It's a huge difference despite the fact that my evolved pokemon has a higher CP!.
3 Answers
As you can see the bar above your Pokemon is more or less full depending on the evolution. This is basically because the more evolved Pokemon has a higher potential for its upper-limit on Combat Power.
So the reason it costs less after you evolved it is because you are further from filling that bar completely. As you get closer to the upper-limit on Combat Power, the Stardust and candy costs go up.
This upper-limit is also determined based on your current level, and the upper-limit will be higher after you have leveled.
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Wow. This is really valuable information. Considering that stardust is often more valuable than candy, this is a solid argument that its better to evolve THEN power up. Commented Jul 15, 2016 at 19:28
The stardust cost is proportional to how much Combat Power it has compared to it's maximum. As Kevin Tian says below, this seems to ignore evolution. I initially believed that a higher evolution would cost at least some more. I was wrong.
The stardust cost as you approach the maximum is different sometimes (like the final power up on Vaporeon to reach 1,000CP vs the final one on Pidgey to reach 150CP), but it seems to be related to type, trainer level, or just how high the maximum CP is for the individual pokemon. Not the evolution.
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Your second paragraph is wrong, the amount of stardust it takes is ONLY determined by the percentage of maximum CP it is at not at all by evolution. So if both pidgey and pidgeot were at the same percentage then they would also cost the same. Source: Just compared my Jolteon and Eevee Commented Jul 15, 2016 at 14:53
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I already made the edit as you seem to be correct, but something (pokemon type, trainer level, evolution, etc) does actually affect the stardust cost the closer you get to the maximum. If you are one power up away from Vaporeon reaching it's max (where the max is say 1k), it may cost 1600 like on mine... but a pidgey with a max of 150 or so while sitting at 141 only costs 800 (just spent the dust on my son's account to make sure that was it's final power up). So it doesn't seem to be affected by the evolution as you said, but it may be by trainer level and/or pokemon type. Commented Jul 15, 2016 at 15:18
Each species has a different maximum CP - 160CP is high for a Pidgey, but quite low for a Pidgeotto! Some species are naturally stronger than others, and an evolved form of a Pokémon will become much stronger than its previous form.
The higher the Pokémon's current CP is compared to its maximum CP, the more stardust it costs to upgrade.
If you evolve that Pidgey, you'll have a Pidgeotto at about 300-400CP, as it adjusts to the new species.
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If anyone has an official name for what I'm referring to as "inherent strength" here (in the main games, they are Base Stats), or even a list of each Pokémon's inherent strengths, please suggest an edit!– KaiCommented Jul 15, 2016 at 14:50
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