Convert m/s to c metres per second ↔ the speed of light Free Online Secure
Type a value in metres per second and read it in the speed of light at once. The factor is exact by definition, the arithmetic happens in your browser, and nothing is sent anywhere.
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Convert from metres per second
Common values — Convert m/s to c (metres per second ↔ the speed of light)
| m/s | c |
|---|---|
| 1 | 0.00000000333564095198 |
| 2 | 0.00000000667128190396 |
| 3 | 0.0000000100069228559 |
| 5 | 0.0000000166782047599 |
| 10 | 0.0000000333564095198 |
| 20 | 0.0000000667128190396 |
| 50 | 0.000000166782047599 |
| 100 | 0.000000333564095198 |
Where these units come from
Speed has no unit of its own: it is a length divided by a time, so every trade simply kept the length it was already using. That is why the same motion is 100 km/h on a European road sign, 62 mph on an American one and 27.8 m/s in a physics problem. The knot is the oldest of them and the most literal: sailors paid out a line with knots tied at even spacing and counted how many ran through their fingers while a sand glass emptied, so the speed was read off in knots. One knot is one nautical mile per hour, and a nautical mile is a minute of latitude — which is why ships and aircraft still use it. The speed of light is the odd one out: since 1983 it is not measured but fixed at exactly 299,792,458 m/s, because the metre is now defined from it.
Where you meet them
Kilometres and miles per hour live on speedometers and road signs, metres per second in physics, engineering and wind reports, feet per second in ballistics and in American machine shops. Knots carry shipping, aviation and marine weather, and Mach numbers appear wherever an aircraft is fast enough for the air's own stiffness to matter. The speed of light turns up less in daily life than in distances: a light year is simply how far it gets in one.
Questions people ask
Is Mach 1 a fixed speed?
No. Mach is a ratio to the speed of sound in the surrounding air, and sound travels more slowly in colder air. This page uses the standard sea-level figure, 340.294 m/s, so Mach 1 here is about 1225 km/h. At the altitude airliners cruise at, the air is some 50 degrees colder and the same Mach 1 is roughly a tenth slower. An aircraft can therefore hold a constant Mach number while its speed over the ground changes.
Why do ships and aircraft use knots rather than km/h?
Because a nautical mile is one minute of arc of latitude. A vessel making one knot covers one minute of latitude in an hour, so speed, time and position on a chart fit together without conversion. The same reasoning kept the nautical mile at exactly 1852 metres rather than rounding it to something tidier.
Is the answer exact?
Where both units are defined in terms of one another by whole numbers, yes — the page says so above the figure, and the only rounding is in how many digits are shown. Where the ratio has no finite decimal, the page shows twelve significant digits and says the relation is approximate rather than pretending otherwise.
Does anything I type leave my device?
No. The arithmetic runs in your browser; nothing is uploaded and there is no server to upload it to. Load the page once and it keeps working with the network switched off.
Velocities as fractions of c: how fast things move in the cosmos
Astronomers rarely say that a star moves at 230,000 metres per second. They say it moves at about a tenth of one per cent of the speed of light. Writing a velocity as a fraction of c puts planets, probes, galaxies and pulsars on one scale and shows at once whether relativity matters. To convert m/s to c, divide by 299,792,458: 100,000,000 m/s comes to 0.3336 c, 200,000,000 m/s to 0.667 c and 29,979,246 m/s to exactly 0.1 c. The calculator above divides while you type, and the sections below tour the speeds of the solar system and beyond.
Below you will find the rule with worked examples, a profile of each unit, a comparison and many astronomical examples, then the usual slips. Everything is computed in your browser and nothing is sent to a server. For research, use the official value of the constant and state your units.
How to convert m/s to c: divide by 299,792,458
The rule
The speed of light in a vacuum is exactly 299,792,458 m/s by definition. To find what fraction of c a velocity represents, divide it by that number. 3,000,000 m/s gives 0.01 c, 50,000,000 m/s gives 0.1668 c and 250,000,000 m/s gives 0.834 c. In the other direction, multiply the fraction of c by 299,792,458.
Worked examples
The Earth orbits the Sun at 29,780 m/s, which is 0.0000993 c. The Parker Solar Probe reached 192,222 m/s, 0.00064 c. A supernova ejecta cloud at 10,000,000 m/s is at 0.0334 c, and a millisecond pulsar's equator at 72,000,000 m/s is at 0.24 c.
An exact division
The constant is fixed by the definition of the metre, so the division adds no uncertainty. The only approximation is the rounding you apply: using 3 × 10⁸ in place of 2.998 × 10⁸ gives an error of 0.07 per cent.
