Foot-Pounds of Energy (FPE)
FPE measures kinetic energy of projectiles in the imperial unit ft-lb. Formula E = wv²/450240 uses weight in grains and velocity in fps. Essential for ballistics, archery, and air gun analysis — velocity squared dominates energy.
Why This Physics Calculation Matters
Why: FPE indicates stopping power and penetration potential for ballistics. Hunters, shooters, and archers use it to compare loads and ensure ethical, effective terminal performance.
How: Energy scales with velocity squared — doubling velocity quadruples energy. Weight in grains (1 lb = 7000 gr) and velocity in fps are standard in US ballistics.
- ●E = wv²/450240; w in grains, v in fps. 1 ft-lb = 1.356 J.
- ●Velocity is more important than weight — doubling v gives 4× energy.
- ●Typical ranges: Airguns 5–50 ft-lb, Handguns 200–500 ft-lb, Rifles 1000–5000+ ft-lb.
- ●Momentum p = mv (in consistent units) affects penetration; energy affects expansion.
🎯 Common Projectiles
⚙️ FPE Parameters
Projectile Weight
Velocity
📚 What is Foot-Pounds of Energy?
FPE (Foot-Pounds of Energy) is the kinetic energy of a projectile, commonly used in ballistics. One foot-pound equals the energy to lift one pound by one foot against gravity.
This formula converts grain-fps units directly to foot-pounds.
📊 FPE Reference Table
| Projectile | Weight (gr) | Velocity (fps) | FPE (ft-lb) |
|---|---|---|---|
| .177 Airgun | 8 | 1000 | 18 |
| .22 LR | 40 | 1200 | 128 |
| 9mm | 124 | 1150 | 364 |
| .45 ACP | 230 | 850 | 369 |
| .223 Rem | 55 | 3240 | 1282 |
| .308 Win | 168 | 2650 | 2619 |
📜 Historical Development
Origin of Foot-Pound
The foot-pound originated in 18th century England as a practical unit. It's the work done lifting 1 pound by 1 foot against gravity - relatable for everyday tasks and engineering.
Ballistics Adoption
The firearms industry adopted ft-lbs in the 1800s because grain (bullet weight) and fps (muzzle velocity) were standard US measurements. The 450,240 divisor makes conversion clean.
The Grain Unit
One grain was originally the weight of a single grain of wheat. 7,000 grains = 1 pound. It's now precisely defined as 64.79891 milligrams.
Modern Usage
FPE remains the standard in US firearms ballistics, archery, airguns, and hunting. Most of the world uses Joules, but conversion is straightforward.
🎓 Practice Problems
Problem 1: 9mm vs .45 ACP
9mm: 124 gr at 1,150 fps. .45 ACP: 230 gr at 850 fps. Which has more muzzle energy?
Problem 2: Velocity Effect
A 55 gr bullet at 2000 fps vs 3000 fps. How much more energy at 3000 fps?
Problem 3: Weight Effect
Two .308 loads at 2,650 fps: 150 gr vs 180 gr. Calculate the energy difference.
Problem 4: Airgun Comparison
.177 (8 gr at 1,000 fps) vs .22 (14.3 gr at 800 fps). Which has more energy?
🎯 Hunting Energy Requirements
| Game | Min FPE at Impact | Typical Cartridge |
|---|---|---|
| Small game (rabbit) | 50+ | .22 LR, .17 HMR |
| Coyote | 300+ | .223 Rem |
| Whitetail deer | 1,000+ | .243 Win, .308 Win |
| Elk | 1,500+ | .30-06, .300 Win Mag |
| Moose | 2,000+ | .338 Win Mag |
| African dangerous game | 4,000+ | .375 H&H, .458 Win Mag |
Note: These are minimum recommendations. Bullet construction and shot placement matter as much as raw energy.
