How to calculate the impermanent loss of uniswap V3?

According to a survey, 49% of uniswap V3 LPs are losing money. A lot of people are afraid of impermanent loss while providing AMM liquidity, especially uniswap V3 amplifies the impermanent loss. However, most people do not know how to calculate the impermanent loss of uniswap V3. Now let’s deduce in detail how to calculate this:
V3 LP satisfies:

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https://preview.redd.it/adhv2dv0vz391.png?252&format=png&auto=webp&s=7d21c249404898d7a083cd3c3906082fc8444780

Then the price satisfies:

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https://preview.redd.it/0he7gt62vz391.png?586&format=png&auto=webp&s=6337e6be3caa6a32261eadc472f0b0dfde4d548c

Obtained from the above solution:

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https://preview.redd.it/62sts2f3vz391.png?167&format=png&auto=webp&s=9b69b7dc4eb28460c83e1c8d17c97000281fcf5b

Assuming liquidity L is set within the price range of (Pa, Pb) at p0,
Then at Pn, only the market value of just holding:

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https://preview.redd.it/g893y0p4vz391.png?329&format=png&auto=webp&s=22f55e3d47ce89a668668672698e9cda503fd5fb

Then the value of the position of V3:

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https://preview.redd.it/uxo9efn6vz391.png?281&format=png&auto=webp&s=8c473e3f0af56e3dcd6b9864643c88a628b37fdf

Then the impermanent loss of V3:

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https://preview.redd.it/f8l7efr7vz391.png?431&format=png&auto=webp&s=03acf47b61a1ada18bc87f7df87ae5c8eed20a79

if you worried about impermanent loss, you can try X3 protocal providing an unique zero impermanent loss solution by providing single-sided AMM liquidity.

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https://preview.redd.it/eub98o5avz391.png?700&format=png&auto=webp&s=294e2471e96dd14360df26b0c21d8fe4946b98bb

https://x3finance.medium.com/how-to-calculate-the-impermanent-loss-of-uniswap-v3-98d2a3dc370b