Foot per second (ft/s) - Unit Information & Conversion

Quick Answer

What is a foot per second? Feet per second (ft/s) is the US/Imperial unit of speed measuring the distance in feet traveled in one second. It's the standard for ballistics (bullet speed: 1,000-3,000 ft/s), archery (arrow speed: 300 ft/s), and US hydraulic engineering. 1 ft/s = 0.6818 mph = 0.3048 m/s = 1.097 km/h. The critical conversion 60 mph = 88 ft/s is essential for driver safety (reaction distance: 1.5 seconds × 88 ft/s = 132 feet traveled before braking). Use our speed converter for all your ft/s conversions.

Quick Comparison Table

Speed	ft/s	mph	m/s	Common Example
Very slow	2 ft/s	1.4 mph	0.6 m/s	Slow walk
Walking	4-5 ft/s	2.7-3.4 mph	1.2-1.5 m/s	Normal walking pace
Jogging	10 ft/s	6.8 mph	3 m/s	Light jog
Running	20 ft/s	13.6 mph	6 m/s	Good running pace
Sprinting	30 ft/s	20.5 mph	9 m/s	Fast sprint
Usain Bolt peak	40.7 ft/s	27.8 mph	12.4 m/s	World record sprint speed
City driving	44 ft/s	30 mph	13.4 m/s	Urban speed limit
Highway (60 mph)	88 ft/s	60 mph	26.8 m/s	Key conversion for safety
Nerf dart	60 ft/s	41 mph	18 m/s	Toy projectile
Cheetah	100 ft/s	68 mph	30 m/s	Fastest land animal
Compound bow arrow	300 ft/s	205 mph	91 m/s	Modern archery
Paintball	280-300 ft/s	191-205 mph	85-91 m/s	Safety-regulated max
Baseball pitch	100-150 ft/s	68-102 mph	30-46 m/s	MLB fastball
9mm handgun	1,200 ft/s	818 mph	366 m/s	Common pistol round
.223 Remington	3,240 ft/s	2,209 mph	988 m/s	AR-15 rifle round
Speed of sound	1,125 ft/s	767 mph	343 m/s	Mach 1 at sea level (68°F)

Definition 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

History 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:

1. Historical momentum: 19th-century firearms development used FPS system
2. Industry standardization: Millions of existing specifications in ft/s
3. Practical scale: 1,000-3,000 ft/s range fits projectile velocities well
4. 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)

Real-World Examples and Applications

Projectile Velocities

Toys and recreational:

• Nerf dart (standard): 50-70 ft/s
• Foam ball: 30-50 ft/s
• Frisbee throw: 30-60 ft/s
• Paper airplane: 10-20 ft/s

Paintball and airsoft:

• Paintball (regulated max): 280-300 ft/s (safety limit to prevent injury)
• Airsoft (field limit): 300-400 ft/s for rifles, 280-350 ft/s for pistols
• Higher velocities banned at recreational fields due to injury risk

Archery:

• Longbow: 150-180 ft/s
• Recurve bow (Olympic): 200-225 ft/s
• Compound bow (hunting): 300-350 ft/s
• Crossbow: 300-400 ft/s

Sports balls:

• Baseball pitch (MLB fastball): 130-150 ft/s (90-102 mph)
• Baseball pitch (knuckleball): 95-105 ft/s (65-72 mph)
• Softball pitch: 80-110 ft/s (55-75 mph)
• Tennis serve (pro): 180-220 ft/s (120-150 mph)
• Golf ball (driver): 220-280 ft/s (150-190 mph)
• Soccer ball (penalty kick): 80-120 ft/s (55-82 mph)

Firearms (Muzzle Velocity)

Handguns:

• .22 LR: 1,200-1,700 ft/s (subsonic to supersonic)
• .380 ACP: 900-1,000 ft/s
• 9mm Luger: 1,100-1,300 ft/s
• .40 S&W: 1,000-1,200 ft/s
• .45 ACP: 800-900 ft/s (subsonic, heavier bullet)
• .357 Magnum: 1,400-1,800 ft/s
• .44 Magnum: 1,400-1,600 ft/s

Rifles:

• .223 Remington / 5.56 NATO: 3,000-3,300 ft/s (AR-15 platform)
• .308 Winchester / 7.62 NATO: 2,600-2,800 ft/s
• .30-06 Springfield: 2,700-2,900 ft/s
• .300 Winchester Magnum: 3,000-3,200 ft/s
• .50 BMG: 2,800-3,000 ft/s (anti-materiel rifle)
• Rimfire .22 LR: 1,200-1,400 ft/s

Subsonic vs supersonic:

• Subsonic: < 1,125 ft/s (no sonic boom, quieter with suppressor)
• Supersonic: > 1,125 ft/s (creates sonic crack/boom)

Why it matters: Higher velocity = flatter trajectory, longer range, more energy transfer. Ballistic calculators require muzzle velocity in ft/s for trajectory predictions.