🔫 Airgun FPE Categories
Plinking/Target (5-15 ft-lbs)
- • Safe for backyard use
- • .177 cal most common
- • CO2 and spring-piston
- • ~500-800 fps
Pest Control (15-30 ft-lbs)
- • Effective on rats, starlings
- • .177 and .22 cal
- • Break barrel and PCP
- • ~800-1000 fps
Small Game (30-50 ft-lbs)
- • Rabbits, squirrels
- • .22 and .25 cal preferred
- • PCP platforms
- • Accuracy critical
Big Bore (100+ ft-lbs)
- • Coyotes, deer (legal varies)
- • .30, .357, .45, .50 cal
- • High-power PCP
- • Can exceed 500 ft-lbs
🏹 Archery FPE
FPE Formula for Arrows
KE = (mv²)/2
FPE = (arrow_wt × fps²)/450,240
Or: KE = (bow_eff × draw_wt × draw_length)/12
Typical Values
- • Target recurve: 25-40 ft-lbs
- • Hunting compound: 55-85 ft-lbs
- • Crossbow: 70-150 ft-lbs
- • Minimum for deer: ~40 ft-lbs
📐 The 450,240 Constant Explained
Derivation
KE = ½mv² (basic formula)
To convert: grains to pounds (÷7000), fps to ft/s (already ft/s), then multiply by 1/2
1/2 × 7000 × (1/g) = 1/2 × 7000 × (1/32.174) = 108.75
But we also need fps² factor: 1/2 × 1/(7000 × 32.174) = divisor
450,240 = 7000 grains/lb × 32.174 ft/s² × 2
⚠️ Energy vs. Effectiveness
Why Energy Isn't Everything
- • Bullet construction affects energy transfer
- • Penetration depth matters for vitals
- • Shot placement trumps raw energy
- • Momentum affects penetration
Energy Transfer Factors
- • Expanding bullets: 80-100% transfer
- • FMJ: 30-50% (pass-through)
- • Frangible: 100% (no exit)
- • Bonded: 70-90% (controlled expansion)
🔄 Unit Conversions
| From | To | Multiply By |
|---|---|---|
| Foot-pounds | Joules | 1.3558 |
| Joules | Foot-pounds | 0.7376 |
| Grains | Grams | 0.0648 |
| Grains | Pounds | 0.000143 |
| Feet per second | Meters per second | 0.3048 |
💡 Common Misconceptions
Misconception: Double the bullet weight = double the energy
Reality: True, but only at the same velocity. Heavier bullets are usually slower, so the relationship isn't that simple in practice.
Misconception: Higher FPE is always better for hunting
Reality: Too much energy can cause excessive meat damage. The goal is enough energy for clean kills, not maximum energy.
Misconception: FPE at the muzzle is what matters
Reality: Energy at impact is what counts. A .223 loses 50% of energy by 300 yards while a .338 Lapua only loses 30%.
🏆 Quick Reference Card
Core Formula
FPE = (wt × v²) / 450,240
wt = weight in grains
v = velocity in fps
Key Relationships
• Double velocity = 4× energy
• Double weight = 2× energy
• 1 ft-lb = 1.356 J
• 7000 gr = 1 lb
📚 Key Takeaways
Key Concepts
- ✓ FPE = wv²/450,240
- ✓ 1 ft-lb = 1.356 J
- ✓ Velocity squared effect
- ✓ 7000 grains = 1 pound
Applications
- ✓ Ballistics comparison
- ✓ Archery & air guns
- ✓ Hunting regulations
- ✓ Terminal performance
📊 Extended Cartridge Comparison
| Cartridge | Bullet (gr) | Velocity (fps) | FPE | Category |
|---|---|---|---|---|
| .22 Short | 29 | 1045 | 70 | Rimfire |
| .22 LR | 40 | 1200 | 128 | Rimfire |
| .22 WMR | 40 | 1875 | 312 | Rimfire |
| .380 ACP | 95 | 980 | 203 | Handgun |
| 9mm | 124 | 1150 | 364 | Handgun |
| .40 S&W | 180 | 1000 | 400 | Handgun |
| .45 ACP | 230 | 850 | 369 | Handgun |
| .357 Mag | 158 | 1250 | 548 | Revolver |
| .44 Mag | 240 | 1350 | 971 | Revolver |
| .223 Rem | 55 | 3240 | 1282 | Rifle |
| .308 Win | 168 | 2650 | 2619 | Rifle |
| .30-06 | 180 | 2750 | 3022 | Rifle |
🎯 Self-Defense Ballistics
FBI Protocol
FBI testing requires 12-18" penetration in ballistic gel through various barriers. Energy alone doesn't predict this - bullet construction matters enormously.
