There seems to be a lot of confusion here about PSUs, so just to clear things up.
1. Different ATX standards will isolate 12V_1 or 2 for the CPU only. This essentially renders any additional amperage on that rail unusable by the rest of the 12V system including the GPU. So look at the design standard, if it doesn't have EPS, then you should assume unless stated otherwise, that the 12V_1 is not part of the equation.
2. Another way to look at the above is to divide the total wattage on the 12V rail by 12. This will give you the number of available amps. It needs to be 26 or greater for any PCIe card.
3. Calculators are crap. They dont factor in capacitor ageing, derating curves etc and give a super unrealistic outcome. Also component TDPs mean little in the real world, especiallly if you overclock or similar.
4. Once you have your 12V amperage figure, deduct 0.1 - 0.3 amps for every degree (C) that it will operate under during summer. Most cheaper PSUs are rated at 25oC, so during summer, inside your computer (with other heatloads), it could easily be 50oC. That is delta 25oC. So that means that you need to deduct up to 8.25A off the 12V rail due to derating (temp). So now that cheap 500W PSU that had 15A on the 12V rail can only in reality provide less than 10A. (8.25A/2 = 4.125A per rail deducted + capacitor ageing (below)).
5. Add to the above losses - capacitor ageing. Remove a further 15% for capacitor ageing.
6. So what you're left with is a PSU that during summer in a year from now may only be able to provide 5A (60W) to the GPU once you remove the CPU rail.
Of course higher quality single rail PSUs with active PFC, MTFB measured at 40oC, japanese capacitors etc, will only derate by a few amps, and given a single rail design, a high quality 500W PSU can deliver 40A or more, vs a cheap brand 500W PSU delivering 10A.
Extreme cases of course, but shows the lack of information wattage rating tells you.
You need 26A on the 12V rail, but I would recommend 30A as this is achievable in the corsair 400 - 500W range for not much money.