FOC Formula and AMO/ATA Standard Measurement Method
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Full bio →The ATA FOC Formula
FOC% = (A − L/2) / L × 100Where:
- A = distance from the nock throat to the balance point (inches or cm)
- L = total arrow length from nock throat to end of shaft (not including point)
- Both measurements in the same unit
Why the Nock Throat, Not the Nock
The nock throat is the groove that contacts the bowstring — the exact reference point for all archery measurements. Not the tip of the nock, not the rear of the nock. Using a consistent reference is critical because different nocks vary in length by up to 5mm.
Measuring Balance Point Correctly
Full arrow setup: Install point, insert, nock, and vanes before measuring. FOC changes with every component added.
Method: Balance the arrow horizontally on a narrow edge (a pen, ruler edge, or finger). The balance point is where the arrow rests level. Mark with a marker dot.
Measure: Use a stiff tape measure or caliper. Measure from the nock throat groove to the balance point mark. This is A.
Measure arrow length: From nock throat to the end of the shaft (not the point tip). This is L.
Component Contributions to FOC
The balance point is the weighted average position of all component weights:
Balance Point from Nock = Σ(weight_i × position_from_nock_i) / total_weightFor a typical hunting arrow:
| Component | Weight | Position from nock | Contribution |
|---|---|---|---|
| Shaft | GPI × L | L/2 | Neutral |
| Point (100 gr) | 100 gr | L (front) | Strong forward |
| Insert (12 gr) | 12 gr | L−1” | Forward |
| Nock (9 gr) | 9 gr | 0 | Strong rear |
| Vanes ×3 (6 gr each) | 18 gr | 2” | Rear |
Adding 50 gr to the point shifts the balance point forward roughly 1 inch on a 28-inch, 400-grain arrow, increasing FOC by approximately 3.5%.
Effect of Arrow Length on FOC
At the same component weights, a longer arrow has lower FOC because L is in the denominator of the formula. A 28-inch arrow with a 100-grain point has higher FOC than a 30-inch arrow with the same point (all else equal). Cutting arrows shorter increases FOC; longer arrows require more forward weight to achieve the same FOC%.
For how this formula interacts with arrow spine selection when using heavy points, see the Arrow Spine and FOC Reference. For common measurement errors when applying this formula, see 5 FOC Measurement Mistakes.