Minimum Energy Guidelines
General consensus: 200+ ft-lbs for self-defense minimum. Most defensive handgun loads fall in the 300-500 ft-lb range, balancing energy with controllability.
Expansion Factors
Modern hollow points can expand to 1.5-2× original diameter. This increases energy transfer by creating a larger wound channel without over-penetration.
Shot Placement vs. Energy
A .22 LR (128 ft-lbs) in a vital area is more effective than a .44 Mag (971 ft-lbs) in a non-vital area. Train for accuracy first, then consider caliber.
🔬 Energy Retention at Distance
Ballistic Coefficient (BC)
BC measures how well a bullet retains velocity against air resistance. Higher BC = less velocity loss = more energy at distance. Long, streamlined bullets have higher BC.
Typical BC Values
- • Round nose: 0.15-0.25
- • Flat base spitzer: 0.30-0.45
- • Boat tail match: 0.45-0.60
- • VLD/ELD match: 0.55-0.75
Energy at 300 Yards
- • .223 (BC 0.26): ~600 ft-lbs (47%)
- • .308 (BC 0.47): ~1660 ft-lbs (63%)
- • 6.5 CM (BC 0.58): ~1600 ft-lbs (71%)
Why It Matters
For hunting, you need sufficient energy at impact range, not just at the muzzle. A 1000 ft-lb minimum for deer means choosing cartridges that maintain this energy.
📖 Additional FAQs
Why do some countries ban by FPE?
UK limits airguns to 12 ft-lbs (.177) and 12.5 ft-lbs (airpistols) without a license. This threshold roughly separates recreation from weapons capable of serious injury.
Is FPE or velocity more important for expansion?
Velocity is more critical for expansion. Most hollow points need 850-900 fps minimum to expand reliably. A 230gr .45 at 750 fps may not expand, despite high energy.
Why is momentum sometimes preferred over energy?
Momentum (p = mv) better predicts penetration depth. Heavy, slow bullets may have less energy but penetrate more than light, fast bullets. Both metrics matter.
How accurate are chronograph readings?
Quality chronographs are accurate to ±1%. This means your calculated FPE could be off by ±2% (since velocity is squared). Average multiple shots for best results.
🎯 Rimfire Cartridge Comparison
| Cartridge | Bullet (gr) | Velocity (fps) | FPE | Best Use |
|---|---|---|---|---|
| .22 BB Cap | 18 | 780 | 24 | Indoor plinking |
| .22 Short | 29 | 1045 | 70 | Small pests |
| .22 LR (subsonic) | 40 | 1050 | 98 | Quiet shooting |
| .22 LR (standard) | 40 | 1200 | 128 | General purpose |
| .22 LR (high velocity) | 40 | 1280 | 146 | Small game |
| .22 LR (hyper velocity) | 32 | 1640 | 191 | Varmints |
| .17 HMR | 17 | 2550 | 245 | Varmints at range |
| .22 WMR | 40 | 1875 | 312 | Small game hunting |
🔬 Chronograph Testing
Optical Chronographs
Use sky screens to detect shadow. Accuracy ±1-2%. Affected by lighting conditions. Budget-friendly ($70-150). Require careful setup and good lighting.
Doppler Radar Chronographs
Use radar to track bullet. Accuracy ±0.5%. Not affected by lighting. More expensive ($300-500). Can measure velocity throughout flight, not just one point.
Testing Protocol
- • Shoot 5-10 round strings
- • Calculate average and SD
- • Discard obvious errors
- • Note temperature, altitude
Extreme Spread (ES)
ES = max velocity - min velocity. Good ammo has ES under 30 fps. ES directly affects FPE consistency. A 50 fps ES means ~8% variation in energy for typical rifle loads.
