Virtual and Real Reserves in Uniswap v3

This is great question. what are the real reserves and virtual reserves ?

The liquidity in Uniswap v3 is allocated within a custom price range.

x: The amount of x token

y:The amount of y token

L²: Liqudity

P= y/x ( This is price of x)

x*y=L²

Some boring math:

x*x*P=L²

x=L / sqrt(P) [ This is x]

y/P * y=L²

y= L * sqrt(P) [ This is y]

The liquidity was distributed uniformly along the price curve between 0 and infinity in Uniswap v1 and v2.

Virtual Reserves

We understand that liquidity is allocated within a custom price range. We called it “real reserves” . Real reserves is only some part of the virtual reserves because reasl reserves is limited by maximum x minimum price(y maximum price) and y minimum price(x maximum price).

real reserves

x-x(pb)=real reserves of x

y-y(pa)=real reserves of y

x(pb)= L / sqrt(pb)

x(pb) is the x amount in Pb price.

y(pa)= L * sqrt(pa)

y(pa) is the y amount in Pa price.

x virtual reserves=x real reserves + x(pb)

y virtual reserves= y real reserves + y(pa)

Dr. Engin YILMAZ