Foot per second to Speed of light Converter
Convert feet per second to speed of light with our free online speed converter.
Quick Answer
1 Foot per second = 1.016703e-9 speed of light
Formula: Foot per second × conversion factor = Speed of light
Use the calculator below for instant, accurate conversions.
Our Accuracy Guarantee
All conversion formulas on UnitsConverter.io have been verified against NIST (National Institute of Standards and Technology) guidelines and international SI standards. Our calculations are accurate to 10 decimal places for standard conversions and use arbitrary precision arithmetic for astronomical units.
Foot per second to Speed of light Calculator
How to Use the Foot per second to Speed of light Calculator:
- Enter the value you want to convert in the 'From' field (Foot per second).
- The converted value in Speed of light will appear automatically in the 'To' field.
- Use the dropdown menus to select different units within the Speed category.
- Click the swap button (⇌) to reverse the conversion direction.
How to Convert Foot per second to Speed of light: Step-by-Step Guide
Converting Foot per second to Speed of light involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
1 Foot per second = 1.0167e-9 speed of lightExample Calculation:
Convert 60 feet per second: 60 × 1.0167e-9 = 6.1002e-8 speed of light
Disclaimer: For Reference Only
These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.
Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.
Need to convert to other speed units?
View all Speed conversions →What is a Foot per second and a Speed of light?
and Standards
The foot per second is defined as:
US Customary Definition
1 ft/s = the velocity of a body that travels a distance of one foot in a time interval of one second.
Formula: v (ft/s) = distance (feet) / time (seconds)
Exact SI conversion (since 1959 International Yard and Pound Agreement):
- 1 ft/s = 0.3048 m/s (exactly)
- 1 foot = 0.3048 meters (exactly)
Why ft/s Instead of mph?
Time scale appropriateness: Many technical applications involve sub-second events:
- Ballistics: Bullet flight time measured in milliseconds (0.001 seconds)
- Reaction distance: Driver reaction (1-2 seconds) × speed in ft/s = distance in feet
- Hydraulics: Flow velocities through pipes/channels measured continuously, not per hour
Intuitive scale for small objects:
- "Arrow travels 300 ft/s" vs "arrow travels 205 mph"—ft/s gives clearer sense of per-second distance
- Easier mental math: "How far does projectile travel in 0.1 seconds?" → 30 feet (at 300 ft/s)
Engineering calculations: US hydraulic formulas (Manning's, Darcy-Weisbach) use ft/s natively
Standard Conversions
Imperial/US conversions:
- 1 ft/s = 0.681818 mph (or 15/22 mph exactly)
- 1 ft/s = 3,600 feet/hour
- 1 ft/s = 720 feet/minute
Key conversion (memorize):
- 60 mph = 88 ft/s (exactly: 60 × 5,280 ÷ 3,600 = 88)
- 1 mph = 1.46667 ft/s (or 22/15 exactly)
Metric conversions:
- 1 ft/s = 0.3048 m/s (exactly)
- 1 ft/s = 1.09728 km/h
- 1 ft/s = 30.48 cm/s
Marine/aviation:
- 1 ft/s = 0.592484 knots
- 1 ft/s = 0.000888 Mach (at sea level, 68°F)
Relationship to Acceleration
Feet per second squared (ft/s²) measures acceleration:
- Gravity: g = 32.174 ft/s² (standard gravity, often rounded to 32.2 ft/s²)
- Car acceleration: 0-60 mph in 5 seconds = 88 ft/s ÷ 5 = 17.6 ft/s² average
- Comparison: SI gravity = 9.80665 m/s²
The speed of light in vacuum (symbol: c) is a universal physical constant that is exactly equal to 299,792,458 meters per second.
Formula: Energy (E) = Mass (m) × Speed of Light squared (c²)
Key Characteristics:
- Universal Limit: It is the upper limit for the speed at which conventional matter, energy, or information can travel through space.
- Constant: It is the same for all observers, regardless of their own speed or the speed of the light source (a core principle of Special Relativity).
- Exact: Since 1983, it is an exact value used to define the length of the meter.
Why 'c'? The symbol 'c' stands for celeritas, the Latin word for "swiftness" or "speed."
Speed in Different Mediums
While 'c' refers to the speed in a vacuum, light slows down when passing through transparent materials:
- Vacuum: 100% of c (299,792,458 m/s)
- Air: ~99.97% of c (very slightly slower)
- Water: ~75% of c (225,000,000 m/s)
- Glass: ~66% of c (200,000,000 m/s)
- Diamond: ~41% of c (124,000,000 m/s)
Note: The Foot per second is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Speed of light belongs to the imperial/US customary system.
