Archery Pro Tools

Archery Formulas & Calculations

This learning page separates core archery formulas from general content so beginners can understand each equation quickly, apply it, and move to real setup decisions with confidence.

FOC (Front of Center)
Kinetic Energy
Momentum
Arrow Speed / FPS
Spine & Trajectory

📌 FOC Calculation

FOC

🧮 Formula

FOC% = ((A - L/2) / L) x 100

📖 FOC tells you how far the arrow balance point sits in front of the center. Higher FOC can improve front-end stability when spine and tune are correct.

Where:

  • A = Distance from nock to balance point
  • L = Total arrow length

📊 Example Calculation

  1. Given: A = 20, L = 30
  2. Compute midpoint: L/2 = 15
  3. Subtract: 20 - 15 = 5
  4. Divide: 5 / 30 = 0.1667
  5. Convert to percent: 0.1667 x 100 = 16.67%

💡 Practical Tip

Many hunting builds stay near 10-15% FOC as a practical baseline, then tune broadhead flight to confirm.

Try Calculator Read FOC Guide
Expand Diagram & Notes
Nock L/2 Balance (A) FOC compares A against midpoint L/2

📌 Kinetic Energy Calculation

Energy

🧮 Formula

KE = (W x V^2) / 450240

📖 Kinetic energy estimates impact energy in foot-pounds. It combines arrow mass and speed into one value.

Where:

  • W = Arrow weight in grains
  • V = Arrow speed in feet per second

📊 Example Calculation

  1. Given: W = 450 gr, V = 275 fps
  2. Square speed: 275² = 75,625
  3. Multiply: 450 x 75,625 = 34,031,250
  4. Divide: 34,031,250 / 450,240 = 75.6 ft-lb

💡 Practical Tip

Use KE together with momentum and arrow flight quality. One number alone is not full performance.

Try Calculator KE vs Momentum

📌 Momentum Calculation

Momentum

🧮 Formula

Momentum = (W x V) / 225218

📖 Momentum emphasizes how strongly mass carries through impact. Heavier arrows can increase this metric even if speed drops.

Where:

  • W = Arrow weight in grains
  • V = Arrow speed in fps

📊 Example Calculation

  1. Given: W = 450 gr, V = 275 fps
  2. Multiply: 450 x 275 = 123,750
  3. Divide: 123,750 / 225,218 = 0.55 slug-ft/s

💡 Practical Tip

When comparing two setups, momentum often shows why slightly slower heavy arrows can still hit with authority.

Try Calculator Learn Comparison

📌 Arrow Speed / FPS Estimate

Speed

🧮 Formula

Speed = Ref Speed x sqrt(Ref Weight / Your Weight) x (Efficiency/100)

📖 This gives a practical estimate when changing arrow weight from a known setup.

Where:

  • Ref Speed = Baseline speed in fps
  • Ref Weight = Reference arrow grains
  • Your Weight = Your arrow grains
  • Efficiency = Practical adjustment percentage

📊 Example Calculation

  1. Given: Ref Speed 300, Ref Weight 350, Your Weight 450, Efficiency 95%
  2. Weight ratio: 350/450 = 0.7778
  3. Root: sqrt(0.7778) = 0.8819
  4. Speed: 300 x 0.8819 x 0.95 = 251.3 fps

💡 Practical Tip

Always verify estimated FPS with a chronograph before setting final sight tapes.

Try Calculator Speed + KE Tool

📌 Spine & Trajectory (Practical Models)

Tuning

🧮 Core Models

Spine: Dynamic Load Index -> Nearest Spine Class Drop: Drop = 0.5 x g x t^2, where t = Distance / Speed

📖 Spine and trajectory tools use practical models to speed up decisions. Final tune still comes from real shooting feedback.

Where:

  • Dynamic Load = Practical stiffness demand on the shaft
  • g = Gravity constant (about 32.174 ft/s²)
  • t = Flight time to target distance

📊 Example Calculation

  1. Distance = 40 yd = 120 ft, Speed = 270 fps
  2. t = 120 / 270 = 0.444 s
  3. Drop = 0.5 x 32.174 x 0.444² = 3.17 ft (gravity-only baseline)

💡 Practical Tip

Use these outputs to narrow choices, then validate with bare-shaft testing and broadhead grouping.

Try Spine Calculator Try Drop Calculator

Complete Practice Dataset (Learning Table)

Category Input Set Formula Applied Output Interpretation
FOC A=20, L=30 FOC% = ((A - L/2)/L) x 100 16.67% Front-heavy profile; confirm spine match.
Kinetic Energy W=450, V=275 KE = (W x V²)/450240 75.6 ft-lb Strong energy range for many big-game setups.
Momentum W=450, V=275 Momentum = (W x V)/225218 0.55 slug-ft/s Solid carry-through profile.
Arrow Speed 300 fps ref, 350->450 gr, 95% Ref model with sqrt mass ratio 251.3 fps Weight increase lowers speed as expected.
Trajectory 120 ft @ 270 fps Drop = 0.5 x g x t² 3.17 ft baseline Gravity-only estimate; real drag may increase drop.
Spine 65 lb, 29 in, 125 gr point Dynamic load heuristic ~340 spine class Use as start point, then tune and verify.

Source context: ATA IBO speed baseline, common KE/momentum conversion constants, and practical archery tuning workflows. Always validate with measured chronograph and field grouping.