Well there is a million different circumstances and probably a million people who understand it better than I do but despite this being the wrong thread here goes an example based on roughly what you should be doing anyway. This makes the assumption
1. You will race to Political Philosophy pushing culture hard at the start (ideally around T50)
2. You will then race to Feudalism pushing culture because you want better builders.
Lets say you end up with 6 cities by T50.... you placed a campus in each 1 at T20, 1 at T25, 1 at T30, 1 at T35, 1 at T40 and one at T50
Lets also assume (wrongly but for example... at these turns you get an extra civic)...6 civic by T50 = Political Philosophy.
When you place your first campus the cost is calculated based on the higher number of techs or civic but as you are pushing civic at the beginning of the game they are normally higher. So the campuses are placed but not being built. The cost to complete these campuses is based on the number of civic you had at the time so the costs are (on standard speed)
City 1 - 70 prod
City 2 - 81 prod
City 3 - 91 prod
City 4 - 102 prod
City 5 - 112 prod
City 6 - 123 prod
So you can see the cost of campuses increases noticeably with increase in civics/techs
If I built a builder at T50 it would be able to chop a jungle for 21 Prod, trees for 41 prod or stone/deer for 51 prod... so I would have to chop 6 jungle to complete my City 6 campus or or 3 trees. My builder would be used up and so roughly 3 normal chops = a campus.
If I wait until Feudalism I get 5 chops out of a builder (6 with pyramids) so a builder is 66%or 100% more efficient because of the builder charges at feudalism.
Better still at Feudalism I am 9 civics in meaning my chops are now worth 51 production not 41. So I have builders that are more powerful and also have more chops if I delay.
If at this stage I chopped that's great but I spent a long time getting to feudalism and in just a few short turns I could pick up maybe 4 more civics (
and a few envoys) giving me 65 production per chop...
Lets say I did not get pyramids and only had 5 chops per builder.... My builder could get 325 production while about 20 -25 turns earlier the same builder could get 123 production. That's a huge difference.
Now in this example I am building campuses so surely building them earlier would get me a lot more science than later?.... well campuses get a lot of their science from city states (so do most districts) We tend to place a district not for adjacency but for speed so often it does not get much adjacency... so the campus is only of great value once the science CS have envoys... Remember earlier I highlighted when I get envoys... I get envoys just before my builders get a good chop boost So this is a great time to chop in my campuses.
Now my science skyrockets and the number of techs starts overtaking my number of civics quickly and by T100 I could easily have 30 techs which equals 100 production per chop. Mt first chopping soon after feudalism allowed my science to skyrocket so my second chopping wave can be more powerful as well as having a great tech level.
Now also lets go back to my campus chopping a bit and give you a simple overflow example...
I place my 100% production bonus for building walls (limes) card in place and start building a wall in city 6 where my campus needs 126 production to be built. My builder gets 65 per chop so needs 2 chops to complete my campus. The turn before I finish my wall I have 5 production left to complete it and on this turn my builder chops 1 set of trees..... Because I have a +100% card for walls and am building walls my chop also gets 100% so I suddenly get 130 production... -5 production to finish my wall leaving me 125 production.... I then place my campus in to build (which need 126 production) and next turn (including my paltry city production my campus finishes. My campus took 1 turn and 1 chop to make timing it with a 100% bonus card. If I had Monarchy I would have got an extra 50% for that as well.
Chopping in a settler with a 50% settler build card is a great example of where you would use it early or building 2 galleys quickly off 1 chop with the 100% navy card.
Hopefully these tables are fairly accurate and help you understand the values. If you use builders too quickly they start getting expensive.
If you have a lot of woods late game you can chop a wonder in 1 turn
When you build pyramids all existing builders get an extra charge so people try to leave early builders with 1 charge.
Crabs and copper are double production bonus for chop so once you have all techs or civics every crab you chop is worth 500 gold but only produces a few gold per turn... better to chop crabs and bronze once your game is nearing its end if you have spare builders.
Jungle produces as much food as production when you chop it and wheat/cows/rice as much food as if there were stone for production.
Builder costs escalate slower than chopping costs so it is not really worth chopping a builder in early but it certainly is late.
1 simple rule of thumb.... if I chop a district the same turn I place it... it will be 3 chops. But if i wait and or use bonus cards it can be 2 or 1 chop... so 1 builder can chop in 3 campuses not 1.