Velocity Conversion

Supported units

Every unit below is defined against the metre per second. To convert between any two, divide their factors.

Several factors do not terminate — a metre per hour is exactly 1/3600 m/s — so they are stored as exact ratios and divided at the point of use rather than being rounded into the data. The knot is 1852 m/h exactly and the speed of light 299 792 458 m/s exactly, both by definition rather than measurement (SI Brochure, NIST SP 811).

Metric

Millimeters / Hour (mm/h)

One millimetre travelled in an hour — about 0.28 micrometres per second. It is the natural unit for movement too slow to watch, such as the creep of a glacier or the drift of a tectonic plate.

Geology

Rates of tectonic drift, glacier flow and land subsidence.

Materials testing

Crosshead speeds in very slow creep and corrosion tests.

Biology

Growth rates of roots, shoots and slow-moving organisms.

Millimeters / Minute (mm/min)

One millimetre travelled in a minute. This is the usual feed-rate unit on machine tools and on the crossheads of tensile testing machines.

Machining

Feed rates on mills, lathes and CNC machinery.

Materials testing

The standard crosshead speed for tensile and compression tests.

Additive manufacturing

Filament feed and layer deposition rates.

Millimeters / Second (mm/s)

One thousandth of a metre per second. It suits the deliberate motion of actuators, print heads and laboratory stages, where a metre per second would be far too coarse.

Robotics

Linear actuator and stage speeds.

3D printing

Print head travel and extrusion speeds.

Vibration analysis

Vibration velocity amplitudes on rotating machinery.

Centimeters / Hour (cm/h)

One centimetre travelled in an hour. Slow seepage and gradual growth are reported at this scale, where the numbers stay small and readable.

Hydrology

Infiltration and seepage rates through soil.

Botany

Plant growth rates over the course of a day.

Chromatography

Solvent front migration in thin-layer chromatography.

Centimeters / Minute (cm/min)

One centimetre travelled in a minute. Common on conveyor lines and in laboratory instruments where a slow, steady feed is what matters.

Process control

Conveyor and web speeds on slow production lines.

Laboratory instruments

Chart recorder and paper advance speeds.

Welding

Travel speeds in some automated welding processes.

Centimeters / Second (cm/s)

One hundredth of a metre per second, and the velocity unit of the CGS system. Fluid flows and small-scale laboratory motion are usually quoted in centimetres per second.

Fluid dynamics

Flow velocities in pipes and channels at laboratory scale.

Medicine

Blood flow velocities measured by Doppler ultrasound.

Seismology

Peak ground velocity during an earthquake.

Meters / Hour (m/h)

One metre travelled in an hour. Drilling, tunnelling and excavation progress is reported this way, since a shift is measured in hours and the advance in metres.

Drilling

Rate of penetration in boreholes and wells.

Tunnelling

Advance rates for tunnel boring machines.

Groundwater

Flow velocities through aquifers.

Meters / Minute (m/min)

One metre travelled in a minute, or 0.06 kilometres per hour. Industrial line speeds and cutting speeds are conventionally given in these terms.

Manufacturing

Conveyor, web and production line speeds.

Machining

Surface cutting speeds for tools and workpieces.

Textiles

Winding and weaving line speeds.

Meters / Second (m/s)

The SI unit of speed, derived directly from the metre and the second. Every other unit here is defined as a multiple of it, and physics calculations are almost always carried out in metres per second.

Physics and engineering

The reference unit for all velocity calculations in SI.

Meteorology

Wind speeds in scientific and aviation reports.

Athletics

Average speeds over a measured distance.

Kilometers / Hour (kph)

One kilometre travelled in an hour, which is exactly 1/3.6 metres per second. This is the road speed unit almost everywhere outside the United States and the United Kingdom.

Road traffic

Speed limits, speedometers and traffic enforcement.

Weather reports

Wind speeds given to the public.

Rail

Train operating and line speeds.

Kilometers / Minute (km/min)

One kilometre travelled in a minute — 60 km/h, or about 16.7 metres per second. Rarely used for vehicles, but convenient for aerospace and ballistic trajectories where distances are large and times short.

Aerospace

Ascent and descent rates for launch vehicles.

Ballistics

Long-range projectile trajectories.

Kilometers / Second (km/s)

One thousand metres per second. At this scale the unit belongs to astronomy and spaceflight: orbital velocities, escape velocities and the recession of galaxies are all quoted in kilometres per second.

Astronomy

Stellar and galactic radial velocities.

Spaceflight

Orbital velocities and delta-v budgets.

Geophysics

Seismic wave propagation speeds through the Earth.

Imperial

Yards / Hour (yd/h)

One yard travelled in an hour, or exactly 0.9144 metres per hour. An uncommon unit, met mainly in older imperial engineering records.

Historical engineering

Excavation and dredging progress in imperial records.