A quick sanity test
The result is hundreds of millions of times smaller than the number of m/s. If a “convert m/s to c” calculation gave a larger figure than you began with, you multiplied by mistake.
The metre per second
The unit of observed velocity
The metre per second is the SI unit of speed. Observatories and mission teams often publish velocities in km/s, but the underlying quantity is the same, and the SI value is what goes into equations.
Where it appears
Mission data, observatory catalogues, simulations and textbooks.
The speed of light, c
The cosmic yardstick
The symbol c denotes the speed of light in vacuum. Writing a velocity as a fraction of c, often called β, makes it dimensionless and shows immediately how close the motion is to the universal limit.
Where it appears
Astrophysics, particle physics, relativity and cosmology.
Metres per second or fractions of c?
A velocity of one m/s corresponds to 3.3356 × 10⁻⁹ c, so the number in c is nearly three hundred million times smaller. For 10 million m/s the fraction is 0.0334 and for 100 million m/s it is 0.3336. Written in units of c, speed is dimensionless and relativity is easy to judge.
The conversion is exact, with no hidden rounding. The only trap is the direction: from m/s to c the figure drops enormously.
Where the conversion shows up
The solar system
The Earth's equator turns at 465 m/s, 1.55 × 10⁻⁶ c. The Earth orbits at 29,780 m/s, 9.9 × 10⁻⁵ c. Mercury, the fastest planet, moves at 47,360 m/s, 1.6 × 10⁻⁴ c. Even the swiftest planet is at a fraction of a percent of the speed of light. A “convert m/s to c” calculation puts these motions on one scale.
Our galaxy and beyond
The Sun moves round the galaxy at about 230,000 m/s, 0.00077 c. Relative to the cosmic microwave background, our galaxy moves at 370,000 m/s, 0.00123 c. The Local Group of galaxies moves at around 620,000 m/s, 0.0021 c.
Compact objects
A millisecond pulsar spinning 716 times a second with a radius of 16 km has an equator moving at 72,000,000 m/s, 0.24 c. Matter near a black hole moves at significant fractions of c, and the star S2 near the centre of our galaxy passes at 7,650,000 m/s, 0.0255 c.
Spacecraft
Voyager 1 moves at about 17,000 m/s, 5.7 × 10⁻⁵ c. New Horizons passed Pluto at roughly 16,260 m/s, 5.4 × 10⁻⁵ c. The Helios 2 probe reached 70,220 m/s, 2.3 × 10⁻⁴ c, a record that stood for decades. The Parker Solar Probe has reached 192,222 m/s, 6.4 × 10⁻⁴ c.
The mental shortcut
To convert m/s to c in your head, divide by 3, then by 10⁸, and add 0.07 per cent. For 150,000,000 m/s: 1.5 / 3 gives 0.5, plus 0.0003 gives 0.5003, which is the exact value.
Spreadsheet formulas
For a “convert m/s to c” calculation in a worksheet, type the velocities in column A and =A2/299792458 in column B. A third column with =1/SQRT(1-B2^2) gives the Lorentz factor. Scientific notation keeps the tiny results readable.
Rounding and precision
When you convert m/s to c for a paper, four significant figures are usually enough: 0.3336 c for 100,000,000 m/s. If the result will go into 1/√(1 − β²), keep every digit, since for β near 1 small differences make large effects.
Landmarks to memorise
299,792 m/s is 0.001 c. 2,997,925 m/s is 0.01 c. 29,979,246 m/s is 0.1 c. 99,930,819 m/s is one third of c. 149,896,229 m/s is 0.5 c. 269,813,212 m/s is 0.9 c. With these you can convert m/s to c at a glance.
Reference ladder
1 m/s is 3.34 × 10⁻⁹ c. 10 m/s is 3.34 × 10⁻⁸ c. 1,000 m/s is 3.34 × 10⁻⁶ c. 11,186 m/s is 3.73 × 10⁻⁵ c. 1,000,000 m/s is 0.00334 c. 10,000,000 m/s is 0.0334 c. 100,000,000 m/s is 0.3336 c. A ladder like this speeds up any convert m/s to c check.
Checking by reversing
To check a “convert m/s to c” calculation result, multiply the answer by 299,792,458. If 100,000,000 m/s became 0.3336 c, then 0.3336 times 299,792,458 returns almost exactly 100,000,000. A second test is size: for speeds of order 10⁸ m/s the result is about a third.
Link to km/s and km/h
100,000,000 m/s is 100,000 km/s or 360 million km/h. To move from km/s to fractions of c, divide by 299,792.458. The three scales describe the same velocity.
