🏹 Arrow Speed Calculator
Calculate arrow velocity
How to Use This Calculator
Enter Draw Weight
Input your bow's draw weight in pounds (lbs). This is the maximum force required to pull the bowstring to full draw. Typical values range from 30-70 lbs for most archers.
Enter Draw Length
Enter your draw length in inches. This is the distance from the nock point to the pivot point plus the length to the arrow rest. Average draw length is 26-30 inches.
Enter Arrow Mass
Input the arrow's total mass in grains. This includes the shaft, fletching, nock, and point. Standard arrows range from 300-500 grains.
Click Calculate
Press the "Calculate" button to compute the arrow speed in meters per second (m/s) and feet per second (fps), along with the kinetic energy.
Formula
E = F × d
v = √(2E/m)
Where:
- E = Energy stored in the bow (Joules)
- F = Draw weight (Newtons) = Draw Weight (lbs) × 4.448
- d = Draw length (meters) = Draw Length (inches) × 0.0254
- v = Arrow velocity (m/s)
- m = Arrow mass (kg) = Arrow Mass (grains) / 1000
Example Calculation:
For a bow with 50 lbs draw weight, 28" draw length, and 400 grain arrow:
1. Convert units: F = 50 × 4.448 = 222.4 N, d = 28 × 0.0254 = 0.7112 m, m = 400/1000 = 0.000258 kg
2. Calculate energy: E = 222.4 × 0.7112 = 158.2 J
3. Calculate velocity: v = √(2 × 158.2 / 0.000258) = √(1,227,131) = 1,108 m/s
Note: This is a simplified calculation. Actual arrow speeds are typically lower due to energy losses from string oscillation, limb vibration, and air resistance.
About Arrow Speed Calculator
The Arrow Speed Calculator determines the velocity at which an arrow leaves a bow based on the bow's mechanical properties and the arrow's physical characteristics. Understanding arrow speed is crucial for archers, bowhunters, and competitive shooters as it affects accuracy, trajectory, and kinetic energy delivered to the target.
Key Factors Affecting Arrow Speed
- Draw Weight: Higher draw weights store more energy, resulting in faster arrow speeds. However, there's a practical limit based on the archer's strength and shooting form.
- Draw Length: Longer draw lengths allow more energy to be stored in the bow, increasing arrow velocity. This is why longer draw lengths produce faster arrows.
- Arrow Mass: Lighter arrows travel faster but may lack penetration power. Heavier arrows are slower but deliver more energy on impact. The relationship follows the kinetic energy formula: doubling the arrow weight halves the speed (if energy is constant), but the heavier arrow still has more momentum.
- Bow Efficiency: Modern compound bows can be 80-90% efficient, while traditional recurve bows are typically 70-75% efficient due to energy losses.
Practical Applications
- Bowhunting: Understanding arrow speed helps estimate trajectory at various distances, improving shot placement accuracy.
- Target Archery: Faster arrows are less affected by wind and have flatter trajectories, making long-range shooting more consistent.
- Equipment Selection: Compare different bow setups to find the optimal balance between speed and shootability.
- Safety: Calculate kinetic energy to ensure arrows meet minimum requirements for ethical hunting (typically 25-40 ft-lbs for small game, 40+ ft-lbs for large game).
Understanding the Results
Arrow Speed (m/s or fps): The velocity at which the arrow leaves the bowstring. Typical speeds range from 150-350 fps (45-107 m/s) for traditional bows to 300-450 fps (91-137 m/s) for modern compound bows.
Kinetic Energy (Joules): The energy the arrow carries, calculated as E = ½mv². This determines the arrow's ability to penetrate targets. More kinetic energy means deeper penetration.
Frequently Asked Questions
Why does my calculated speed differ from my chronograph reading?
This calculator uses a simplified energy transfer model. Real-world arrow speeds are typically 10-20% lower due to energy losses from string oscillation, limb vibration, arrow flex, and air resistance. For accurate measurements, use a chronograph.
What is a good arrow speed for hunting?
Most hunters prefer arrows traveling 250-350 fps. However, kinetic energy (typically 40+ ft-lbs for large game) is more important than pure speed. A heavier arrow at 250 fps may be more effective than a light arrow at 350 fps due to better penetration.
How does arrow weight affect speed?
Lighter arrows travel faster but carry less kinetic energy. Heavier arrows are slower but deliver more energy on impact. The relationship follows the kinetic energy formula: doubling the arrow weight halves the speed (if energy is constant), but the heavier arrow still has more momentum.
Does draw length really matter that much?
Yes! Draw length has a significant impact on arrow speed. A longer draw length allows more energy storage. Increasing draw length from 26" to 30" can increase arrow speed by 15-25 fps with the same draw weight.
Can I use this calculator for compound bows?
This calculator provides a basic estimate for compound bows, but actual speeds may vary due to the cam system's let-off and efficiency. Compound bows often achieve higher speeds than this calculation suggests because they store energy more efficiently.
What's the difference between grains and grams?
Grains are the traditional unit for arrow weight in archery. One grain equals approximately 0.0648 grams. Arrows are typically weighed in grains because it's a more precise unit for the small masses involved (e.g., 400 grains = 25.9 grams).