The V3 calculators follow the math presented from the Uniswap whitepaper. We designed the estimations to be based on previous volume data and use the same math that the smart contracts of the pools use.

You can see the breakdown of how it works here. 👇

Calculation Breakdown

1. Calculate deposit amount of token0 and token1

• Refer to Uniswap V3 Whitepaper (Formula: 6.29, 6.30, P.8), we can calculate total amount of each token by using these formulas: (if il <= ic < iu; where il = lowerTickId, ic = currentTickId, iu = upperTickId, Pl = lower price, Pu = upper price)

  • deltaY = deltaL * (sqrt(P) - sqrt(Pl))
  • deltaX = deltaL * (1 / sqrt(P) - 1 / sqrt(Pu))

• For estimation of the amount of token0 (deltaX) and token1 (deltaY) we need to know deltaL that make:

  • deltaY * priceUSDY + deltaX * priceUSDX = depositAmountUSD

• So we can write a equation like this:

  • deltaL * (sqrt(P) - sqrt(Pl)) * priceUSDY + deltaL * (1 / sqrt(P) - 1 / sqrt(Pu)) * priceUSDX = depositAmountUSD
  • Then: deltaL = depositAmountUSD / ((sqrt(P) - sqrt(Pl)) * priceUSDY + (1 / sqrt(P) - 1 / sqrt(Pu)) * priceUSDX)

• After we've calculated deltaL, we can calculate deltaX and deltaY using these formulas mentioned in Uniswap v3 Whitepaper

  • deltaY = deltaL * (sqrt(P) - sqrt(Pl)) (Formula: 6.29, P.8)
  • deltaX = deltaL * (1 / sqrt(P) - 1 / sqrt(Pu)) (Formula: 6.30, P.8)

2. Calculate estimated fee

• Estimated fee (daily) can be calculated by this equation:

  • fee = feeTier * volume24H * (deltaL / (L + deltaL)) where:

    • volume24H = average of 24h volume from [currentDay - 7, currentDay - 1]

    • L = total liquidity (cumulative of liquidityNet from all ticks that il <= ic)

    • deltaL = delta liquidity, can be calculated from:

      • liquidityAmount0 = amount0 * (sqrt(pu) * sqrt(pl)) / (sqrt(pu) - sqrt(pl))

      • liquidityAmount1 = amount1 / (sqrt(pu) - sqrt(pl))

      • if ic < il; deltaL = liquidityAmount0

      • if ic > iu; deltaL = liquidityAmount1

      • if ic >= il && ic <= iu; deltaL = min(liquidityAmount0, liquidityAmount1)

Check out this video and blog post to learn more about providing liquidity and how to calculate fees. We even offer a full video course on how to make moeny liquidity providing.

Poolfish was previously called Uniswap.fish and received a couple of grants from the Uniswap Foundation as well as GitCoin.

Let us know if you have any questions! You can always contact us.