A worked example
The star S2 passes the black hole at the centre of the galaxy at 7,650 km/s. In m/s that is 7,650,000, and dividing by 299,792,458 gives 0.0255 c. The Lorentz factor is 1.0003, so relativistic effects are tiny but measurable, and observers have detected the gravitational redshift in its light.
Time dilation
A clock moving at 0.6 c runs 20 per cent slower, since the Lorentz factor is 1.25. At 0.9 c it runs 2.29 times slower and at 0.99 c 7.09 times. For the Earth's orbit at 9.9 × 10⁻⁵ c, the slowing is a few parts in 10⁹, small but included in the corrections made for GPS and pulsar timing.
Pulsar timing
Radio telescopes time pulsars to microsecond precision, and the Earth's motion of 29,780 m/s matters. The Doppler shift of 9.9 × 10⁻⁵ changes a 1.5 ms pulse period by 0.15 microseconds, which is corrected by referring all times to the centre of the Solar System.
Journey times to the nearest star
Alpha Centauri is 4.37 light-years away. At the speed of Voyager 1 the trip would take about 77,000 years. At the speed of the Parker Solar Probe, 6,800 years. At 0.1 c, 44 years, and at 0.2 c, 22 years. That is why proposals for interstellar probes aim for a fifth of the speed of light.
Stellar velocities
Most stars in our neighbourhood move at tens of km/s relative to the Sun, a few times 10⁻⁵ c. Barnard's Star approaches at about 110 km/s, 3.7 × 10⁻⁴ c. Stars near the galactic centre are the fastest, with velocities of thousands of km/s.
Solar wind and flares
The solar wind blows at 400 to 800 km/s, 0.0013 to 0.0027 c. Energetic particles from flares reach 0.1 to 0.5 c, 30 to 150 million m/s, and can arrive at Earth in tens of minutes. A “convert m/s to c” calculation shows how quickly they reach us.
Light-travel time
Because c is finite, any convert m/s to c on a distant object describes it as it was. The Sun is seen as it was 499 seconds ago, Jupiter about 33 to 54 minutes ago, and the nearest star more than four years ago. Distance and time are two sides of the same measurement.
Rømer, 1676
Ole Rømer noticed that eclipses of Jupiter's moon Io came later when the Earth was farther from Jupiter. The delay of about 22 minutes across the Earth's orbit gave a speed near 220,000 km/s, 0.73 c. It was the first evidence that light does not travel instantly.
Aberration of starlight
Because the Earth moves at 29.8 km/s, the stars' apparent positions shift by about 20.5 arcseconds over a year. Bradley used this in 1728 to estimate the speed of light, 301,000 km/s. The shift is nothing but the ratio v/c of the Earth's speed to light's.
Particle beams
An electron beam of 100 kV runs at 0.548 c, 164,352,474 m/s, while the protons of the Large Hadron Collider run at 0.999999991 c, 299,792,455.3 m/s. In both machines energy keeps rising enormously as the speed creeps towards c.
Dimensionless units
Theorists often set c = 1, so a velocity is simply β. A proton with β = 0.875 moves at 262,318,401 m/s. The equations become simpler, but any experiment ends by converting back into m/s.
Cherenkov light
In water light travels at 0.75 c, 224,900,569 m/s. A charged particle moving at 0.8 c, 239,833,966 m/s, is faster than light in water and emits a blue glow called Cherenkov radiation. It is the glow seen around reactors immersed in water.
Massless particles
Photons and gluons always travel at exactly c, whereas anything with mass has β strictly below 1, however much energy is supplied. A conversion of a massive particle's speed can therefore never return 1.
The 2011 neutrino scare
In 2011 the OPERA experiment reported neutrinos arriving 60 nanoseconds earlier than light. The claim was traced to a loose fibre-optic cable. It shows that any result that appears to beat c must be checked with great care.
Breakthrough ideas
Concepts for light-sail probes propose pushing gram-scale craft to 0.2 c, 59,958,492 m/s, with a ground-based laser. At that speed the 4.37 light-years would be crossed in about 22 years. The craft would carry almost no mass, because the energy needed rises with the square of the velocity.
A check by two paths
The fraction of c can be found directly, by dividing m/s by 299,792,458, or by first turning m/s into km/s and dividing by 299,792.458. The answers must be identical; if they are not, a digit has been mistyped.
