Convert Mach to km/h Mach numbers ↔ kilometres per hour Free Online Secure
Type a value in Mach numbers and read it in kilometres per hour at once. The arithmetic happens in your browser and nothing is sent anywhere — and the figure it uses is named below, because this one depends on the air.
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Convert from Mach numbers
Convert to kilometres per hour
Common values — Convert Mach to km/h (Mach numbers ↔ kilometres per hour)
| Mach | km/h |
|---|---|
| 0.5 | 612.5292 |
| 0.8 | 980.04672 |
| 1 | 1225.0584 |
| 1.5 | 1837.5876 |
| 2 | 2450.1168 |
| 3 | 3675.1752 |
| 5 | 6125.292 |
| 10 | 12250.584 |
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.
Mach numbers in kilometres per hour: from the sound barrier to re-entry
News about hypersonic missiles, space capsules and experimental aircraft quotes speeds in Mach numbers, and the figure only becomes tangible when you see it in kilometres per hour. A Mach number is a ratio: the speed of an object divided by the speed of sound in the air around it. To convert Mach to km/h at standard sea-level conditions, multiply by 1,225.06: Mach 1 is 1,225 km/h, Mach 5 is 6,125 km/h and Mach 10 is 12,251 km/h. The calculator above uses the speed of sound at 15 °C, 340.294 m/s, and the sections below explain how far that can differ from real flight conditions, especially far above the ground and on other planets.
The page gives the rule with worked examples, a profile of each unit, a comparison and a long run of cases from rocketry and aerospace, followed by the usual mistakes. The calculation happens in your browser and your numbers are not sent anywhere. For flight or mission planning, rely on the original data.
How to convert Mach to km/h: multiply by 1,225.06
The rule
Sound travels through standard sea-level air at 340.294 m/s, which is 340.294 × 3.6 = 1,225.06 km/h. To convert Mach to km/h, multiply the Mach number by 1,225.06. That makes Mach 0.5 equal to 612.5 km/h, Mach 1.5 equal to 1,837.6 km/h and Mach 3 equal to 3,675 km/h. To go the other way, divide km/h by 1,225.06.
Worked examples
Mach 0.8 at sea level is 980 km/h. Mach 2 is 2,450 km/h. Mach 5, the hypersonic threshold, is 6,125 km/h, and Mach 25, the order of a re-entering spacecraft, is 30,626 km/h by the sea-level factor.
A factor with conditions attached
Mach is a ratio and not a speed, so the factor holds only for the air it was derived for. At 11 km altitude, at −56.5 °C, the speed of sound is 295 m/s, or 1,062 km/h, and Mach 1 there means 13 per cent fewer km/h than at the ground.
A quick sanity test
The answer in km/h is more than a thousand times the Mach number. If a “convert Mach to km/h” calculation gave a smaller figure than you started with, you divided instead of multiplying.
The Mach number
A ratio to the speed of sound
The Mach number is named after the Austrian physicist Ernst Mach. It is an object's speed divided by the local speed of sound. Below Mach 1 the flow is subsonic, near it transonic, above it supersonic and from Mach 5 upward hypersonic.
Where it appears
Aerodynamics, rocketry, wind tunnels, missile and spacecraft design.
The kilometre per hour
The everyday unit
The kilometre per hour is the unit most people use to judge speed, on roads, rails and in sport. It is easy to feel but poor at describing aerospace speeds, which quickly run to five-digit numbers.
Where it appears
Road signs, timetables, vehicle specifications and press reports.
Mach against kilometres per hour
One Mach is 1,225 km/h at sea level, so the figure in km/h is more than a thousand times larger. Mach 2 is 2,450 km/h and Mach 0.85 is 1,041 km/h. The two differ in kind as well as in scale, since Mach depends on air temperature and km/h does not.
The conversion is exact only under stated conditions. The chief trap is to apply the sea-level factor to a vehicle at 11,000 metres or to a planet other than Earth.
Where the conversion shows up
Re-entry from orbit
A spacecraft returning from low Earth orbit moves at about 7.8 km/s, which is 28,080 km/h. At the altitude where the heating is greatest, the speed of sound is around 300 m/s, so that is roughly Mach 26. A “convert Mach to km/h” calculation using the sea-level factor would give Mach 22.9, which is the wrong answer for that altitude.
Experimental air-breathing flight
The unmanned X-43A reached about Mach 9.6 in 2004, close to 11,200 km/h at its test altitude. The sea-level factor would give 11,760 km/h, a difference of five per cent. Reports usually quote the speed in miles per hour or km/h, together with the altitude.
Missiles and projectiles
A hypersonic missile cruises above Mach 5, more than 5,300 km/h in the stratosphere. A rifle bullet at 850 m/s is Mach 2.5 at sea level, or 3,060 km/h. Reports of such speeds should always state the altitude, since Mach changes with it.
