Convert c to m/s the speed of light ↔ metres per second Free Online Secure
Type a value in the speed of light and read it in metres per second at once. The factor is exact by definition, the arithmetic happens in your browser, and nothing is sent anywhere.
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Convert to metres per second
Common values — Convert c to m/s (the speed of light ↔ metres per second)
| c | m/s |
|---|---|
| 0.001 | 299792.458 |
| 0.01 | 2997924.58 |
| 0.1 | 29979245.8 |
| 0.25 | 74948114.5 |
| 0.5 | 149896229 |
| 0.75 | 224844343.5 |
| 0.9 | 269813212.2 |
| 1 | 299792458 |
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.
The speed of light in metres per second: why the internet has a speed limit
The letter c stands for the speed of light in a vacuum, and for network engineers, traders and satellite operators it is not an abstraction but a hard budget. A signal cannot cross the Atlantic faster than about 18.6 milliseconds, no matter how much money is spent, and ordinary fibre needs nearly 27. To convert c to m/s, multiply by 299,792,458: 1 c is exactly 299,792,458 m/s, 0.5 c is 149,896,229 m/s and 0.1 c is 29,979,245.8 m/s. The calculator above multiplies as you type, and the sections below turn the number into delays on real routes, from the chip to the Moon.
The page gives the rule with worked examples, a profile of each unit, a comparison and a long run of cases from networking and space communications, followed by common mistakes. The calculation runs in your browser and nothing you type is sent anywhere. For scientific work, always use the official value of the constant.
How to convert c to m/s: multiply by 299,792,458
The rule
Since 1983 the metre has been defined from the speed of light, which is therefore exactly 299,792,458 m/s. To convert c to m/s, multiply the fraction of c by that number. That gives 0.01 c as 2,997,924.58 m/s, 0.2 c as 59,958,491.6 m/s, 0.9 c as 269,813,212.2 m/s and 2 c as 599,584,916 m/s. To go the other way, divide m/s by 299,792,458.
Worked examples
Light in an optical fibre travels at about 0.68 c, which is 203,858,871 m/s. Light in water travels at 0.75 c, or 224,844,344 m/s. A hypothetical probe at 0.05 c would move at 14,989,623 m/s, nearly 15,000 kilometres per second.
An exact factor
The value is exact by definition, not a measurement. The only approximation comes from quoting "300,000 km/s", which is 0.07 per cent too high.
A quick sanity test
The answer in m/s is nearly three hundred million times the figure in c. If a “convert c to m/s” calculation gave a smaller number than you started with, you divided instead of multiplying.
The speed of light, c
The universal constant
The speed of light in vacuum, c, is the speed of all electromagnetic waves and, according to relativity, the ceiling for the speed of any signal. It appears in E = mc² and in the definition of the metre.
Where it appears
Physics, astronomy, telecommunications, satellite navigation and relativity.
The metre per second
The SI unit of speed
The metre per second is the SI unit of speed. From a snail to a beam of light, every velocity can be written in m/s, which allows comparison on one scale.
Where it appears
Physics textbooks, research papers, standards and experimental data.
c against metres per second
One c is 299,792,458 m/s, so the figure in m/s is nearly three hundred million times larger. An object at 0.01 c moves at almost three million m/s, which is 3,000 km/s. The unit c expresses speed as a fraction of the universal limit and m/s as an absolute quantity.
The conversion is exact and hides no rounding. The only trap is the direction: from c to m/s the number grows enormously.
Where the conversion shows up
Transatlantic latency
New York to London is 5,570 km. Light in a vacuum would need 18.6 ms, light in fibre at 0.68 c needs 27.3 ms, and a round trip through fibre cannot take less than 54.5 ms. Real routes add switching and detours, typically ending at 60 to 70 ms. A “convert c to m/s” calculation gives engineers the floor that no technology can break.
Satellite links
A geostationary satellite at 35,786 km makes a signal travel 71,572 km up and down, which takes 239 ms. A request and its response need 477 ms. A low-orbit satellite at 550 km needs just 3.7 ms for the same up-and-down trip, 7.3 ms for the round trip.
Deep space
The Moon is 1.28 light-seconds away. The Sun is 499 light-seconds, 8 min 19 s. Mars is 3 to 22 light-minutes, depending on positions, and Voyager 1 is about 22.7 light-hours. Every command sent to a probe has to wait for these delays.
Light in glass fibre
Glass with a refractive index of 1.468 slows light to 204,218,296 m/s, about 0.68 c. Each kilometre of fibre adds 4.9 microseconds. On a 5,570 km route that is 27.3 ms, 8.7 ms more than in a vacuum. The extra delay is built into the material, which is why engineers look for hollow-core fibre.
The mental shortcut
To convert c to m/s in your head, multiply by 3 and by 10⁸; the answer is 0.07 per cent high. For 0.5 c: 1.5 × 10⁸ = 150,000,000 against the exact 149,896,229. For finer work use 2.998 × 10⁸.
