Formulas and Tech Details

Weight Forward of Center  or  F.O.C.

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The abbreviation FOC stands for “weight forward of center”. The acronym FOC is just what it describes. It is the percentage of arrow weight that is located in the front half of the arrow. Earlier in the momentum section we analyzed how weight of the arrow varies the rate of momentum thus penetration. Reviewing the results of Dr.Ed Ashby’s conclusions on FOC, one will be amazed how the FOC of an arrow affects penetration.( See the 2008 Study Update, Part 6 by Dr. Ed Ashby. This is an important read for all archers.)


There are a several categories of forward of center (FOC) used to describe the percentage of weight forward an arrow has.
    Normal FOC = 0 percent to 12 percent
    High FOC= 12 percent to 19 percent
    Extreme FOC =19 percent to 30 percent
    Ultra Extreme FOC = more than 30 percent

There is a very simple procedure to calculate the arrow's FOC percentage. These steps are outlined below:

A. Take an arrow, placing your finger in the approximate center of the shaft, attempt to balance the arrow. Once you know the location of the balance point (BP), place some sort of mark at this point.

B. Measure the distance from the deepest part of your nock groove to the BP. This is the Balance Point (BP) measurement.

C. Next you need to measure the Total Arrow Length (TAL). You do this by measuring from the bottom of the nock groove down the edge of your arrow shaft to the end of your arrow. ( Note. There are two ways to measure the arrow: with the tip on or without the tip or broadhead. For our purpose we are going to exclude the broadhead or tip. This method of measuring FOC is the AMO method and the most commonly used. Using the AMO or the standard method we will be able to better compare our results to Normal FOC, High FOC, Extreme FOC and Ultra FOC
Ashby says the following: ...Insert/tip/broadhead. Which is “correct”? Neither. True FOC is based on the center of pressure. We simulate the CP location in both formulas.
The AMO formula was adopted as “standard” because, of the two common formulas, it uses a “simulation point” nearer the actual CP location for most arrows in flight. Note the CP does not reflect the point of greatest shaft flex, but that upon which “flexional force” is greatest. Shaft design and material has a significant effect on both CP location and where the shaft will flex most. For practical applications, those for which archers use FOC, either common formula works equally well. All that matters is that the method used be stated; so everyone “reads off the same page” when making comparisons.)

Note: Using the FOC measurement method to include the tip or broadhead will not give the same result as the standard method or AMO. The result is distorted because you are making the arrow measurement longer the resulting FOC percent will have a lesser result

D. Take the balance point measurement (BP) and divide it by the total length of the arrow as found in (C) Total Arrow Length (TAL). This gives you a fraction or the decimal equivalent of of the overall shaft length where the balance point falls.

E. Take the Quotient or decimal derived in (D) by dividing (BP) by (TAL) and subtract .50 or the decimal equivalent of 50%. Multiply the results by 100 and you will have %FOC.

 The formula format is:

%FOC = (Dist. of knock throat to Balance Point BP / Shaft Length TAL)  minus .50 x 100

Example using the diagram below: FOC= (18) ÷ (30) = .60-.50 x100 = 10% FOC


AMO Method

For your convenience use FOC calculator provided below

Try this out.

Enter both the Total AMO SShaft length and the Noc to Balance Point values and hit the Calculate button.

Try different values and see what effects they have on FOC.

FOC Calculator

Enter AMO Total Length AND Nock to Balance Point
then press the "Calculate" button:

Arrow Length

Nock to Balance Point

( % FOC )

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