🌡️ Temperature Effects on FPE
Powder Temperature Sensitivity
Velocity changes ~1-3 fps per °F with most powders. A 50°F change can mean 50-150 fps difference. Temperature-stable powders minimize this effect.
Cold Weather (-20°F)
Velocity may drop 100-200 fps from standard (70°F). FPE can decrease 15-25%. Lubricants thicken, affecting cycling. Store ammo warm before use.
Hot Weather (100°F+)
Velocity may increase 50-100 fps. Higher pressure can stress older firearms. Store ammo in shade. Never leave ammo in direct sunlight in vehicles.
Altitude Effects
Less air resistance at altitude means slightly higher retained velocity downrange. Muzzle velocity is minimally affected. Drop calculations change significantly.
🏹 Crossbow FPE
Crossbow Categories
- • Entry level: 70-100 ft-lbs
- • Hunting: 100-130 ft-lbs
- • Premium: 130-175 ft-lbs
- • Speed demon: 175-200+ ft-lbs
Bolt Weight vs Speed
Heavier bolts (450+ gr) sacrifice speed but retain energy better downrange and are quieter. Lighter bolts (350 gr) maximize speed but lose energy faster. Match bolt weight to draw weight.
Minimum Hunting FPE
- • Turkey: 40+ ft-lbs
- • Whitetail: 65+ ft-lbs at impact
- • Elk: 90+ ft-lbs at impact
- • Most states require 75+ ft-lbs
Efficiency Matters
Crossbows convert 70-85% of stored energy to bolt kinetic energy. The rest is lost to limb vibration, noise, and friction. Premium cams and limbs improve efficiency.
⚖️ FPE vs. Momentum Debate
When FPE Matters More
- • Soft target damage potential
- • Temporary cavity size
- • Frangible bullet effectiveness
- • Hydrostatic shock (debated)
When Momentum Matters More
- • Penetration through barriers
- • Non-expanding bullet performance
- • Large, dangerous game
- • FMJ military rounds
Example: 9mm vs .45 ACP
9mm (124gr @1150): 364 ft-lbs, 12.5 lb-ft/s momentum. .45 ACP (230gr @850): 369 ft-lbs, 17.1 lb-ft/s momentum. Similar energy, but .45 has 37% more momentum.
Taylor Knockout Factor
TKO = (bullet_gr × velocity_fps × caliber_in) / 7000. Includes caliber size. Still debated, but popular for dangerous game cartridge comparison.
🏹 Archery and Crossbow FPE
Compound Bow Energy
- • 40 lb draw: 30-40 ft-lbs
- • 60 lb draw: 50-65 ft-lbs
- • 70 lb draw: 65-85 ft-lbs
- • Speed bows: 80-100+ ft-lbs
Crossbow Categories
- • Entry: 80-100 ft-lbs
- • Mid-range: 100-130 ft-lbs
- • High-end: 130-175 ft-lbs
- • Speed crossbows: 175-200+ ft-lbs
Arrow/Bolt Selection
Heavier projectiles (450+ gr) sacrifice speed but retain energy better at distance. Match arrow weight to your draw weight for optimal performance and safety.
Hunting Requirements
- • Turkey: 40+ ft-lbs at impact
- • Whitetail: 50-65+ ft-lbs
- • Elk/moose: 65-80+ ft-lbs
- • Shot placement matters most
🔬 Ballistic Gel Testing
Standard Protocol
10% gelatin at 4°C (39°F) simulates soft tissue. FBI standard requires 12-18" penetration through barriers. Calibrated with BB shot to ensure consistent density.
Energy Transfer
Observe temporary and permanent cavity formation. High-velocity impacts create larger temporary cavities. Permanent cavity width correlates with actual wound channel.
Barrier Testing
- • Heavy clothing: 4 layers denim
- • Wallboard: 2 sheets drywall
- • Plywood: 3/4" pine board
- • Auto glass: laminated windshield
Interpreting Results
FPE determines maximum potential damage, but bullet behavior is crucial. A well-designed hollow point at 350 ft-lbs often outperforms FMJ at 500 ft-lbs for defensive use.
📜 Historical Development
Origins of FPE
The foot-pound energy unit emerged in 19th century Britain as engineers needed to quantify mechanical work. James Watt used it to compare steam engines to horse power.