Spreadsheet formulas
To convert c to m/s in a spreadsheet, put the fractions of c in column A and enter =A2*299792458 in column B. For the reverse, =B2/299792458. Format column B in scientific notation so that large results stay readable.
Rounding and precision
When you convert c to m/s for a general text, 0.5 c is "nearly 150,000 km/s". In a calculation, use the exact value, since formulas like E = mc² square c and magnify any rounding. Using 3 × 10⁸ instead of 2.998 × 10⁸ causes an error of 0.14 per cent in energy.
Landmarks to memorise
0.001 c is 299,792 m/s. 0.01 c is 2,997,925 m/s. 0.1 c is 29,979,246 m/s. 0.5 c is 149,896,229 m/s. 0.9 c is 269,813,212 m/s. 1 c is 299,792,458 m/s. To convert c to m/s by eye, scale from these values.
Reference ladder
0.02 c is 5,995,849 m/s. 0.05 c is 14,989,623 m/s. 0.2 c is 59,958,492 m/s. 0.3 c is 89,937,737 m/s. 0.75 c is 224,844,344 m/s. 0.99 c is 296,794,533 m/s. 2 c is 599,584,916 m/s. A ladder like this makes quick checks easy.
Checking by reversing
To check a “convert c to m/s” calculation result, divide the answer by 299,792,458. If 0.1 c became 29,979,246 m/s, then dividing returns 0.1. A second test is size: the result for 0.1 c should have eight digits before the decimal point.
Link to km/h, mph and knots
One c is 299,792.458 km/s, 1,079,252,849 km/h, 670,616,629 mph and about 582,749,919 knots. These figures have no practical meaning, but they show how different the world of light is from that of vehicles.
A worked example
A particle moves at 0.6 c, which is 179,875,475 m/s or 647,551,709 km/h. In one second it covers 179,875 km, 4.5 times round the Earth. The Lorentz factor is 1.25, so its total energy is 25 per cent more than its rest energy.
The first measurements
In 1676 Ole Rømer noticed delays in eclipses of Jupiter's moon Io when Earth moved away from Jupiter and concluded that light has a finite speed, about 220,000 km/s, or 0.73 c. In 1849 Fizeau measured 313,000 km/s with a toothed wheel and a mirror 8.6 km away, and in 1862 Foucault got 298,000 km/s with a rotating mirror. Michelson's 1879 value, 299,910 km/s, lasted for decades.
The definition of the metre
Before 1960 the metre was a platinum-iridium bar. Then came a wavelength of krypton light, and in 1983 the present definition: the distance light travels in a vacuum in 1/299,792,458 of a second. Since then c cannot be measured better, because the metre derives from it.
Hollow-core fibre
In hollow-core fibre the light travels mostly through air, at about 0.997 c. A kilometre then costs 3.35 microseconds instead of 4.9, a saving of 1.55 microseconds per kilometre. Over 5,570 km that is 8.6 ms. Traders and cloud operators pay for the gain in latency.
Why nothing outruns light
According to special relativity, the energy required to accelerate a body with mass grows without limit as its speed nears c. The Lorentz factor is 2.29 at 0.9 c, 7.09 at 0.99 c and about 7,450 for the protons of the Large Hadron Collider at 0.999999991 c. Reaching c would take infinite energy.
Protons at the LHC
The protons in the Large Hadron Collider move at 299,792,455.3 m/s, only 2.7 m/s below c. At such speeds their energy increases enormously while their speed barely changes. This is why physicists speak of energy, not speed, when describing the beam.
Light inside materials
Light in water travels at 0.75 c, or 224,900,569 m/s, in glass at 0.67 c, 199,861,639 m/s, and in diamond at 0.41 c, 123,881,181 m/s. In air it is 299,702,547 m/s, only 89,911 m/s less than in a vacuum. The difference matters in precision surveying, where a refraction correction is applied.
Light-year and astronomical unit
A light-year is 9,460,730,472,580,800 metres, the distance light covers in a year. An astronomical unit, the mean distance from Earth to the Sun, is 149,597,870,700 metres and takes light 499 seconds. Both units come from c.
Radar and laser ranging
A radar finds range from the echo time as d = c × t / 2. An echo returning after 1 millisecond comes from 149.9 km. A laser rangefinder with a timing resolution of 1 nanosecond gives distance to 15 centimetres.
Solar wind and cosmic rays
The solar wind blows at 400 to 800 km/s, 0.0013 to 0.0027 c. Cosmic rays can exceed 0.99999 c. The Parker Solar Probe has reached 192 km/s, about 0.0006 c, the fastest human-made object.
Everyday speeds as fractions of c
Earth moves round the Sun at 29.78 km/s, 0.0001 c. The International Space Station moves at 7.66 km/s, 0.000026 c. A person running at 10 m/s is at 3 × 10⁻⁸ c. In daily life, fractions of c are tiny, and they become large only in particle physics.
