Arrow Speed Calculator

Category: Physics
- October 31, 2025
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This calculator helps you determine the speed of an arrow based on different physical parameters like draw weight, arrow mass, and bow efficiency.

You can choose between different calculation methods depending on the information you have available.

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About Arrow Speed & Kinetic Energy

The speed of an arrow is determined by several factors including the draw weight of the bow, the mass of the arrow, the efficiency of the bow, and the draw length.

Draw Weight Method:

This method calculates arrow speed based on the energy transfer from the bow to the arrow.

  • Formula: v = √(2 × E / m)
  • Where:
  • v = Arrow velocity
  • E = Energy transferred to the arrow (Draw weight × Draw length × Efficiency)
  • m = Mass of the arrow
Kinetic Energy Method:

This method calculates arrow speed based on known kinetic energy and arrow mass.

  • Formula: v = √(2 × KE / m)
  • Where:
  • v = Arrow velocity
  • KE = Kinetic energy of the arrow
  • m = Mass of the arrow
Chronograph Correction Method:

This method estimates the actual initial arrow speed based on the measured speed at a certain distance, accounting for drag.

  • Formula: v_initial = v_measured + (0.5 × ρ × Cd × A × d × v_measured² / m)
  • Where:
  • v_initial = Initial arrow velocity
  • v_measured = Measured arrow velocity
  • ρ = Air density
  • Cd = Drag coefficient
  • A = Cross-sectional area of the arrow
  • d = Distance traveled
  • m = Mass of the arrow
Kinetic Energy and Momentum:

Kinetic energy determines the penetration power of an arrow, while momentum affects its ability to pass through a target.

  • Kinetic Energy Formula: KE = ½ × m × v²
  • Momentum Formula: p = m × v
  • Where:
  • KE = Kinetic energy
  • p = Momentum
  • m = Mass of the arrow
  • v = Velocity of the arrow
Bow Efficiency:

Bow efficiency represents the percentage of stored energy in the drawn bow that is transferred to the arrow.

  • Modern compound bows: 80-85% efficient
  • Recurve bows: 65-75% efficient
  • Traditional longbows: 50-65% efficient

Understanding Arrow Speed Calculation

The Arrow Speed Calculator is a handy tool for archers and enthusiasts. This calculator lets you find out how fast an arrow travels based on important factors like draw weight and arrow mass. With it, you can choose the method that fits your needs best, ensuring accurate and helpful results.

Three Methods to calculate speed

There are three main methods you can use with the Arrow Speed Calculator. Each method uses different information to calculate the speed of the arrow:

  • Draw Weight Method: This method calculates speed based on the energy transferred from the bow to the arrow.
  • Kinetic Energy Method: Here, you input known kinetic energy and arrow mass to find the speed.
  • Chronograph Correction: This method uses measured speeds at a distance, adjusting for drag to estimate the actual speed.

Key Inputs for Accurate Results

To get accurate results, you’ll need to enter some key information. Depending on the method you choose, here are the inputs you'll commonly use:

  • Draw Weight: Select from pounds, kilograms, or newtons.
  • Arrow Mass: Use grains, grams, or ounces.
  • Bow Efficiency: Often set at 75% unless you know your bow's exact efficiency.

Visualize Your Data

The calculator also provides visualizations to help you understand your results better. You can see charts illustrating energy transfer and performance comparisons among different bow types. This visual data makes it easier to grasp how different factors affect arrow speed.

Understanding the Physics

Different methods to calculate arrow speed depend on basic physics principles. For example, the Draw Weight Method focuses on energy transfer, while the Kinetic Energy Method zeros in on energy and mass. Understanding these principles can help you see why certain inputs matter and how they influence the speed.

Why Bow Efficiency Matters

Bow efficiency plays a significant role in arrow speed calculations. It reflects how much of the bow's stored energy is converted to the arrow's speed. Higher efficiency means more speed. Here’s a quick breakdown of common bow efficiencies:

  • Compound Bows: 80-85% efficient
  • Recurve Bows: 65-75% efficient
  • Traditional Longbows: 50-65% efficient

Applications of the Arrow Speed Calculator

This calculator is perfect for various users, from competitive archers to casual hobbyists. By knowing the speed of your arrows, you can improve your performance, adjust your equipment, and refine your techniques. It allows you to make informed decisions that can lead to better results in your archery pursuits.

Final Thoughts on Arrow Speed

In summary, the Arrow Speed Calculator is an essential tool for anyone looking to understand and improve their archery skills. With its various calculation methods, clear inputs, and valuable insights, it provides a comprehensive way to grasp arrow dynamics and enhance your shooting experience.