Why temperature matters
The speed of sound in a gas rises with the square root of absolute temperature. For air it is about 20.05 times √T, with T in kelvins. At 15 °C it is 340.3 m/s, at 0 °C 331.3 m/s, at 20 °C 343.2 m/s and at −56.5 °C 295.1 m/s. In km/h: 1,225, 1,193, 1,236 and 1,062. Pressure and altitude themselves do not matter, only their effect on temperature.
Rockets passing through Mach 1
Before you convert Mach to km/h for a launch, note that a rocket reaches the speed of sound about a minute after lift-off, at an altitude of around 10 kilometres. It then passes the point of maximum dynamic pressure, called max Q, at a speed near 1,300 km/h. Engineers reduce thrust briefly to keep loads on the structure within limits.
The mental shortcut
To convert Mach to km/h in your head, multiply by 1,200 and add 2 per cent. For Mach 2: 2,400 plus 48 gives 2,448, close to 2,450. For Mach 0.5: 600 plus 12 gives 612, against 612.5. At stratospheric altitude use 1,060 instead of 1,225.
Spreadsheet formulas
To convert Mach to km/h in a spreadsheet, put the Mach numbers in column A and enter =A2*1225.0584 in column B. For other temperatures, add a column for the speed of sound =20.0468*SQRT(273.15+T)*3.6, where T is in degrees Celsius, and multiply by the Mach number.
Rounding and honesty
When you convert Mach to km/h for a poster, Mach 9.6 means about 11,800 km/h at the sea-level factor. In a technical note, give the altitude and temperature that went with it. The uncertainty in the assumed speed of sound is larger than any rounding you do with the multiplication.
Landmarks to memorise
Mach 0.5 is 612 km/h. Mach 0.8 is 980 km/h. Mach 1 is 1,225 km/h. Mach 2 is 2,450 km/h. Mach 3 is 3,675 km/h. Mach 5 is 6,125 km/h. Mach 10 is 12,251 km/h. When you want to convert Mach to km/h by eye, think of Mach 1 as a little over 1,200 km/h at sea level.
Reference ladder
Mach 0.3 is 367 km/h. Mach 0.75 is 919 km/h. Mach 0.9 is 1,103 km/h. Mach 1.2 is 1,470 km/h. Mach 1.5 is 1,838 km/h. Mach 2.5 is 3,063 km/h. Mach 6 is 7,350 km/h. Mach 20 is 24,501 km/h. A table like this makes any check quick.
Checking by reversing
To check a “convert Mach to km/h” calculation result, divide it by 1,225.06. If Mach 2 became 2,450 km/h, then 2,450 divided by 1,225.06 returns 2. A second test is the size: the figure in km/h should be more than a thousand times the Mach number.
Link to m/s and mph
Mach 1 is 340.3 m/s, 1,225 km/h and 761.2 mph at sea level. You can go through m/s by multiplying by 340.294 and then by 3.6. The result matches a direct multiplication by 1,225.06, and the check catches slips.
A worked example
A spacecraft at Mach 25 sits at an altitude where the speed of sound is 300 m/s, which is 1,080 km/h. Its speed is therefore 27,000 km/h, or 7.5 km/s. With the sea-level factor you would get 30,626 km/h, about 13 per cent too much. Crossing 5,570 km of Atlantic at 27,000 km/h would take about 12 minutes.
Scramjets
A supersonic-combustion ramjet works only at high Mach numbers, because the engine relies on the air being compressed by the vehicle's own speed. Designs begin at about Mach 5, 6,125 km/h at sea level and 5,300 km/h at altitude, and aim for Mach 10 or higher. Nothing in a scramjet can run at lower speed, so it has to be carried by a booster.
Mach 1 on other worlds
The atmosphere of Mars is mostly carbon dioxide at about −60 °C, and sound there travels at roughly 240 m/s, or 864 km/h. Mach 1 on Mars is therefore only 0.7 of Earth's. On Venus the hot, dense atmosphere carries sound at about 410 m/s, 1,476 km/h. Probes designed for these worlds are modelled with local sound speeds, not with 1,225 km/h.
Wind tunnels
Wind tunnels are classed by Mach range: subsonic below 0.8, transonic from 0.8 to 1.2, supersonic from 1.2 to 5 and hypersonic above 5. A subsonic tunnel at Mach 0.5 produces an airflow of 612 km/h at sea level. Test data are always labelled with the Mach number, not with km/h.
Range and time with a Mach figure
At Mach 0.8 and 11 km altitude the speed is 850 km/h. A 5,000 km flight takes 5 h 53 min. Using the sea-level figure, 980 km/h, would give 5 h 6 min, which is 47 minutes too optimistic. For a “convert Mach to km/h” calculation intended for planning, always use the speed of sound at flight level.
