If yes, how much is it?
I have two pieces, one giant one small.
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Every decent rail station in Russia has a luggage storage room. Yekaterinburg is one of the largest Russian cities, so it definitely does have one. However, finding it might sometimes be non-obvious. Look for signs saying "камера хранения" (kamera khraneniya), they usually have a stylized picture of a suitcase, or ask someone. There may even be several storage rooms, in such a case make sure you remember in which you left your luggage.
Most probably it will be a big room somewhere in the basement with a strong guy or two taking your luggage and giving you a receipt. When you come back, you give a receipt back and they give you the luggage. In such a setting, the price usually does not depend on the size of a luggage piece; that is, leaving two small bags will be twice as expensive as leaving twice as big bag. Bags that are really uncommonly large can be denied.
The price per 24 hours should be something between 100 and 400 rubles, but it may be rather odd, up to some kopecks. Sometimes a different rate may be applied for shorter terms, but sometimes you have to pay for 24h even if you leave the luggage for 1 hour only. This 24 hours may be either midnight-to-midnight, either exact 24 hours since the moment you leave your luggage; better find this out in advance.
Such storage rooms might have some short periods of time when they are closed. Make sure you know the schedule (it is usually displayed near the room) before you leave bags, so that when you come to get your luggage, you do not find the room closed.
Several rail stations in Russia have also automated storage rooms, but these are rather uncommon. These are big rooms filled with automatic deposit boxes. You buy a special coin or a card from an attendant at the entrance, then find a free box, put your belongings there and lock it. You might see old soviet-style boxes with mechanical locks where you set a 4-digit code, lock it, then come back and open it with that code; or you might see modern ones where you use a plastic card to open/close the box. Make sure you remember the number of your box, as it is very easy to get lost there. Also make sure you know what is the maximal amount of time you can store your luggage there. Maybe you need to know this time in advance and tell it to the attendant at the entrance when you buy a coin or a card, and therefore pay in advance.
In such automatic boxes you pay for one box, independend on the number of luggage items you put there. The boxes are usually rather spacious, although unusually big suitcases might not fit in, and then you are out of luck.
Note also that both in manned and automatic storage rooms you most probably be charged anew each time you take your luggage out. Make sure you take out everything that you might need while you go around the city, because if you come back and say: "oh, I forgot to take out something", they will charge you for one more period.
Also, it is a good idea not to leave anything really valuable in the luggage. I have not heard much of anything stolen at these rooms, but better safe than sorry.