Planet Mercury and relativity
Mercury's orbit speed, 47,360 m/s, is 1.58 × 10⁻⁴ c. That small fraction is enough to produce a measurable relativistic effect: the planet's orbit precesses by 43 arcseconds per century more than Newton's law predicts. The discrepancy was explained by general relativity in 1915, and a “convert m/s to c” calculation shows how small the speeds involved are.
Comets and meteors
A comet falling toward the Sun may reach 600,000 m/s near perihelion, 0.002 c. Meteoroids enter the atmosphere at 11,000 to 72,000 m/s, 3.7 × 10⁻⁵ to 2.4 × 10⁻⁴ c. These are the greatest velocities that natural bodies in the solar system reach, and all are far from the speed of light.
Cosmic rays
Cosmic-ray particles from outside the solar system travel at more than 0.99999 c, and the rarest carry the energy of a thrown baseball. A particle at 0.99999 c moves at 299,789,460 m/s, only 2,998 m/s below c, and has a Lorentz factor above 220. Use of a “convert m/s to c” calculation reminds us that such particles are almost, but never quite, at the limit.
Supernovae
The outer layers of an exploding star leave at about 10,000 km/s, which is 10,000,000 m/s or 0.033 c. The fastest ejecta reach 0.1 c. Observers measure these speeds from the Doppler shift of spectral lines, and report them in km/s.
Relativistic jets
Jets from the neighbourhood of black holes can reach 0.99 c, 296,794,533 m/s, and the Lorentz factor of 7 means that time runs seven times slower in the jet. Astronomers see some blobs apparently moving faster than light, an illusion caused by the geometry of motion towards the observer.
Expansion of the universe
A galaxy 100 megaparsecs away recedes at about 7,000 km/s, 7,000,000 m/s, 0.023 c. At 4,283 megaparsecs the recession speed in the simple Hubble law reaches c. The universe is much larger than that, and the recession is due to expansion of space, not motion through it.
Escape speeds
The Earth's escape velocity is 11,186 m/s, 3.7 × 10⁻⁵ c. At the Sun's surface it is 617,700 m/s, 0.0021 c. For a neutron star about 12 km in radius it is roughly 176,000,000 m/s, 0.59 c. A black hole is an object whose escape velocity equals c at its horizon.
The speed of gravity
Gravitational waves travel at c. The merger of two neutron stars in 2017 sent gravitational waves and light that arrived at Earth within about two seconds of each other after a journey of 130 million years. This showed that their speeds agree to within one part in 10¹⁵.
Sound and light in comparison
Sound in air at 340.3 m/s is 1.135 × 10⁻⁶ c, so light is nearly 881,000 times faster. In a thunderstorm the flash of lightning reaches the eye in 3.3 microseconds from a kilometre away, and the thunder takes 2.94 seconds.
More values for convert m/s to c
A longer list of conversions
If the value you need is not in the first list, these further conversions may be close enough to read off directly:
- 0.1 m/s = 0.000000000333564 c
- 0.5 m/s = 0.00000000166782 c
- 3 m/s = 0.0000000100069 c
- 4 m/s = 0.0000000133426 c
- 7 m/s = 0.0000000233495 c
- 15 m/s = 0.0000000500346 c
- 20 m/s = 0.0000000667128 c
- 75 m/s = 0.000000250173 c
- 200 m/s = 0.000000667128 c
- 500 m/s = 0.00000166782 c
- 2,000 m/s = 0.00000667128 c
- 10,000 m/s = 0.0000333564 c
Common slips with a “convert m/s to c” calculation
Multiplying instead of dividing
From m/s to c the number shrinks. If 100,000,000 m/s became 3 × 10¹⁶, you multiplied by mistake.
Mixing km/s and m/s
100,000 km/s is 100,000,000 m/s. If you enter 100,000 as m/s you get 0.000334 c, a thousand times too little. Check the unit before calculating.
Classical formulas at high speed
Above 0.1 c the classical formulas for energy and momentum give visible errors. Use relativity.
Questions in brief
What is the rule for a “convert m/s to c” calculation?
Divide the speed in m/s by 299,792,458.
How much of c is 100,000,000 m/s?
0.3336 c.
How much of c is 29,979,246 m/s?
Exactly 0.1 c.
What is 1 c in m/s?
299,792,458 m/s.
Is the figure sent anywhere?
No, everything is calculated in your browser.
Related pages and a summary
You may also want Convert m/s to mph, Convert m/s to km/h, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C, Convert bar to Pa, Convert L to fl oz, Convert mm to µm. For the opposite direction, see Convert c to m/s.
Summing up: divide m/s by 299,792,458 to get a fraction of c, and write the unit beside the result. Everything stays in your own browser, with no account and no upload.