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Echeveria should be repotted when roots start sprouting from the drainage holes or when you notice the plant is absorbing water too quickly (a sign the soil is saturated and compact). Usually this happens once a year, best done in spring when the plant starts growing again. If the pot is really tiny, you can wait until mid-spring to avoid stressing it while it's still dormant in winter.
For the actual repotting: get a pot only slightly larger (max 1-2 cm more in diameter), because echeveria doesn't like huge spaces where soil stays wet too long. Use a very well-draining mix, like succulent soil mixed with sand or perlite - it should be almost grainy. Take the plant out of the old pot, gently shake off the old soil from the roots, and position it in the center of the new container, filling in the gaps around it.
Important: don't water right after repotting, wait at least a week. The roots need to callus over after the trauma, and if you water too soon you risk rot. Make sure the new pot always has drainage holes - that's non-negotiable with succulents. After about ten days you can go back to your normal watering schedule.
How small exactly is the pot you have right now?
What the others are saying is right, but there's something that often gets overlooked: if the pot is really tiny (like 5-6 cm in diameter), it might not be that the plant is suffering because of the lack of space, but simply because a pot that small dries out and gets wet in a really uneven way. With succulents this is a pain. If you water and the soil doesn't have room to hold anything, either it dries out too fast or stays waterlogged in the middle. It's better to repot not when you see signs of stress, but when the plant has reached a reasonable size (maybe it has a few baby rosettes around the main one) so it "deserves" a more stable pot.
When you do it, be gentle with the roots - echeveria have pretty fragile roots - and use good succulent soil, ideally mixed with sand or perlite. Avoid regular garden soils that hold too much moisture. Then wait at least a week before watering after repotting, so any roots that get damaged during the process don't rot right away.
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