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Aquariums

Water change

How much water to swap to bring nitrate, TDS, or any dilutable parameter down to a target value.

Water change to hit a target Volume in L
Nitrate ppm, TDS, salinity, whatever you're diluting.
Tap, RO, well, whatever you'll refill with. Most tap is 0 for nitrate but worth checking.
Change fraction -- percent
Volume to remove -- L
Notes --
Works for anything that dilutes linearly (nitrate, TDS, salinity, most ions). Doesn't work for pH, because pH is buffered by KH and won't move proportionally to a water swap.

The math

Replacing fraction f of your water with source water gives:

C_after = C_before * (1 - f) + C_source * f

Rearranged for f:

f = (C_before - C_target) / (C_before - C_source)

That's the whole calculator. Plug in current, target, and source values to find the swap fraction.

When the math lies

The dilution math assumes the parameter you're targeting can't be created inside the tank. For nitrate that's almost true, it's the end product of the cycle and only goes up between changes. For TDS, also close. For pH, false: pH is buffered by KH, and a 50% water change won't necessarily move pH halfway to your source water's pH. Use this for things that dilute linearly. Don't use it for pH or buffered chemistry.

Don't change too much at once

Anything past 50% in one go risks shocking fish via osmotic shift, temperature swing, or pH movement. If the math wants 70%, do three changes of 25 to 30% spaced a few hours apart. The fish don't care that it's slower, but they do care if everything moves at once.

Further reading