Cold to Fire

I have a question regarding cold to fire: I'm thinking of making a burning arrow build. Most likely with a marauder or templar base but I haven't decided yet. My question though, has to do with hatred. Considering that hatred scales off my weapon damage and applies to my burning arrow as it is an attack skill I was wondering if attaching a cold to fire gem to my burning arrow would convert my hatred dmg. If so it seems like some strong synergy for my build. Thanks in advance for any responses.
And yes, I am a noob when it comes to mechanics... hawlp

that will work just fine, hatred gives added cold in percent from physical, then cold to fire will shift some of that to fire. i suggest adding added fire support for even more fire.

Perhaps a stupid question. But if I have a lot of +cold damage passives, this gem will make me lose DPS, right? Or will the partial fire damage calculate after +cold % ?

it'll calculate like this:
100 cold base *convert ratio = fire
new ice = (base - convert) * (1 + %ice)
fire = covert * (1 + %ice + %fire)

no loss in dps if using cold to fire, convert gains boosts of original type and adds new type's bonuses together. does not multiply.

Thank you that helps a lot! This opens up new interesting possibilities for me.

So what if i use cold to fire with freezing pulse and i have crit of 35%. Will the fire burn when i crit with the freezing pulse and freeze?

it'll cause freeze if damage is more than 3% of foe's hp, which crits typically easily manage.
burning happens period and damage value is based of fire damage delt on the trigger (crit in this case). 1/3rd damage each second for 4 seconds.

i am playing mostly cold-witch and was thinking of the uses for this support-gem.
however its looks like that you dont gain any extra damage from this gem when using only +cold-dmg nodes and passives from items.

for this gem to be useful one would need to take additional + % fire-dmg nodes from the passive-tree, but i think its a waste of a skill point to take passive +dmg nodes which are only as effective as the %-based conversion-rate (i.e. 40% cold to fire conversion means that a +10% firedmg node would only add 4% of the basedmg as extra dmg to the spell, while a 10% colddmg node would add the whole 10% of the basedmg to the spell).

now the other problems is the penetration support gems, which basically eliminates the use for a spell to have multiple dmg-types to battle resistances, plus not having a dual penetration-gem for the same purpose.

so far the only use for this gem is when an actually fire witch wants to use freezing-pulse or ice-spear as secondary spell (because of the passive pierce from freezing-pulse or ice-spear) and not have the extra firedmg do nothing to increase the dmg for the secondary spells.

now the question is, did i miss something in how passive + % fire-dmg nodes or items with +% dmg interact with the conversed fire dmg portion of the spell so that it would be more effective as a think or did the penetration gems made the "Cold to Fire support-gem" kind of useless for a cold-witch ?

500 cold damage vs 75% res =125 cold damage. this is the control test. we are testing how much more damage getting out of bypassing res from just two different supports.

500 cold vs 55% res (lv 5 cold pene) = 225
500 vs 50% res (lv 10) = 250
vs 45% res (lv 15) = 275
40% res (20) = 300
so
225/125 = 1.8 multiplier for damage
250/125 = x2 damage
275/125 = 2.2
300/125 = 2.4

cold to fire gem of 40% (lv 1)
300 cold damage and 200 fire damage vs 75% cold = 75 cold and 200 fire, total of 275
C2F of 50% (lv 6 ish to my memory)
250 cold and 250 fire vs 75% cold = 62.5 cold and 250 fire, total 312.5
60% (somewhere near lv 12)
200 cold 300 fire -> 50 and 300, total 350
70% cold to fire lv 17
150 + 350 to 37.5 + 350 = 387.5
then
275/125 = x2.2 damage
312.5/125 = 2.5
350/125 = 2.8
387.5/125 = 3.1

summary, "Swapping" damage type via converting to get around resistances excels but both have pros and cons not listed here.
1) those using penetration gems would also have curses to reduce further. thus above information is warped in practical use.
2) fire damage has burning, which is extra damage. ice spear takes advantage of this via crit boost.
3) cold to fire doesn't actually increase damage as pointed out by someone that wanted this test done. however, there is a curse for all elements, also elemental equilibrium (specially EE).

How does cold to fire work with certain keystones and skills, say if I were to use pain attunement and/or righteous fire, will the bonus apply twice?

Example (numbers not representative of actual numbers):

50% of cold dmg converted to fire
200 cold damage
10% increased cold damage
10% increased fire damage
50% bonus from righteous fire
30% from pain attunement

Does it go:

cold damage: 100 * (1+ 0.1 + 0.5 + 0.3)
fire damage: 100 * (1+ 0.1 + 0.1 + 0.5 + 0.3)

Or does it work in another way?

EDIT: I'm confused; does spell damage work for the converted damage?

EDIT2: I guess what I'm asking is; if I have 0% increased fire damage, is there any way to increase my damage through using the cold to fire support gem (minus the burn status)? If my calculations/assumptions are correct it is not possible.

EDIT3: would there be any incentive to get, say, 10% fire/10% cold damage over just 20% cold damage?