History of the Foot per second and Speed of light
and Evolution
Ancient Feet to Modern Standardization
The foot through history:
- Ancient civilizations: Egyptian, Greek, Roman feet varied (285-335 mm)
- Roman pes: ~296 mm (11.65 inches)—basis for many European feet
- Medieval England: Multiple feet existed regionally (London foot, York foot)
- 1588: Queen Elizabeth I attempted standardization
- 1824: British Imperial system defined foot as 1/3 yard
- 1959: International Yard and Pound Agreement defined 1 foot = 0.3048 meters exactly
The second:
- Originally: 1/86,400 of mean solar day (Earth's rotation)
- 1967: Redefined using cesium-133 atomic transition (9,192,631,770 cycles = 1 second)
- Modern definition independent of Earth's rotation (which varies slightly)
The Foot-Pound-Second (FPS) System
British engineering standard (1800s-1960s):
- Length: foot (ft)
- Mass: pound (lb)
- Time: second (s)
- Force: poundal (1 lb·ft/s²) or pound-force (lbf)
- Energy: foot-poundal or foot-pound-force (ft·lbf)
- Velocity: feet per second (ft/s)
FPS system applications:
- Railway engineering: Train speeds, braking distances
- Ballistics: Muzzle velocity, projectile range calculations
- Hydraulics: Water flow in pipes, channels, rivers
- Structural engineering: Wind loads, beam deflections
Decline and persistence:
- 1960: SI system established internationally
- 1970s-1980s: Most countries transitioned to metric
- US holdout: American industry, construction, and firearms sectors retained FPS
- Current: US ballistics universally uses ft/s; engineering mixed (metric in automotive/aerospace, imperial in civil/construction)
Ballistics and the ft/s Standard
Why ballistics uses ft/s:
- Historical momentum: 19th-century firearms development used FPS system
- Industry standardization: Millions of existing specifications in ft/s
- Practical scale: 1,000-3,000 ft/s range fits projectile velocities well
- Reloading data: Powder charge tables, pressure curves all in imperial units
Ammunition velocity standards (all in ft/s):
- .22 LR: 1,200-1,700 ft/s
- 9mm Luger: 1,100-1,300 ft/s
- .45 ACP: 800-900 ft/s
- .223 Remington / 5.56 NATO: 3,000-3,300 ft/s
- .308 Winchester / 7.62 NATO: 2,600-2,800 ft/s
- .50 BMG: 2,800-3,000 ft/s
Chronograph measurements: All ballistic chronographs (devices measuring projectile speed) display in ft/s in US market.
US Hydraulic Engineering
Manning's Equation (open channel flow): v = (1.49/n) × R^(2/3) × S^(1/2)
Where:
- v = velocity in ft/s
- n = Manning's roughness coefficient
- R = hydraulic radius in feet
- S = channel slope (dimensionless)
Note: The 1.49 coefficient is specific to ft/s (metric version uses 1.0 with m/s)
US civil engineering applications:
- Storm drainage design
- Sanitary sewer sizing
- Irrigation canal design
- River and stream analysis
- Flood control structures
Persistence reason: US infrastructure built over 150+ years using imperial units—retrofitting millions of engineering drawings impractical.
Driver Education and Safety
The "60 mph = 88 ft/s" Rule:
Used universally in US driver education to teach reaction distance:
Reaction time (typical): 1.5 seconds Distance traveled (at 60 mph): 1.5 × 88 = 132 feet before braking begins
Stopping distance breakdown (60 mph on dry pavement):
- Reaction distance: 132 feet (time to perceive, react, move foot to brake)
- Braking distance: ~180 feet (actual braking to stop)
- Total stopping distance: ~312 feet (longer than a football field!)
Why ft/s is better than mph for this:
- Intuitive: "I travel 88 feet every second at highway speed"
- Easy calculation: seconds × ft/s = feet
- Using mph requires: mph × 1.467 × seconds = feet (harder mental math)
Ancient to Medieval: Instantaneous or Finite?
For centuries, thinkers like Aristotle believed light was instantaneous—that it filled space immediately. Others, like Empedocles and Alhazen, argued it must have a finite speed, but it was too fast to measure with human senses.
1676: The First Measurement
Ole Rømer, a Danish astronomer, made the first quantitative estimate. He noticed that the eclipses of Jupiter's moon Io happened earlier than predicted when Earth was closer to Jupiter and later when Earth was farther away. He correctly deduced that this time difference was due to the time it took light to travel the extra distance. He estimated light took about 22 minutes to cross Earth's orbit diameter (the modern value is about 16 minutes).
