Uniswap Liquidity Calculation issue on Arbitrum Chain

zhangyuting 0
Viewed 37

According to the "Liqudity Math in uniswap v3", the liqudity of a position should be:

L = amt0 * (sqrt(upper) * sqrt(cprice)) / (sqrt(upper) - sqrt(cprice))
or
L = amt1 / (sqrt(cprice) - sqrt(lower))

I tried to calculate the liquidity of the below position on Arbitrum: enter image description here The nft token ID of the position is 69171, so I can get the liqudity by calling the contract(0xC36442b4a4522E871399CD717aBDD847Ab11FE88) on https://arbiscan.io enter image description here You can see it shows the liqudity is 50242219347523, and we can do more unit convertion:

enter image description here Now I try to calcuate this number with the uniswap V3 math: enter image description here This is the output: enter image description here As we can see, the code output is very similar to the contract output, but if we look carefully, we will find the unit seems to be different. I know the unit of the contract ouput should be 'wei', but I don't know what the unit of the code results is. Can anybody help? Thanks.

uniswap
1 Answers

I checked that position and pool. Best to query the current price from the pool's contract, for quick look the UI can be found at https://info.uniswap.org/#/arbitrum/pools/0x2f5e87c9312fa29aed5c179e456625d79015299c

The current price is shown as 11.9011 ETH per BTC, and there are 0.3122 BTC and 1.466 ETH in the pool. This gives:

price = 11.9011 * (1e18 / 1e8)
x = 0.3122 * 1e8
y = 1.466 * 1e18

The tick range of the position No. 69171 is 253300 to 259900. Use these values to calculate sp = sqrt(price) and the square roots of the price range boundaries, and from them, the liquidity:

sp = price ** 0.5
sa = 1.0001 ** (253300 // 2)
sb = 1.0001 ** (259900 // 2)
Lx = x * sp * sb / (sb - sp)
Ly = y / (sp - sa)
L = min(Lx, Ly)

The result Lx is 49905251975363.266 and Ly is 51071435112054.96. The Etherscan info shows liquidity L=50242219347523, in between these two values, which have a few % difference. A few % is an acceptable error given the imprecise input values used in this calculation; the UI shows the price and amount values in a rounded format.

kfx0
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