Ballistics Application
With smokeless powder (1880s), higher velocities made energy comparisons essential. The formula E = mv²/450240 became standard for American shooters and remains so today.
The Grain Unit
The grain (1/7000 lb) dates to medieval Europe - originally the weight of a barleycorn. Its precision (0.0648 g) makes it ideal for measuring bullets and powder charges.
Modern Usage
While scientists use Joules, the shooting industry remains committed to ft-lbs and grains. International regulations often specify limits in both systems.
💡 Common Misconceptions
Misconception: Higher FPE always means more effective
Reality: Effectiveness depends on energy TRANSFER, not just total energy. Over-penetrating rounds waste energy beyond the target.
Misconception: Muzzle energy equals impact energy
Reality: Bullets lose energy to air resistance. A .308 at 300 yards retains only ~60% of its muzzle energy. Always consider energy at target distance.
Misconception: Doubling bullet weight doubles energy
Reality: Energy scales linearly with mass but with velocity SQUARED. Increasing velocity is far more effective for increasing energy.
🏆 Quick Reference Card
Core Formula
FPE = (gr × fps²) / 450,240
gr = bullet weight in grains
fps = velocity in feet per second
Key Conversions
1 ft-lb = 1.356 Joules
1 grain = 0.0648 grams
1 fps = 0.3048 m/s
450,240 = 2 × 7000 × 32.174
📖 Additional FAQs
Why is the 450,240 constant used?
It converts grains to pounds (÷7000), accounts for the ½ in kinetic energy formula (×2), and includes gravitational constant (×32.174). The result: 7000 × 2 × 32.174 = 450,436, rounded to 450,240 in common usage.
How do I measure my own FPE?
Use a chronograph to measure velocity (fps) and weigh your projectile in grains. Apply the formula: FPE = (grains × fps²) / 450,240. Take 5-10 shots and average for accuracy.
Does barrel length affect FPE?
Yes. Longer barrels generally produce higher velocity (more time for propellant gases to accelerate the projectile). Expect ~25-50 fps per inch for rifle cartridges.
What's the minimum FPE for hunting?
Guidelines vary by game: small game 40+, deer 1000+ at impact, elk 1500+ at impact. These are minimums - more energy provides a margin for imperfect shots.
🔬 Advanced Concepts
Energy Decay at Distance
Bullets lose energy to air resistance. Use ballistic coefficient (BC) and drag models to predict energy at any range. High BC = less energy loss.
Power Factor
Competition shooting uses Power Factor = (weight × velocity) / 1000. Unlike FPE, it's linear in velocity - useful for scoring recoil management.
Sectional Density
SD = bullet weight (lb) / caliber². Higher SD means better penetration. A 180gr .308 has SD of 0.271, excellent for game. SD above 0.25 is considered good.
Ballistic Coefficient
BC measures how well a bullet resists air drag. Higher BC = better velocity retention = more energy at distance. Modern long-range bullets have BC > 0.5.
📝 Summary Points
Key Formula: FPE = (grains × fps²) / 450,240 gives energy in foot-pounds.
Velocity Dominates: Because velocity is squared, increasing speed is more effective than increasing weight for boosting energy.
Range Considerations: Always consider energy at target distance, not just muzzle energy. High BC bullets retain more energy.
Practical Limits: Match energy to purpose - 1000+ ft-lbs for deer, 1500+ for elk. More is better but not necessary.
Temperature Effects: Cold weather can reduce velocity 50-150 fps, significantly impacting energy. Check your loads in expected conditions.
Chronograph Testing: Always verify with a chronograph. Published data uses test barrels - your actual velocity may differ substantially.
Energy vs. Momentum: Energy predicts damage potential; momentum predicts penetration. Both matter for terminal performance.
Barrel Length: Shorter barrels reduce velocity. A 16" barrel may give 100-200 fps less than a 24" barrel, significantly reducing FPE.
Altitude Effects: Higher altitude means less air resistance - bullets retain velocity better. Muzzle velocity is essentially unchanged.