19th Century: Precision on Earth
- 1849 (Hippolyte Fizeau): Used a rotating toothed wheel and a mirror 8 km away to measure the speed. Result: ~313,300 km/s.
- 1862 (Léon Foucault): Improved the method using rotating mirrors. Result: ~298,000 km/s.
- 1887 (Michelson-Morley): Their famous experiment attempted to detect the "luminiferous aether" (the medium light was thought to travel through). The null result proved that the speed of light is constant in all directions, regardless of Earth's motion.
20th Century: The Ultimate Standard
- 1905 (Albert Einstein): Published Special Relativity, postulating that the speed of light is a constant for all observers.
- 1972 (Evenson et al.): Used laser interferometry to measure c with incredible precision: 299,792,456.2 m/s.
- 1983 (The Definition): The General Conference on Weights and Measures (CGPM) decided to stop measuring c and instead define it. They fixed the speed of light at exactly 299,792,458 m/s. This effectively redefined the meter as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."
Common Uses and Applications: feet per second vs speed of light
Explore the typical applications for both Foot per second (imperial/US) and Speed of light (imperial/US) to understand their common contexts.
Common Uses for feet per second
Across Industries
Ballistics and Firearms
- Ammunition specifications: All US ammo rated in ft/s muzzle velocity
- Chronograph testing: Velocity measurement devices display ft/s
- Ballistic calculators: Trajectory prediction software requires ft/s input
- Reloading data: Powder charge tables show expected ft/s velocities
Archery and Hunting
- Bow performance: IBO (International Bowhunting Organization) speed ratings in ft/s
- Arrow selection: Spine charts factor in bow speed (ft/s)
- Kinetic energy calculations: KE = (arrow weight × velocity²) ÷ 450,240 (weight in grains, velocity in ft/s → energy in foot-pounds)
US Civil Engineering
- Open channel flow: Manning's equation uses ft/s for rivers, canals, drainage
- Storm water management: Inlet design, detention pond sizing
- Sanitary sewer design: Minimum 2 ft/s to prevent settling
- Flood analysis: Peak flow velocities in ft/s
Driver Education and Safety
- Reaction distance teaching: "At 60 mph, you travel 88 feet every second"
- Following distance: "3-second rule" = 3 × 88 = 264 feet at 60 mph
- Crash reconstruction: Skid mark analysis uses ft/s for velocity calculations
Sports Science
- Baseball/softball: Pitch speed tracking (radar guns display ft/s or mph)
- Golf: Launch monitors measure clubhead and ball speed in ft/s
- Track and field: Sprint speeds converted to ft/s for analysis
Aviation (Limited Use)
- Rate of climb/descent: Feet per minute (fpm), but convertible to ft/s
- Ground speed calculations: Sometimes expressed in ft/s for short-field operations
- Note: Aviation primarily uses knots (nautical miles per hour)
When to Use speed of light
Astronomy and Astrophysics
- Light-year: The distance light travels in one year (~9.46 trillion km).
- Redshift: Measuring how fast stars move away by how their light stretches (Doppler effect for light).
- Lookback Time: Using the finite speed of light to study the early universe by looking at distant galaxies.
Telecommunications
- Latency: The delay in signal transmission.
- Ping: The time for a signal to go to a server and back. Even at light speed, a signal to the other side of the world and back takes theoretically ~133ms minimum (in fiber), plus routing time.
- Satellite Internet: Geostationary satellites are 35,786 km up. A round trip (Earth -> Satellite -> Earth) takes ~240ms, causing noticeable lag compared to fiber.
High-Energy Physics
- Particle Accelerators: The Large Hadron Collider (LHC) accelerates protons to 99.9999991% of the speed of light.
- Relativistic Mass: As particles approach c, they gain mass/energy rather than just speed, requiring immense energy to push them closer to the limit.
Additional Unit Information
About Foot per second (ft/s)
Is ft/s faster than mph?
No—ft/s is a smaller unit, so the number is bigger for the same speed.
- 1 mph = 1.467 ft/s
- 100 ft/s = 68 mph (the ft/s number is bigger, but it's actually slower than "100 mph")
Think of it like inches vs feet: 12 inches = 1 foot. "12" is bigger than "1", but they're the same length. Similarly, "100 ft/s" looks bigger than "68 mph", but they're the same speed.
What is the speed of sound in ft/s?
