How are deposit amounts calculated on Uniswap?

Is there a mathematical formula for calculating deposit amounts in Uniswap’s V3? I was trying to add liquidity to the USDC/ETH pair but couldn’t make sense of the deposit amounts for different price ranges.

Assuming a current price of about $1950/ETH, the deposit requirements for USDC increase (significantly) when I decrease the lower bound of my price range and likewise the USDC deposit amount decreases when I increase the upper bound of my price range? This is assuming I keep my ETH deposit amount fixed at, say, 1 ETH.

I tried looking all over for a formula explaining this relationship but couldn’t make sense of it.

What do you think?

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  1. To oversimplify the concepts a bit, 1. the rarer something is, the more expensive it becomes. And 2. once you have 100% of a token, your price limit is reached.

    So if you put in $1950 and 1ETH, you would have a 1:1 ratio of USDC and ETH. and your upper and lower price ranges would be about equal. For simplicity let’s say your price range is $1000/ETH – $4000/ETH at this ratio

    If you were to put in $3900 USDC and 1ETH at $1950/ETH, then you would have a 2:1 ratio of USDC and ETH, or 67%USDC 33%ETH.

    So if you want to keep your lower limit of $1000/ETH, then you would have less ETH to keep your pool in range if people start buying ETH. So you need to lower your upper limit so you have something like $1000/ETH – $2500/ETH.

    Or conversely, if you want to keep the upper limit of $4000/ETH, you can think of it like you have more USDC to sustain your pool if people start swapping ETH for USDC, so you can lower your lower limit to $250/ETH – $4000/ETH

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