off a meter if you think it’s too long, but you definitely can’t add one back on.)
Expert climber Steph Davis address the cord diameter issue on her blog, by consult with an expert from Mammut. He says to always use 7 mm cord. (Bold text below is mine,)
“Although some climbers may use cord thinner than 7mm for constructing belay anchors, it is important to note just how much stronger the slings and 7mm cord are in comparison, especially when you consider that these are often weakened by knotting them and by concentrated wear at the knots.
We definitely do not advise people to use 5 and 6mm cord for anchor construction, and if climbers choose to do so they should be acutely aware that they are putting themselves at extra risk by doing so and take any necessary precautions (frequent wear-checks, being extra conservative in deciding what is worn and discarding it, always placing protection specifically to protect the belay from high impact, using a dynamic belay device and techniques, terrain and belay location choices, etc).
A calculated risk may be acceptable to some people if it is truly calculated, but done out of ignorance or by guesswork it is asking for trouble. Because most people aren’t willing or able to objectively test these out for themselves to see what their true level of safety (or lack thereof) is, if a nylon cord is used I’d strongly recommend using 7mm for anchor construction, and if the weight and bulk is a significant problem using a Contact sling with a 22kn breaking strength, remembering to tie into the anchor with the rope.”
Dave Furman, Hardgoods Category Manager, Mammut Sports Group, USA and Canada