Approximately 1,125 ft/s at sea level, 68°F (767 mph, 343 m/s) = Mach 1
Temperature dependence:
- 32°F (0°C): 1,087 ft/s
- 68°F (20°C): 1,125 ft/s (standard reference)
- 86°F (30°C): 1,145 ft/s
Practical rule: "Sound travels about 1,100 feet per second"
Lightning distance trick:
- See lightning flash
- Count seconds until thunder: "one Mississippi, two Mississippi, three..."
- Multiply seconds by 1,100 feet
- Divide by 5,280 (feet per mile) to get miles
- Example: 5 seconds → 5,500 feet → ~1 mile away
Why bullets are "supersonic" or "subsonic":
- Supersonic (> 1,125 ft/s): Creates sonic boom/crack
- Subsonic (< 1,125 ft/s): No sonic crack (quieter with suppressor)
How do I convert mph to ft/s in my head?
Method 1 (rough): Multiply by 1.5
- 60 mph × 1.5 = 90 ft/s (actual: 88, close!)
- 40 mph × 1.5 = 60 ft/s (actual: 58.7, pretty close)
Method 2 (better): Use the "22/15 rule" or remember key values
- 30 mph = 44 ft/s
- 60 mph = 88 ft/s
- 90 mph = 132 ft/s
- Scale from these: 45 mph = halfway between 30 and 60 → (44+88)/2 = 66 ft/s
Method 3 (precise): Multiply by 1.467 (or 22/15)
- 50 mph × 1.467 = 73.35 ft/s
Why do bullets use ft/s instead of mph?
Four main reasons:
- Historical: US firearms industry developed using FPS system (foot-pound-second)
- Practical scale: Bullet velocities (1,000-3,000 ft/s) fit well, whereas 700-2,000 mph sounds awkward
- Short-duration events: Bullets travel for fractions of a second, so "per second" is more intuitive than "per hour"
- Ballistic calculations: Easier math for drop (inches), time of flight (milliseconds), energy (foot-pounds) when velocity is in ft/s
Example: .223 Rem bullet at 3,200 ft/s
- Distance in 0.1 seconds: 320 feet (easy mental math)
- If stated as 2,182 mph: distance in 0.1 sec requires mph × 1.467 × 0.1 = 320 feet (harder)
What is terminal velocity in ft/s?
Human skydiver:
- Belly-to-earth (stable, arms/legs spread): 176 ft/s (120 mph, 54 m/s)
- Head-down streamline (diving position): 295 ft/s (200 mph, 90 m/s)
- With parachute deployed: 15-25 ft/s (10-17 mph)—safe landing speed
Other objects:
- Raindrop (small, 1mm): 20 ft/s
- Raindrop (large, 5mm): 30 ft/s
- Baseball: 146 ft/s (100 mph)
- Penny (myth-busting): 30-50 ft/s (not lethal!)
- Bowling ball: 335 ft/s (228 mph)—dangerous!
Why terminal velocity varies: Air resistance balances weight. Bigger, heavier, or more streamlined = higher terminal velocity.
How fast is 300 ft/s in mph?
300 ft/s = 204.5 mph
Formula: 300 ft/s × 0.682 = 204.5 mph
Context: This is a common archery speed (compound bow arrow) or paintball velocity limit (280-300 ft/s)
Comparison:
- 300 ft/s = subsonic (below 1,125 ft/s speed of sound)
- 300 ft/s = 91.4 m/s (metric)
- 300 ft/s = 199 knots (marine/aviation)
What does "subsonic ammo" mean?
Subsonic ammunition: Muzzle velocity < 1,125 ft/s (speed of sound)
Why use subsonic:
- No sonic crack: Supersonic bullets create a sonic boom as they break the sound barrier—sounds like a loud "crack"
- Suppressor-friendly: With a suppressor (silencer), subsonic ammo is much quieter—only the muzzle blast is heard, not the sonic crack
- Hearing protection: Even without suppressor, subsonic is less loud
Common subsonic rounds:
- .45 ACP: 850-900 ft/s (naturally subsonic, heavy bullet)
- 9mm subsonic: 950-1,050 ft/s (special loads, lighter powder charge)
- .22 LR subsonic: 1,050-1,100 ft/s
Supersonic ammunition: Velocity > 1,125 ft/s
- Standard .223 Rem: 3,200 ft/s (almost 3× speed of sound!)
- Standard 9mm: 1,200 ft/s (just barely supersonic)
How far does a car travel in 1 second at 60 mph?