E = mc²
The square of the speed of light, 8.98755 × 10¹⁶ m²/s², links mass to energy. One gram corresponds to 8.99 × 10¹³ J, equivalent to 21.5 kilotons of TNT. A common mistake is to put c in km/s into a formula written in metres.
Faster-than-light neutrinos
In 2011 the OPERA experiment reported neutrinos arriving 60 nanoseconds ahead of light. The claim made headlines before it was traced to a loose fibre-optic cable. The story shows that any measurement close to c needs strict verification, as does every “convert c to m/s” calculation used in a precision experiment.
Natural units
In theoretical physics it is common to set c = 1 and measure distances in light-seconds. In these units one metre is 3.34 nanoseconds and the Moon is 1.28 seconds away.
Microwave links for trading
Between Chicago and New Jersey, 1,180 km, light in a vacuum needs 3.94 ms. A microwave link through air needs 3.94 ms plus a little for detours, while a fibre route takes 5.78 ms. The difference of about 1.8 ms is worth millions to automated traders, which is why they built chains of towers.
Two routes to one result
You can go from c to m/s directly, with 299,792,458, or through km/s: multiply by 299,792.458 and then by 1,000. The results must agree. If they do not, a digit has been copied wrongly.
Satellite constellations
At 550 km altitude, a low-orbit satellite adds under 4 ms to a path. Between London and Sydney, 17,000 km, vacuum light takes 56.7 ms, while the fibre needs 83.2 ms one way. Laser links between satellites travel at c, so a constellation can beat fibre on very long routes.
Medium-Earth orbit
Satellites at about 8,000 km altitude need 54 ms for the up-and-down trip. That is far less than the 239 ms of geostationary links, while keeping a wider view of the ground than low orbit. Operators of such systems quote latency in milliseconds, and the origin of every figure is c.
Inside a computer
In a 3 GHz processor each cycle lasts 0.33 ns, and light covers 10 cm in that time. A signal on a circuit board travels at about half of c, 15 cm each nanosecond. A chip with a diagonal of 2 cm needs 0.13 ns for a trip across it. The limit set by c is one reason clocks are not much faster.
Radio wavelengths
The wavelength of a radio wave is c divided by its frequency. FM at 100 MHz has 3 m, AM at 1 MHz 300 m, Wi-Fi at 2.4 GHz 12.5 cm and 5G at 3.5 GHz 8.6 cm. Antenna sizes follow the same relationship.
Light-time to space targets
A ping to the Moon would take 2.56 seconds. A signal to Mars near closest approach needs 3 minutes one way, and 22 minutes at the farthest. Rover drivers on Earth therefore give commands in batches instead of steering in real time.
GPS timing
A GPS satellite at 20,200 km sends signals that arrive in 67 ms. A clock error of one microsecond means 300 metres of position error, and one of a nanosecond 30 centimetres. Atomic clocks on board are corrected for relativity, otherwise the position would drift by kilometres every day.
More values for convert c to m/s
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 c = 29,979,245.8 m/s
- 0.5 c = 149,896,229 m/s
- 3 c = 899,377,374 m/s
- 4 c = 1,199,169,832 m/s
- 7 c = 2,098,547,206 m/s
- 15 c = 4,496,886,870 m/s
- 20 c = 5,995,849,160 m/s
- 75 c = 22,484,434,350 m/s
- 200 c = 59,958,491,600 m/s
- 500 c = 149,896,229,000 m/s
- 2,000 c = 599,584,916,000 m/s
- 10,000 c = 2,997,924,580,000 m/s
Common slips with a “convert c to m/s” calculation
Dividing instead of multiplying
From c to m/s the number grows enormously. If 0.5 c turned into 0.0000000017, you divided by mistake.
Mixing km/s and m/s
The speed of light is 299,792 km/s but 299,792,458 m/s. Confusing them gives an error of a thousand. Check the unit in which you use the result.
Rounding to 3 × 10⁸
The approximation is fine for estimates, but in formulas with c² errors double. Use the exact value for serious calculations.
Short answers
How do I convert c to m/s?
Multiply the fraction of c by 299,792,458.
How many m/s is 1 c?
Exactly 299,792,458 m/s.
How many m/s is 0.1 c?
29,979,245.8 m/s.
How many c is 1 m/s?
3.3356 × 10⁻⁹ c.
Does my number leave my device?
No, the calculation runs in your browser.
More pages and a wrap-up
For other speed conversions see Convert Mach to m/s, Convert ft/s to m/s, Convert m/s to knots, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C, Convert qt to gal, Convert yd² to m². The reverse direction is Convert m/s to c.
In short, a “convert c to m/s” calculation comes down to multiplying by 299,792,458 and writing the unit beside the answer. Your number is computed locally, with no account and no upload.