Ammunition Quality: Premium ammo has tighter velocity SD (standard deviation). Low SD means consistent FPE shot to shot.
Bullet Design: The same FPE can perform very differently depending on bullet construction. Modern designs optimize energy transfer for specific uses.
Legal Minimums: Some jurisdictions require minimum energy for hunting. Check local regulations for specific cartridge and game requirements.
Reloading Variables: Powder charge, seating depth, and primer choice all affect velocity and thus FPE. Keep detailed records when developing loads.
Suppressor Effects: Suppressors can add 10-25 fps by extending effective barrel length. The energy gain is small but the sound reduction is substantial.
Accuracy vs. Energy: The most energetic load isn't always the most accurate. Find the balance that delivers consistent hits AND sufficient energy at range.
Real-World Testing: Paper specs matter less than field performance. Test your complete system (firearm + ammo + shooter) for reliable terminal performance.
Safety Margins: Use cartridges that exceed minimum requirements. This accounts for imperfect shots, range estimation errors, and velocity variations.
Ethical Considerations: For hunting, choose energy levels that ensure quick, humane kills. Wounded game that escapes is a conservation and ethical issue.
Training Ammo: Practice with similar FPE loads to match recoil characteristics. Training with .22 LR won't prepare you for .300 Win Mag recoil.
Retained Energy: What matters is energy at the target, not at the muzzle. Long-range hunters must account for significant energy loss over distance.
Modern Advances: Today's bullets transfer energy more efficiently than ever. A 2024 hunting bullet may outperform a 1990s design with the same FPE.
Shot Placement: A well-placed shot with marginal energy beats a poor shot with excessive energy. Practice accuracy first, then optimize energy.
Game Response: Different animals respond differently to the same FPE. Thin-skinned game drops quickly; heavy game may require more or better-placed shots.
Airgun FPE: Air rifles range from 5 ft-lbs (plinking) to 100+ ft-lbs (big bore hunting). PCP guns offer higher, more consistent energy than springers.
Regulatory Compliance: Some regions regulate airguns by FPE. UK limit is 12 ft-lbs without license. Other countries vary widely.
Industry Standards: SAAMI and CIP publish standard pressure and velocity specs. Manufacturer data should be verified against your specific firearm.
Documentation: Keep records of your FPE testing for load development and legal compliance where required. Consistency matters for performance and safety.
Conclusion: FPE is a useful metric for comparing projectiles, but it's only one factor in terminal performance. Consider bullet construction, shot placement, and conditions for best results.
Further Learning: Study ballistics tables for your specific cartridges. Understand how velocity drops at range, and how that affects your effective hunting distance.
Resources: Hornady, Nosler, and Sierra publish detailed ballistics data. Many free online calculators can model your specific loads at various ranges and conditions.
Final Thought: Understanding FPE helps you make informed decisions about ammunition selection. Combine this knowledge with practice for the best field results.
Stay Safe: Always follow firearm safety rules. Know your target and what's beyond it. Higher energy means greater responsibility for safe shooting practices.
Have Fun: Shooting sports are rewarding hobbies. Understanding the physics enhances your appreciation and makes you a more effective, responsible shooter.
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
FPE formula E = wv²/450240 derives from KE = ½mv² with grain and fps units.
— SAAMI Standards
1 ft-lb = 1.356 J — standard energy conversion for ballistics and mechanics.
— NIST
Velocity squared: 1200 fps vs 600 fps gives 4× energy for same projectile weight.
— Ballistics handbooks
Arrows: 400 gr at 300 fps ≈ 80 ft-lb; crossbow bolts can exceed 100 ft-lb.
— Archery standards
What is Foot-Pounds of Energy (FPE)?
Foot-pounds of energy (FPE) is a unit of kinetic energy commonly used in ballistics to measure the energy delivered by a projectile. It represents the work done by a force of one pound acting through a distance of one foot. FPE is calculated using the formula E = wv²/450240, where w is weight in grains and v is velocity in feet per second. This measurement is essential for understanding stopping power, penetration, and terminal ballistics.