Textiles

Slow fabric feed rates on traditional machinery.

Yards / Minute (yd/min)

One yard travelled in a minute, or 0.01524 metres per second. Used for line speeds in industries that still work in yards, notably textiles and paper.

Textiles

Loom and winding speeds in imperial mills.

Paper and printing

Web speeds on older presses.

Yards / Second (yd/s)

One yard travelled in a second — exactly 0.9144 metres per second, so slightly under one metre per second. Occasionally used in sport where distances are measured in yards.

Sport

Player and ball speeds on fields measured in yards.

Ballistics

Projectile speeds in imperial shooting records.

Feet / Hour (ft/h)

One foot travelled in an hour, or exactly 0.3048 metres per hour. It appears in drilling and mining logs kept in imperial units.

Drilling

Rate of penetration in imperial well logs.

Mining

Advance rates in shafts and tunnels.

Feet / Minute (ft/min)

One foot travelled in a minute, exactly 0.00508 metres per second. It is the standard unit for air velocity in HVAC duct design and for lift speeds in North America.

HVAC

Air velocities in ducts and at diffusers.

Elevators

Rated car speeds in North American installations.

Machining

Surface feet per minute for cutting tools.

Feet / Second (ft/s)

One foot travelled in a second, exactly 0.3048 metres per second. It remains the working unit of US engineering mechanics and of ballistics, where muzzle velocities are always quoted in feet per second.

Ballistics

Muzzle velocities and projectile speeds.

Engineering mechanics

Velocities in US customary calculations.

Hydraulics

Flow velocities in pipes and open channels.

Miles / Hour (mph)

One statute mile travelled in an hour, which works out to exactly 0.44704 metres per second. This is the road speed unit of the United States and the United Kingdom.

Road traffic

Speed limits and speedometers in the US and UK.

Weather reports

Wind and storm speeds for the public in the US and UK.

Sport

Pitch, serve and swing speeds.

Miles / Minute (mpm)

One mile travelled in a minute — 60 mph, or exactly 26.8224 metres per second. Chiefly a convenience for aviation and motorsport, where covering a mile a minute is a memorable benchmark.

Aviation

A rule of thumb for ground speed and flight planning.

Motorsport

Lap speeds on mile-based ovals.

Miles / Second (mps)

One mile travelled in a second, exactly 1 609.344 metres per second. Far beyond any terrestrial vehicle, it is used for meteors, spacecraft and other astronomical speeds in sources that work in imperial units.

Astronomy

Meteor entry and cometary speeds in imperial sources.

Spaceflight

Escape and orbital velocities quoted in miles.

Nautical

Knot (UK) (kt)

The old British knot, one Admiralty nautical mile of 1 853.184 metres per hour. It is fractionally larger than the international knot, and the United Kingdom abandoned it in 1970 in favour of the international value.

Historical navigation

Speeds in British charts and logs recorded before 1970.

Naval archives

Interpreting Royal Navy records in their original units.

Knots (kn)

One international nautical mile per hour, exactly 1 852 metres per hour. Because a nautical mile is one minute of latitude, a vessel making one knot covers one minute of latitude in an hour — which is what keeps the unit standard in marine and air navigation worldwide.

Marine navigation

Vessel speed through water and over ground.

Aviation

Airspeed and ground speed on instruments and in clearances.

Meteorology

Wind speeds in aviation and marine forecasts.

Physical Constants

Light Velocity in Vacuum (c)

The speed of light in vacuum, exactly 299 792 458 metres per second. The value is exact by definition: since 1983 the metre has been defined from it, so it is a fixed constant rather than a measurement. Nothing carrying information travels faster.

Relativity

The universal speed limit, and the constant in E = mc².

Astronomy

Light years and light travel times between objects.

Telecommunications

Signal propagation delay in fibre and free space.

Cosmic Velocity First (v1)

The first cosmic velocity, about 7 900 metres per second: the speed needed to maintain a circular orbit just above the Earth’s surface. Reaching it is what separates a suborbital hop from an orbit.

Spaceflight

The target speed for reaching low Earth orbit.

Orbital mechanics

The baseline for circular orbit calculations.

Cosmic Velocity Second (v2)

The second cosmic velocity, about 11 200 metres per second: Earth’s escape velocity. An object launched at this speed leaves Earth’s gravity without further propulsion. It is the first cosmic velocity multiplied by the square root of two.

Interplanetary missions

The minimum speed for departing Earth.

Planetary science

Whether a planet can retain a given atmospheric gas.

Cosmic Velocity Third (v3)

The third cosmic velocity, about 16 700 metres per second: the speed needed, relative to Earth, to escape the Sun’s gravity altogether. The Voyager probes reached it with the help of gravity assists.

Interstellar probes

The threshold for leaving the solar system.

Mission design

Planning gravity assists to reach solar escape.