88 feet (exactly)
Breakdown:
- 60 mph = 60 miles/hour
- 60 miles/hour × 5,280 feet/mile ÷ 3,600 seconds/hour = 88 feet/second
Why this matters for safety:
- Reaction time: Average driver takes 1.5 seconds to react to hazard
- Distance during reaction: 1.5 seconds × 88 ft/s = 132 feet (before even touching brake!)
- Braking distance: Additional ~180 feet to stop (dry pavement)
- Total stopping distance: 132 + 180 = 312 feet at 60 mph
Following distance "3-second rule":
- At 60 mph, maintain 3 × 88 = 264 feet behind car ahead
- Gives 2× reaction distance (safer margin)
Can I use ft/s in scientific equations?
Yes, but you must use imperial units consistently:
Kinetic energy (imperial): KE (foot-pounds) = ½ × mass (slugs) × velocity² (ft/s)²
- 1 slug = 32.174 pounds-mass
- Or: KE (ft·lbf) = weight (lbf) × velocity² (ft/s)² / (2 × 32.2)
Force (imperial): F (pound-force) = mass (slugs) × acceleration (ft/s²)
- Or: F (lbf) = (weight in lbf / 32.2) × acceleration (ft/s²)
For scientific work, SI units (m/s, kg, Newtons, Joules) are strongly preferred:
- No slugs vs pounds confusion
- International standards require SI
- Easier unit conversions (all decimal)
Bottom line: You can use ft/s in calculations, but it's more complex than metric. For ballistics and US engineering where ft/s is standard, imperial equations exist. For research/publication, convert to m/s.
What's the difference between ft/s and ft/s²?
ft/s (feet per second): Velocity—how fast you're moving ft/s² (feet per second squared): Acceleration—how quickly your velocity changes
Example (free fall):
- Gravity acceleration: g = 32.2 ft/s²
- After 0 seconds: velocity = 0 ft/s
- After 1 second: velocity = 32.2 ft/s (acceleration added 32.2 ft/s)
- After 2 seconds: velocity = 64.4 ft/s (acceleration added another 32.2 ft/s)
- After 3 seconds: velocity = 96.6 ft/s
Car example (0-60 mph in 5 seconds):
- Change in velocity: 60 mph = 88 ft/s
- Time: 5 seconds
- Average acceleration: 88 ft/s ÷ 5 seconds = 17.6 ft/s²
Conversion Table: Foot per second to Speed of light
| Foot per second (ft/s) | Speed of light (c) |
|---|---|
| 0.5 | 0 |
| 1 | 0 |
| 1.5 | 0 |
| 2 | 0 |
| 5 | 0 |
| 10 | 0 |
| 25 | 0 |
| 50 | 0 |
| 100 | 0 |
| 250 | 0 |
| 500 | 0 |
| 1,000 | 0 |
People Also Ask
How do I convert Foot per second to Speed of light?
To convert Foot per second to Speed of light, enter the value in Foot per second in the calculator above. The conversion will happen automatically. Use our free online converter for instant and accurate results. You can also visit our speed converter page to convert between other units in this category.
Learn more →What is the conversion factor from Foot per second to Speed of light?
The conversion factor depends on the specific relationship between Foot per second and Speed of light. You can find the exact conversion formula and factor on this page. Our calculator handles all calculations automatically. See the conversion table above for common values.
Can I convert Speed of light back to Foot per second?
Yes! You can easily convert Speed of light back to Foot per second by using the swap button (⇌) in the calculator above, or by visiting our Speed of light to Foot per second converter page. You can also explore other speed conversions on our category page.
Learn more →What are common uses for Foot per second and Speed of light?
Foot per second and Speed of light are both standard units used in speed measurements. They are commonly used in various applications including engineering, construction, cooking, and scientific research. Browse our speed converter for more conversion options.
For more speed conversion questions, visit our FAQ page or explore our conversion guides.
Helpful Conversion Guides
Learn more about unit conversion with our comprehensive guides:
📚 How to Convert Units
Step-by-step guide to unit conversion with practical examples.
🔢 Conversion Formulas
Essential formulas for speed and other conversions.
⚖️ Metric vs Imperial
Understand the differences between measurement systems.
⚠️ Common Mistakes
Learn about frequent errors and how to avoid them.
All Speed Conversions
Other Speed Units and Conversions
Explore other speed units and their conversion options:
Verified Against Authority Standards
All conversion formulas have been verified against international standards and authoritative sources to ensure maximum accuracy and reliability.
National Institute of Standards and Technology — Standards for speed and velocity measurements
Last verified: December 3, 2025