What Is Momentum?
A bolt's weight multiplied by its speed, expressed in slug-ft/s, which rewards heavier bolts more than kinetic energy does.
Momentum: definition
Also called: bolt momentum, slug-ft/s, lb-ft/s
Momentum is mass multiplied by velocity. For a crossbow bolt it describes how much "push" the bolt carries, as opposed to the energy it carries. Heavier bolts do relatively better on momentum than on kinetic energy, because speed is not squared.
With bolt weight in grains and speed in FPS, momentum in slug-ft/s is grains multiplied by FPS and divided by 225,218. The constant comes from converting grains to pounds (divide by 7,000) and pounds to slugs (divide by 32.174).
Momentum is often discussed alongside kinetic energy when people compare light-and-fast bolts with heavy-and-slow ones. Neither number is a complete measure of performance, and neither predicts how a bolt behaves on impact, which also depends on tip design, FOC and the target.
Momentum from grains and FPS
Momentum (slug-ft/s) = bolt weight (grains) x FPS / 225,218
A 400-grain bolt at 400 FPS: 400 x 400 / 225,218, about 0.71 slug-ft/s. A 425-grain bolt at 400 FPS gives about 0.75.
Same momentum, different energy
Two bolts with equal momentum can carry different kinetic energy. Calculated with the formulas on this site.
| Bolt | Speed | Momentum (slug-ft/s) | Kinetic energy (ft-lbs) |
|---|---|---|---|
| 350 grains | 450 FPS | 0.70 | 157 |
| 450 grains | 350 FPS | 0.70 | 122 |
| 400 grains | 400 FPS | 0.71 | 142 |
| 400 grains | 350 FPS | 0.62 | 109 |
Why Momentum matters
The first two rows show why people argue about the right metric. A light, fast bolt and a heavy, slower bolt can have the same momentum but quite different energy. Looking at only one number can favour one setup unfairly.
Both figures are calculated from bolt weight and speed, so neither adds new information about the crossbow. They help you see how a change of bolt weight shifts the balance between speed and weight. Always stay within your crossbow's rated bolt weight range.
How to read it on a spec sheet
- Check the units. Some pages use lb-ft/s, which is a different scale, so confirm the divisor before comparing.
- Look at both momentum and kinetic energy if a page quotes only one.
- Note whether the figure uses the rated or chronographed speed.
- Remember that momentum figures on product pages are rare. If you see one, check the formula.
- Use the same bolt weight in both calculations so the comparison is fair.
Common mistakes
- Using the kinetic energy constant (450,240) for momentum.
- Treating higher momentum as a promise of performance.
- Mixing grains with ounces or grams in the formula.
- Comparing a calculated figure with a measured one.
- Chasing momentum by exceeding the maximum bolt weight in the manual.
How to calculate momentum for your own bolt
- Weigh the finished bolt in grains.
- Record the chronographed speed in FPS from a safe test.
- Multiply the weight by the speed.
- Divide by 225,218 to get slug-ft/s.
- Calculate kinetic energy as well and compare the two.
Frequently Asked Questions
What is momentum in crossbow terms?
It is the bolt's mass multiplied by its speed. In practical units, it is grains times FPS divided by 225,218, giving slug-ft/s. It describes the bolt's push rather than its energy.
How do you calculate bolt momentum?
Multiply the bolt weight in grains by the speed in FPS, then divide by 225,218. A 400-grain bolt at 400 FPS comes to about 0.71 slug-ft/s. Verify your inputs before comparing.
Is momentum more important than kinetic energy?
Neither is a complete measure. Momentum rewards heavier bolts and energy rewards speed. Look at both along with bolt design and the target, and stay within the crossbow's rated bolt weights.
Why does a heavier bolt have more momentum?
Because momentum increases directly with weight. If speed drops only slightly when the bolt gets heavier, momentum can still rise, even when kinetic energy rises less or falls.
What units are used for momentum?
Slug-ft/s uses the slug as the unit of mass. Some people use lb-ft/s with different constants. Always check the units and constants a source uses before comparing.
Do crossbow manufacturers list momentum?
Rarely. Most list FPS and kinetic energy. If you want momentum, calculate it from the bolt weight and a measured speed using the formula on this page.
Keep learning
Guides that use this term
- GuideHow to Choose Crossbow BoltsChoose crossbow bolts in six steps: match rated length and minimum weight, then compare FOC, nocks, tips and tolerances using a spec table.Read the guide
- GuideWhat Is FOC in Crossbow Bolts?What FOC means on a crossbow bolt: the formula, a worked example, how front balance affects flight and penetration, and FOC figures from our bolt reviews.Read the guide
- GuideHow Fast Is a Crossbow Bolt (FPS)How fast a crossbow bolt travels: chronographed speeds from pistol to flagship, what changes bolt speed, and why speed and kinetic energy differ.Read the guide
Related terms
- Kinetic EnergyThe energy a bolt carries, in foot-pounds, calculated from its weight in grains and its speed in feet per second.
- FPS (Feet Per Second)The speed of a bolt as it leaves the crossbow in feet per second, usually rated with one specific bolt weight.
- GrainThe unit used to weigh crossbow bolts and tips, where 7,000 grains equal one pound, so a 400-grain bolt weighs about 0.9 ounce.
- FOC (Front of Center)The percentage of a bolt’s length by which its balance point sits ahead of the geometric midpoint, a measure of front-weighting.
- BoltThe projectile a crossbow shoots: a short carbon or aluminum shaft with a nock, vanes and a tip, often called an arrow.
- Power StrokeThe distance the string travels from its cocked position to rest, which sets how long the limbs have to accelerate the bolt.
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Definitions are general information. Manufacturer figures vary, so follow your crossbow's manual and verify local laws with the relevant authority.