Tap Farm had an update in January that changed the experience levels and added new crops, animals, trees, decorations, and levels. All accounts kept the same amount of experience that they had earned, but the levels now required more experience to achieve. As a result, some accounts (mine included) dropped down in level since the accumulated experience was not enough to have reached the same level under the new accounting. Thus, your level is calculated from your accumulated experience, and that calculation has been changed in the past. Currently, you need somewhere around the following:
(This data comes from Jay Bullington's spreadsheet from Facebook. I've confirmed up to Level 43, and Jay has confirmed up to at least Level 49. The other levels are extrapolated by assuming that each level after 49 requires 1.08 times the previous experience, which may or may not hold to Level 60)
Level
XP
Gain
Level
XP
Gain
Level
XP
Gain
1
0
21
39,000
4,000
41
563,760
41,760
2
20
20
22
43,000
4000
42
608,860
45,100
3
40
20
23
47,000
4000
43
657,569
48,709
4
100
60
24
67,000
20000
44
710,175
52,606
5
200
100
25
87,000
20000
45
766,989
56,814
6
500
300
26
112,000
25000
46
828,348
61,359
7
800
300
27
137,000
25000
47
894,616
66,268
8
1,300
500
28
162,000
25000
48
966,185
71,569
9
1,900
600
29
192,000
30000
49
1,043,480
77,295
10
2,500
600
30
222,000
30000
50
1,126,959
83479
11
3,300
800
31
252,000
30000
51
1,217,116
90157
12
5,000
1700
32
282,000
30000
52
1,314,484
97370
13
8,000
3000
33
312,000
30000
53
1,419,644
105159
14
11,000
3000
34
342,000
30000
54
1,533,215
113570
15
15,000
4000
35
372,000
30000
55
1,655,872
122659
16
19,000
4000
36
402,000
30000
56
1,788,342
132469
17
23,000
4000
37
432,000
30000
57
1,931,409
143067
18
27,000
4000
38
462,000
30000
58
2,085,922
154513
19
31,000
4000
39
492,000
30000
59
2,252,795
166873
20
35,000
4000
40
522,000
30000
60
2,433,020
180224
Rates of experience gain
If you fill your entire farm with artichokes, and wake up in the middle of the night to promptly harvest and replant every four hours, then you could earn 14,850 experience per day. (This can be calculated from 2.75 per hour per square from the crops page times 15 x 15 squares x 24 hours). In actual practice, you'll earn experience more slowly than this assuming you sleep through the night, forget to harvest your crops some days, and devote some land to decorations. But with an artichoke farm at this theoretical rate, it would take 163 days to reach level 60. You'll also accumulate just over three million coins from farming artichokes. This gives you some basic estimates of how long you might be playing this game before you hit Level 60 (assuming you don't lose interest well before that ;-).
The new Valentine Hearts produce experience at 9.0 per hour per square. This equates to a rate of 48,600 per day, or 50 days to Level 60. Obviously I hope you don't plan to try to achieve that, since it's not healthy to wake up every hour of every day for over a month and a half, but you can see that valentine hearts greatly speed up experience production and the speed to Level 60. Additionally, farming Valentine Hearts costs 1,125 coins per crop, or about 1,350,000 coins on the way to Level 60. Therefore, you would need to intersperse other money-making crops, plant some trees, or raise some animals to provide coins while you're farming experience at these rates. In fact, you can easily cover costs by planting Valentine Hearts every hour that you remember to do so during the day, and then planting a crop of Garlic or Cucumbers at night while you sleep to make back the coins. This can easily yield you 15,000-30,000 experience each day without any coin cost.
Of course, you can accumulate coins and experience at a much much faster by raising trees and animals than you can by planting artichokes. Although the Feb 6th, 2010 update has slightly lowered the efficiency at which you can convert coins, you can easily build up a huge stream of coin income from trees and animals and then convert that cash into experience.