Cosmic Velocity Fourth (v4)

The fourth cosmic velocity, roughly 130 000 metres per second: the speed required to escape the Milky Way from our position in it. No spacecraft has come close, and the figure is approximate because the mass of the galaxy is not precisely known.

Astrophysics

Whether a star or object is gravitationally bound to the galaxy.

Hypervelocity stars

Identifying stars moving fast enough to escape.

Earth's Velocity (vE)

The mean orbital speed of the Earth around the Sun, about 29 784.8 metres per second — roughly 107 000 km/h. The actual speed varies over the year, faster at perihelion in January and slower at aphelion in July.

Celestial mechanics

The reference speed for Earth’s orbit.

Mission planning

Departure windows and transfers to other planets.

Velocity of Sound in Air [20°C] (v_sound_air)

The speed of sound in dry air at 20°C, about 343 metres per second. It depends strongly on temperature and barely at all on pressure, which is why the temperature has to be stated alongside the figure.

Aviation

The reference for Mach number, though it varies with altitude.

Acoustics

Wavelength calculations and room acoustic design.

Distance estimation

Timing the gap between a lightning flash and its thunder.

Velocity of Sound in Water (v_sound_water)

The speed of sound in fresh water at 20°C, about 1 481 metres per second — more than four times its speed in air. Sound carries much further underwater than light does, which is why sonar works the way it does.

Sonar

Converting echo timings into range.

Oceanography

Depth sounding and sub-sea profiling.

Medical imaging

Ultrasound assumes a similar speed through soft tissue.

Speed is distance divided by time

Every unit here is a distance unit paired with a time unit, which is why there are so many of them: any length can be combined with any interval. Meters per second, kilometers per hour, feet per second, and miles per hour are the same quantity expressed with different building blocks.

This also means conversion involves two factors, not one. Going from kilometers per hour to meters per second means multiplying the distance by 1,000 and dividing the time by 3,600 — which works out as dividing by 3.6. Handling both parts is where manual conversions usually go wrong.

Strictly speaking, speed and velocity are not identical: velocity includes direction, speed does not. The units are the same either way, and in ordinary use the terms are interchangeable.

Everyday units

Meters per second

The SI unit, and the one used in physics because it combines cleanly with other SI quantities. It is less intuitive for road speeds, where the numbers come out small — 30 m/s is already a brisk highway pace.

Kilometers per hour

The standard for road speed almost everywhere. Convenient because typical speeds land in a readable range and because distances on signs are in kilometers.

Miles per hour

Used for road speeds in the United States and United Kingdom. One mile per hour is about 1.609 km/h, so a 70 mph limit is roughly 113 km/h.

Knots

One nautical mile per hour, used in air and sea navigation. Because a nautical mile is one minute of latitude, speed in knots relates directly to position on a chart. This tool offers both the international knot, based on 1,852 meters, and the slightly larger UK knot.

Reference speeds

Several entries are physical constants rather than ordinary units, which makes them useful for putting a speed in context.

• Speed of sound in air— 343 m/s at 20 °C, about 1,235 km/h. This is the basis of Mach number: Mach 1 is the local speed of sound, which falls as air gets colder.
• Speed of sound in water— 1,481 m/s, more than four times faster than in air, which is why sonar works over long distances.
• Speed of light in vacuum— exactly 299,792,458 m/s. This is a defined value; the meter is derived from it rather than the other way round.
• Earth's orbital velocity— about 29,784.8 m/s, the average speed at which the planet travels around the Sun.

The cosmic velocities

These four thresholds describe the speed needed to escape successively larger gravitational systems, and they are why launching a spacecraft further costs so much more energy.

• First (v1)— about 7,900 m/s, the minimum speed to maintain orbit around Earth without propulsion.
• Second (v2)— about 11,200 m/s, escape velocity from Earth's gravity.
• Third (v3)— about 16,700 m/s, enough to leave the solar system.
• Fourth (v4)— about 130,000 m/s, the speed required to escape the Milky Way.

Worked examples

• A 100 km/h highway speed— about 27.8 m/s, or 62.1 mph.
• A commercial airliner at 500 knots— about 926 km/h, or 257 m/s.
• A 10-second 100 meter sprint— 10 m/s, which is 36 km/h.
• Walking at 5 km/h— about 1.39 m/s, or 3.1 mph.
• A 60 mph car— 88 feet per second, which is where the rule of thumb about stopping distances comes from.

Common uses

• Driving abroad— reading speed limits posted in the other system.
• Aviation and sailing— converting knots to and from kilometers or miles per hour.
• Physics and engineering— converting to meters per second so quantities combine correctly.
• Sport and training— comparing pace figures recorded in different units.
• Weather— wind speeds reported in knots, m/s, km/h, or mph depending on the source.
• Astronomy and spaceflight— relating orbital and escape speeds to familiar units.