📋 Key Takeaways
- • FPE Formula: E = wv²/450240 — energy increases with the square of velocity
- • 1 ft-lb = 1.356 J — standard energy conversion
- • Velocity is more important than weight — doubling velocity quadruples energy
- • Typical ranges: Airguns (5-50 ft-lb), Handguns (200-500 ft-lb), Rifles (1000-5000+ ft-lb)
💡 Did You Know?
How FPE Calculations Work
🔫 Energy Formula
w = weight (grains), v = velocity (fps)
⚡ Energy Conversion
Standard energy unit conversion
🎯 Expert Tips
💡 Velocity Matters Most
Energy increases with velocity squared. Doubling velocity quadruples energy. For maximum energy, prioritize velocity over weight increases.
💡 Understand Energy Levels
Airguns: 5-100 ft-lb. Handguns: 200-500 ft-lb. Rifles: 1000-5000+ ft-lb. Match energy to intended use and legal requirements.
💡 Momentum vs Energy
Energy (E=mv²/2) determines penetration depth. Momentum (p=mv) determines recoil and knock-down power. Both matter for terminal ballistics.
💡 Legal Considerations
Many jurisdictions regulate maximum energy for airguns and crossbows. Check local laws — typically 12-20 ft-lb limits for airguns without license.
⚖️ Energy Levels by Projectile Type
| Projectile Type | Typical Energy | Use Case | Penetration |
|---|---|---|---|
| Airgun (.177) | 5-20 ft-lb | Target shooting | Low |
| .22 LR | 100-200 ft-lb | Small game | Medium |
| 9mm Handgun | 300-400 ft-lb | Self-defense | Medium-High |
| .223 Rifle | 1200-1300 ft-lb | Varmint hunting | High |
| .308 Rifle | 2500-2800 ft-lb | Big game hunting | Very High |
| .50 BMG | 13000+ ft-lb | Long-range/armor | Extreme |
❓ Frequently Asked Questions
What is the difference between FPE and joules?
FPE (foot-pounds) and joules are both energy units. 1 ft-lb = 1.356 J. FPE is traditional in US ballistics, while joules are standard internationally. Both measure the same thing: kinetic energy.
Why does velocity matter more than weight for energy?
Energy formula E = mv²/2 shows energy depends on velocity squared. Doubling velocity quadruples energy, while doubling weight only doubles energy. That's why high-velocity rounds deliver more energy than heavy, slow rounds.
What energy is needed for hunting different game?
Small game (rabbits, squirrels): 50-200 ft-lb. Medium game (deer): 1000-2000 ft-lb. Large game (elk, moose): 2000-3000+ ft-lb. Always check local regulations and use appropriate calibers.
How does FPE relate to stopping power?
FPE measures kinetic energy, which affects penetration depth. However, stopping power also depends on bullet design, shot placement, and momentum. Higher FPE generally means deeper penetration and more tissue damage.
What is the legal limit for airgun energy?
Many jurisdictions limit airguns to 12-20 ft-lb without a firearms license. UK: 12 ft-lb for air rifles without license. Check local laws — regulations vary by country and state.
Can I calculate velocity from energy and weight?
Yes! Rearranging E = wv²/450240 gives v = √(E×450240/w). If you know energy and weight, you can solve for velocity. This is useful for ballistic calculations.
What is the relationship between energy and momentum?
Energy (E=mv²/2) determines penetration. Momentum (p=mv) determines recoil and knock-down power. A heavy, slow bullet has high momentum but lower energy. A light, fast bullet has high energy but lower momentum.
How accurate is the FPE formula?
The formula E = wv²/450240 is accurate for standard ballistics calculations. The constant 450240 accounts for unit conversions (grains to pounds, fps to ft/s). For precise measurements, use chronographs and verified data.
📊 Foot-Pounds of Energy by the Numbers
📚 Official Data Sources
⚠️ Disclaimer: This calculator provides estimates based on standard ballistics equations. Actual energy may vary due to barrel length, powder charge, atmospheric conditions, and other factors. Always verify with chronograph measurements. Not a substitute for professional ballistics analysis. Use responsibly and in compliance with all applicable laws and regulations. Firearms and projectiles can be dangerous — always follow safety protocols.