Arrow Kinetic Energy & Momentum

  • Here it is! The basic calculator, preset with the Rule of 400 installed!
    • Kinetic Energy (ft-lb)
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    Momentum (slug·ft/s)
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    Formulas: KE = (grains × fps²) / 450240; Momentum = (grains × fps) / 225218.

    Arrow Weight Change Calculator

    Assumes the bow delivers roughly the same kinetic energy when you change arrow weight, then solves for the new speed. (Real-world results can vary.)
    Predicted New Speed (fps)
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    Speed Change (fps)
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    Current KE (ft-lb)
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    Bunjie Card Builder

    Row 1

    Row 2

    Row 3

    KE formula: (grains × fps²) / 450240
    Momentum formula: (grains × fps) / 225218
    Momentum is shown in the same style commonly used on crossbow stat cards.

    Crossbow Efficiency Calculator

  • This is a fun one! Crossbows are very inefficient weapons.
  • There's no way to get exact results without measuring the entire draw, but this still gives a decent measurement to compare one crossbow to another, and one arrow setup to another.
    • Kinetic Energy (ft-lb)
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    Stored Energy (ft-lb)
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    Efficiency (%)
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    Notes
    Stored energy model assumes roughly linear draw force (avg force ≈ DW/2).
    Formulas: KE = (gr × fps²) / 450240; Stored = (DW × PS) / 24; Efficiency = (KE / Stored) × 100.

    Efficient Arrow Weight (Estimate)

    This estimates an “efficient” total arrow weight by assuming a linear speed change: k grains of arrow weight ≈ 1 fps change (as used in DBB/OGH’s Arrow Weight Change tool). :contentReference[oaicite:3]{index=3}
    Common guesses: 2–4 gr/fps
    KE peak gives a finite “best” weight under the linear model. Momentum in this model increases as you add weight until speed approaches zero, so we constrain it to a practical range.
    Estimated Efficient Weight (gr)
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    Predicted Speed at that Weight (fps)
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    Kinetic Energy (ft-lb)
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    Momentum (slug·ft/s)
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    Model: V(W)=V0−(W−W0)/k. KE=(W·V²)/450240. Momentum=(W·V)/225218.

    FOC (Front of Center) Calculator

    Measure from the throat of the nock:
    • Arrow Length (L): to the back of the point / end of shaft, not including broadhead
    • Balance Point (B): to the spot where the finished arrow balances with broadhead installed

    Crossbow Minimum Arrow Weight Calculator

    Calculates a recommended minimum finished arrow weight using:
    • GPP method: Draw Weight × Grains-Per-Pound
    • Manufacturer minimum (optional): uses whichever is higher
    Common “minimum” starting point is often 5.0 GPP.
    Example: some TenPoint/Wicked Ridge models specify minimum finished arrow weights (varies by model/year). :contentReference[oaicite:4]{index=4}
    Minimum by GPP (gr)
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    Manufacturer Min (gr)
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    Recommended Minimum (grains)
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    Recommended Minimum (grams)
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    Recommended Minimum (ounces)
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    Conversions: 1 grain = 0.06479891 g :contentReference[oaicite:5]{index=5}; 1 lb = 7000 grains :contentReference[oaicite:6]{index=6}.

    Crossbow Arrow Arc Calculator

    Estimate how high your arrow rises above the straight line between your crossbow and a same-height target.

    FPS
    grains
    yards
    Maximum Estimated Arc Height 27.2 inches 2.26 feet
    Launch Angle 1.73°
    Time of Flight 0.75 sec
    Kinetic Energy 142.1 ft-lb
    Momentum 0.710 slug-ft/s
    CROSSBOW
    TARGET
    27.2" HIGH

    This is an idealized trajectory estimate assuming the crossbow and target are at the same elevation. Aerodynamic drag, arrow diameter, fletching, broadhead design, wind, sight height and actual retained velocity are not included. Real-world arrow trajectories will normally show more arc.