Calculate arrow momentum in slug·ft/s and kg·m/s from arrow weight in grains and speed in fps, or solve for the arrow weight or speed you need.
Arrow Linear Momentum Formula
Linear momentum is mass multiplied by velocity. It scales directly with each variable, unlike kinetic energy’s squared speed term.
How the Calculation Works
Choose the requested output and enter the visible source values. Unit changes convert the current quantity; switching modes retains entered values.
How to Use This Calculator
- Select the value or workflow you want in the Solve for menu.
- Enter only the visible source values and use the units shown beside them.
- Select Calculate and review the primary answer, supporting values, warning, and steps.
- Use Reset before starting a different bow, arrow, or round.
Worked Example
A 450-grain arrow at 280 fps has 2.48859 kg-m/s of momentum, equivalent to about 0.559457 slug-ft/s.
Input and Result Guide
| Item | How to use it |
|---|---|
| Finished mass | Include shaft, point, insert, nock, fletching, wrap, and every installed part. |
| Velocity | Use actual chronographed speed when available. |
| SI momentum | Reported in kilograms-metres per second, equivalent to newton-seconds. |
| Archery momentum | Also reported in slug-feet per second. |
| Comparison | Use identical units and measurement conditions. |
Interpreting the Result
Momentum is useful for comparing the moving mass of two arrow setups. Review it alongside energy, flight, tune, structural integrity, and the intended task.
Assumptions and Limitations
Momentum alone is not a penetration or animal-suitability verdict. Broadhead geometry, impact angle, arrow flight, target medium, and legal requirements are not modeled.
Common Questions
Why did a field disappear after I changed Solve for?
A hidden field is either the requested output or irrelevant to the selected workflow. Enter the remaining visible source values.
Will my last successful calculation be restored?
Yes. Successful source inputs are saved in this browser and the result is recomputed when restored. Reset clears that saved state.
Sources
NIST unit-conversion constants; standard linear-momentum relationship; Easton Archery finished-arrow measurement guidance.
