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Pokémon GO Purify Calculator.

What purifying a Shadow Pokémon does to its IVs, level and CP, what it costs, and how the two compare in raids and on Stardust.

purify: +2 to each IV · level 25 minimum
shadow: 1.2x attack · 0.83x defense
Shadow Pokémon
Level now
IVs (Atk / Def / HP)
Shadow Machamp
Shadow Machampfighting
12/9/14 → 14/11/15
CP after purifying
2,149
Purifying this Shadow Machamp raises its IVs from 12/9/14 to 14/11/15 and its level from 8 to 25, taking it from 667 CP to 2,149 CP. It costs 3,000 Stardust and 3 Candy.
Shadow CP / HP667 / 82
Purified CP / HP2,149 / 148
IV percentage78% → 89%
Level8 → 25
Purify cost3,000 dust, 3 candy

Power-up cost: Shadow vs purified

from the level each one starts at
Stardust to 40Candy to 40Stardust to 50Candy + XL to 50
Shadow (from 8)316,320378616,320378 + 360 XL
Purified (from 25)177,600213402,600213 + 272 XL
Purified totals include the purification cost.

In raids at level 40

best moveset each, neutral 5-star boss
Shadow Machamp
Karate Chop + Dynamic Punch · 18.1 DPS · 404 TDO
Machamp (purified or normal)
Counter + Dynamic Punch · 15.4 DPS · 412 TDO
The Shadow deals 18% more damage per second and 2% less total damage before fainting.

Should you purify a Shadow Pokémon?

Purifying adds 2 to each IV, capped at 15, lifts the Pokémon to level 25 if it was lower, and teaches it Return in place of Frustration. Shadows from Team GO Rocket arrive at level 8 (13 in boosted weather), so purifying one is a free jump of 17 levels. The cost depends on the species: most cost 3,000 Stardust and 3 Candy, some 1,000 or 5,000, and legendaries 20,000 Stardust and 20 Candy.

The catch is battle strength. A Shadow deals 20% more damage and takes about 20% more, which in raids is usually worth more than the extra IVs. For a raid attacker, keep it Shadow. For a Pokémon you only want registered, traded or cheap to power, purify it: power-ups cost 90% of normal for purified Pokémon and 120% for Shadows.

PvP is a separate question. The +2 to every IV, Attack included, usually hurts a purified Pokémon's Great League rank, because higher IVs push it to the CP cap at a lower level. Check both spreads in the PvP rank checker before you decide.