Question
I'm currently taking an environmental science course and my field study project is growing Lima beans in two conditions, the control(plain potting soil), and the other with nitrogen fertilizer mixed in. I've purchased a 12-0-0 organic fertilizer, and I'm growing the Lima beans in plastic, 16 oz cups, one seed per cup. However, the directions on the bag say in terms of square feet. How much fertilizer should I use if i just want to mix it with enough soil to fill 3/4 of a 16 oz cup?

Answer
'Organic' Fertilizer is something of an Oxymoron.

You remember those Oxymorons in English class... 'stupid genius'.  'almost exact'.  'diet soda'.  And the famous one-liner from A Chorus Line, 'Suicide in Buffalo is an Oxymoron.'

Organic Fertilizer?  Organic Gardening begins with one thing:  Spectacular Soil.  The 'Gardening' part refers to the care of the Seeds you plant (in this case, you are growing Lima Beans) like watering, monitoring heat, and controlling the light.

Next, the 12-0-0 Fertilizer you have selected -- let's say it's Fish Emulsion, which has a similar profile -- is high in Nitrogen.  Lima Beans only need that for the LEAVES (to make Chlorophyll among other things).  They are going to need Phosphorus and Potassium for Roots and Cell Activities.  A BALANCED Fertilizer would be preferable.

Finally, may I assume this Fertilizer is NOT liquid (since you want to mix it in the Soil)?  The quantity you use should be very small (you don't want to burn the roots of your baby Lima Beans) but if you want to calculate it perfectly, do it this way:

Calculate the area of the surface of one of your 16 oz. cups.  The formula is PI (3.1416) times the RADIUS of the Circle (the rim of the Cup); take your results, then Square the number for the final Area.  Round up to the nearest inch.  Next, you'll have to calculate the standard Fertilizer application according to the directions; if it says '1 cup per 10 square feet', multiply the square feet 12 to get the inches; now it says '1 cup per 120 square inches', right?  That would also be .1 cup per 12 sq ft; or .01 cup per 1.2 sq ft.  Divide and conquer.

If you give me the application rates I'll do the math for you.  But you probably can do this, too.

Got that?