Coming soon: discussion of rates when comparing conversion to cash to exp. as comparison.
Turning Coins into Experience
So you're probably thinking at this point "I thought this moron was supposed to be telling me the fastest way to produce experience." Well, sure, but I tend to digress :-) But since you'd like to know... crops seem to be the most pleasant way to do get experience. Of course, most of this site focuses instead on production of coins. I've found it hard to separate production of coin and experience, and in fact, it's possible to convert coins to experience.
To convert coins to experience you can simply do the following:
Start with some open grass area.
Create a patch using the "Create Patch" tool. (minus twenty coins, plus one experience)
Plow the Patch using the "Plow" tool. (minus fifteen coins, plus two experience)
Plant Bell Peppers (minus one hundred ten coins, plus eight experience)
Delete the Patch (plus one hundred thirty coins, plus one experience)
Tally up your earnings. (minus fifteen coins, plus twelve experience)
By repeating this process you convert fifteen coins into twelve experience, or about 80% conversion rate of coins. (If you don't have access to Bell Peppers, you can do the same thing with other crops at about 15-20% conversion rate. Before the February 6th, 2010 patch, you could do the same thing without plowing and planting for a whopping 58% conversion rate, but this was nerfed in the patch by changing the delete patch experience from ten to one.) The ability to convert coins to experience is a very interesting fact, since the highest-producing items (trees and animals) produce large amounts of coin, but low amounts of experience. But if you could convert the coins into experience (even at a discounted rate) they would be the highest producers of coins, and thereby experience too.
This is why the tables I produce for the crops, trees, and animals have a row titled "Converted Total xp/hour/square". This figure is what you would get if you take a single 4x4 square of your farm, fill it with that crop, tree, or animal, and then convert all the profits to experience. Assuming that you are willing to convert cash to experience (and that may not be a valid assumption -- I'm not willing to do so), then that number gives you the productivity of the various options in a comparable format. You'll see that the crops are easily beaten by the trees, which are easily beaten by Black Cats.
In fact, converting a measly 3,000,000 coins would get you the experience required for level 60 and access to the Chateau. But before you consider your road to a Chateau solved, consider that there is one really big problem with coin conversion... It's a royal pain. You must create each patch and delete each patch manually, and they don't queue up like harvesting, plowing, and planting crops do. That means it's (probably deliberately) horribly slow and painful to convert experience. One can probably convert at a rate of about 12000 experience per hour, but I can't stand doing that for more than 10 minutes or so. But, if you're willing to do a bunch of tapping, it's a ready source of quick experience that doesn't make you wait on crops.
The Fastest Way to Produce Experience
Well, all that analysis to tell you what you already knew... you'll probably want to farm crops as your fastest route to gaining experience. So assuming that you do not want to convert coins to experience:
If Valentine Hearts are available, the following are the general steps you would want to take to maximizing experience gain:
Fill up all your crop patches by planting Tomatoes
Harvest, replant, and spend the excess coins creating more patches and planting them
Repeat this until you fill up your entire farm with patches.
Plant the entire farm with Valentine Hearts during the day, losing cash
Plant your best 8-hour cash crop overnight (like Garlic or Cucumber)
Repeat days of Valentine Hearts and nights of cash crops.
If Valentine Hearts are not available, the following are the general steps you would want to take to maximizing experience gain:
Fill up all your crop patches by planting Tomatoes
Harvest, replant, and spend the excess coins creating more patches and planting them
Repeat this until you fill up your entire farm with patches.
Plant the entire farm with Artichokes (or Tomatoes if you have not yet unlocked Artichokes)
Repeat Artichoke Farming
However, if you are really patient and love tapping the tool buttons in Tap Farm, the fastest way to get experience is to gain coins in the fastest fashion possible (see the animal pages) and convert the excess coins to experience. This means converting coins to experience until you reach the level required for purchasing Kennels of Dogs, or Herds of Black Cats so that you can producing huge amounts of coins for conversion.