Transportation and Driving

Speed limits (US):

• School zone: 25-30 ft/s (15-20 mph)
• Residential: 37 ft/s (25 mph)
• City street: 44 ft/s (30 mph)
• Urban highway: 66-73 ft/s (45-50 mph)
• Rural highway: 88-103 ft/s (60-70 mph)
• Interstate: 103-117 ft/s (70-80 mph)

Reaction distance (1.5-second reaction time):

• 30 mph (44 ft/s): 66 feet
• 45 mph (66 ft/s): 99 feet
• 60 mph (88 ft/s): 132 feet
• 70 mph (103 ft/s): 154 feet

Total stopping distance (reaction + braking, dry pavement):

• 30 mph: 66 + 75 = ~140 feet
• 45 mph: 99 + 170 = ~270 feet
• 60 mph: 132 + 240 = ~370 feet
• 70 mph: 154 + 325 = ~480 feet

Hydraulics and Fluid Flow

Open channel flow (rivers, canals, storm drains):

• Small stream: 1-3 ft/s
• Moderate river: 3-5 ft/s
• Fast-flowing river: 5-10 ft/s
• Flash flood: 10-20 ft/s (dangerous, can move cars)

Pipe flow (water distribution):

• Residential water supply: 3-8 ft/s (typical design range)
• Too slow (< 2 ft/s): Sediment settling, stagnation
• Too fast (> 10 ft/s): Erosion, noise, pressure surges

Erosion velocity limits (maximum safe velocity):

• Sandy soil: 2-3 ft/s
• Clay soil: 3-5 ft/s
• Gravel: 5-8 ft/s
• Rock: 10+ ft/s

Manning's equation example (concrete channel):

• Slope: 0.5% (0.005)
• Hydraulic radius: 2 feet
• Manning's n: 0.013 (concrete)
• Velocity: 1.49/0.013 × 2^(2/3) × 0.005^(1/2) = 7.2 ft/s

Nature and Weather

Falling objects:

• Raindrop (small, 1mm): 20 ft/s (6 m/s)
• Raindrop (large, 5mm): 30 ft/s (9 m/s)—terminal velocity
• Snowflake: 3-5 ft/s
• Hailstone (golf ball size): 100+ ft/s (dangerous!)

Animals:

• Human walking: 4-5 ft/s (2.7-3.4 mph)
• Human sprinting (Usain Bolt peak): 40.7 ft/s (27.8 mph)
• Housefly: 5-7 ft/s
• Honeybee: 20-25 ft/s
• Peregrine falcon (stoop): 292 ft/s (200 mph)—fastest animal
• Cheetah (sprint): 100 ft/s (68 mph)—fastest land animal
• Greyhound: 65 ft/s (44 mph)

Wind speeds:

• Light breeze: 5-10 ft/s (3-7 mph)
• Moderate breeze: 15-25 ft/s (10-17 mph)
• Strong wind: 35-50 ft/s (24-34 mph)
• Gale: 55-75 ft/s (37-51 mph)
• Hurricane (Category 1): 108-135 ft/s (74-95 mph)
• Hurricane (Category 5): >230 ft/s (>157 mph)

Physics Constants

Speed of sound:

• Air (68°F, sea level): 1,125 ft/s (767 mph, 343 m/s) = Mach 1
• Air (32°F): 1,087 ft/s (colder = slower)
• Water (68°F): 4,860 ft/s (4.3× faster than air)
• Steel: 19,554 ft/s (17× faster than air)

Free fall acceleration:

• Gravity (g): 32.174 ft/s² (standard, often rounded to 32.2 ft/s²)
• After 1 second: velocity = 32 ft/s (ignoring air resistance)
• After 2 seconds: velocity = 64 ft/s
• After 3 seconds: velocity = 96 ft/s

Terminal velocity (human):

• Belly-to-earth: 176 ft/s (120 mph, 54 m/s)
• Head-down streamline: 295 ft/s (200 mph, 90 m/s)

Common Uses 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)

Conversion Guide

ft/s to Other Units

ft/s to mph (miles per hour):

• Formula: mph = ft/s × 0.681818 (or ft/s × 15/22)
• Example: 100 ft/s = 100 × 0.682 = 68.2 mph
• Mental math: Divide by 1.5 for rough estimate (100 ft/s ÷ 1.5 ≈ 67 mph)

ft/s to m/s (meters per second):

• Formula: m/s = ft/s × 0.3048 (exactly)
• Example: 100 ft/s = 100 × 0.3048 = 30.48 m/s
• Mental math: Divide by ~3.3 (100 ft/s ÷ 3.3 ≈ 30 m/s)

ft/s to km/h (kilometers per hour):

• Formula: km/h = ft/s × 1.09728
• Example: 100 ft/s = 100 × 1.097 = 109.7 km/h
• Mental math: Multiply by ~1.1 (100 ft/s × 1.1 ≈ 110 km/h)

ft/s to knots:

• Formula: knots = ft/s × 0.592484
• Example: 100 ft/s = 100 × 0.592 = 59.2 knots
• Mental math: Divide by ~1.7 (100 ft/s ÷ 1.7 ≈ 59 knots)

From Other Units to ft/s

mph to ft/s:

• Formula: ft/s = mph × 1.46667 (or mph × 22/15)
• Example: 60 mph = 60 × 1.467 = 88 ft/s (exactly: 60 × 22/15 = 88)
• Mental math: Multiply by 1.5 for rough estimate (60 mph × 1.5 = 90 ft/s, close!)

m/s to ft/s:

• Formula: ft/s = m/s × 3.28084 (or m/s ÷ 0.3048)
• Example: 30 m/s = 30 × 3.281 = 98.4 ft/s
• Mental math: Multiply by ~3.3 (30 m/s × 3.3 ≈ 99 ft/s)

km/h to ft/s:

• Formula: ft/s = km/h × 0.911344 (or km/h ÷ 1.09728)
• Example: 100 km/h = 100 × 0.911 = 91.1 ft/s
• Mental math: Divide by ~1.1 (100 km/h ÷ 1.1 ≈ 91 ft/s)

knots to ft/s:

• Formula: ft/s = knots × 1.68781
• Example: 50 knots = 50 × 1.688 = 84.4 ft/s
• Mental math: Multiply by ~1.7 (50 knots × 1.7 ≈ 85 ft/s)

Critical Conversions (Memorize)

The "88" rule:

• 60 mph = 88 ft/s (exactly)
• 30 mph = 44 ft/s (exactly)
• 15 mph = 22 ft/s (exactly)
• Pattern: mph × 22/15 = ft/s

Speed of sound:

• 1,125 ft/s ≈ 767 mph ≈ 343 m/s = Mach 1 (at sea level, 68°F)
• Rough: "Sound travels about 1,100 feet per second"

Gravity:

• g = 32.2 ft/s² (standard, exact: 32.174 ft/s²)
• Compare: 9.8 m/s² (SI)

Common Conversion Mistakes

Mistake 1: Using "1.5" for mph to ft/s

Wrong approximation: 60 mph × 1.5 = 90 ft/s Right: 60 mph × 1.467 = 88 ft/s (or exact: 60 × 22/15 = 88)

Why it matters:

• Small speeds: error manageable (20 mph × 1.5 = 30 vs actual 29.3 ft/s)
• High speeds: error grows (100 mph × 1.5 = 150 vs actual 146.7 ft/s—3.3 ft/s error)
• Driver safety calculations: 90 ft/s gives 135-foot reaction distance vs actual 132 feet at 60 mph

Better mental math: Use the "22/15 rule" or remember key conversions (30→44, 60→88)

Mistake 2: Confusing ft/s with fps (frames per second)

Video gaming context: "This game runs at 60 fps"

• fps = frames per second (video frame rate)
• 60 fps = smooth video, 30 fps = standard video

Ballistics context: "This rifle shoots at 3,000 fps"

• fps = feet per second (muzzle velocity)
• 3,000 fps = high-velocity rifle round

How to tell: Context! If talking about computers/video/games → frames. If talking about projectiles/motion/speed → feet.

Mistake 3: Mixing Units in Physics Equations

Wrong: Kinetic energy = ½ × mass (pounds) × velocity² (ft/s)² → Joules Right: If using imperial, you get foot-pounds, not Joules

Imperial kinetic energy formula: KE (foot-pounds) = ½ × mass (slugs, not pounds!) × velocity² (ft/s)²

• 1 slug = 32.174 pounds-mass (confusing!)

Or use weight in pounds directly: KE (foot-pounds) = weight (pounds) × velocity² (ft/s)² / (2 × g)

• Where g = 32.2 ft/s²

For Joules: Convert everything to metric first (kg, m/s)

Mistake 4: Assuming Gravity is 10 ft/s² or 30 ft/s²

Wrong: g = 10 ft/s² (this is thinking of 10 m/s² in metric!) Right: g = 32.2 ft/s² (or exact: 32.174 ft/s²)

Free fall example:

• After 1 second: velocity = 32.2 ft/s (not 10 or 30!)
• After 2 seconds: velocity = 64.4 ft/s

Mistake 5: Forgetting Speed of Sound Varies

Wrong: "Speed of sound is always 1,125 ft/s" Right: Speed of sound varies with temperature and altitude

Temperature effect:

• 32°F (0°C): 1,087 ft/s
• 68°F (20°C): 1,125 ft/s (standard reference)
• 104°F (40°C): 1,159 ft/s
• Formula: v (ft/s) ≈ 1,087 + 1.1 × (T - 32), where T is °F

Altitude effect: Higher altitude = colder = slower sound

• Sea level: ~1,125 ft/s
• 10,000 feet altitude: ~1,077 ft/s

Mistake 6: Reaction Distance vs Stopping Distance

Wrong: "At 60 mph, I can stop in 88 feet" Right: "At 60 mph, I travel 88 feet every second—reaction distance alone (1.5 seconds) is 132 feet, THEN I need 180+ feet to brake"

Total stopping distance breakdown:

• Perception-reaction time: 1.5 seconds typical
• Distance during reaction (60 mph): 1.5 × 88 = 132 feet
• Braking distance (dry pavement): ~180 feet
• Total: 312 feet (longer than a football field!)