The hurricane comparison
The strongest wind gusts ever recorded on Earth are about 100 m/s, 360 km/h, which is Mach 0.29. They are enormously destructive, but still far below the speed of sound. No ordinary weather phenomenon on Earth exceeds Mach 0.4.
Propeller and rotor tips
The tips of propeller blades and helicopter rotors can approach Mach 0.9, which is 1,100 km/h at sea level. Beyond that the noise rises sharply and efficiency drops, so designers keep the tip speed below Mach 0.85.
Supersonic passenger flight
Several companies aim to return supersonic travel to airliners at Mach 1.7 to 2. That would be 1,800 to 2,100 km/h at cruise altitude. A flight from London to New York would take about three and a half hours instead of seven, but regulations on sonic booms over land remain an obstacle.
What "Mach 1" means in the news
Journalists use "Mach 1" casually. Yet Mach 1 has no fixed value: it is 1,225 km/h at sea level, 1,102 km/h at −40 °C, 1,062 km/h in the stratosphere and 864 km/h on Mars. Good reporting states the conditions.
The first supersonic flight
On 14 October 1947 the Bell X-1 passed the speed of sound in level flight at about 13,000 metres. The aircraft reached Mach 1.06, around 1,126 km/h. At sea level the same Mach number would be 1,298 km/h, which shows how strongly altitude changes the meaning of a Mach number.
Records
The speed record for a crewed jet aircraft is 3,529.6 km/h, set by the SR-71 in 1976, at about Mach 3.3 at altitude. The X-15 rocket plane reached 7,274 km/h, Mach 6.7, in 1967. By the sea-level factor those would be Mach 2.9 and Mach 5.9.
Land speed
The Thrust SSC car exceeded 1,228 km/h on the desert floor in 1997. In the cool air of the Nevada morning the speed of sound was somewhat lower than 1,225 km/h, so the car was officially travelling at about Mach 1.02. It remains the only land vehicle to pass the sound barrier.
Free fall from the stratosphere
In 2012 a skydiver jumped from about 39 km and reached 1,357.6 km/h. At that altitude the speed of sound was close to 1,080 km/h, which gave Mach 1.25. With the sea-level factor the same speed would have been Mach 1.11, so official reports used the local figure.
Mach 1 in other substances
In helium sound travels at 965 m/s, which is 3,474 km/h; in water at 1,480 m/s, which is 5,328 km/h; in steel at about 5,000 m/s. A boat at 100 km/h is at Mach 0.019 relative to the water but Mach 0.082 relative to the air above it. Mach is always defined with respect to the medium in question.
Concorde and its heat
Concorde cruised at Mach 2.02, about 2,145 km/h in the cold stratosphere. The stagnation temperature on its nose climbed to roughly 120 °C, and the airframe stretched by up to 25 centimetres in flight. A “convert Mach to km/h” calculation for Concorde gives 2,475 km/h at sea level, a speed it never actually flew at.
The speed of crewed craft
The fastest humans have travelled in Apollo capsules returning from the Moon. Apollo 10 reached 39,897 km/h in 1969, which is 11.08 km/s. By the sea-level factor that would be Mach 32.6, although the real Mach number at high altitude, with the colder air, was a few units higher.
The fastest probe
The Parker Solar Probe passes the Sun at about 692,000 km/h, or 192 km/s. In terms of the sea-level factor that would be Mach 565, but there is no air in space for sound to travel through, so no Mach number exists. It is shown here only to give a sense of scale.
The International Space Station
The station moves at about 27,600 km/h, 7.67 km/s. By the sea-level factor this is Mach 22.5, and by the speed of sound in the thin upper air, near Mach 26. Since there is practically no air at 400 km, the number serves only as an illustration of how fast orbital flight is.
Meteors
A meteoroid hits the atmosphere at speeds between 11 and 72 km/s, i.e. between 40,000 and 260,000 km/h. At 20 km/s, which is 72,000 km/h, the object is at Mach 59 by the sea-level factor. Most burn up long before the denser air at low altitude, which is why only a small fraction reach the ground.
Shock waves and the Mach cone
An object flying faster than sound trails a cone of shock waves whose half angle is arcsin(1 / Mach). At Mach 1.5 the angle is 41.8°, at Mach 2 it is 30° and at Mach 3 it is 19.5°. The sharper the cone, the faster the object is moving compared with sound.
Aerodynamic heating
Air brought to rest on a leading edge heats up. The stagnation temperature is T × (1 + 0.2 M²). At Mach 2 in air at −56.5 °C the figure is about 120 °C, and at Mach 5 it exceeds 1,000 °C. The speeds in km/h, 2,125 and 5,311 at that altitude, make plain why materials limit hypersonic flight.
More values for convert Mach to km/h
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 Mach = 122.50584 km/h
- 0.5 Mach = 612.5292 km/h
- 3 Mach = 3,675.1752 km/h
- 4 Mach = 4,900.2336 km/h
- 7 Mach = 8,575.4088 km/h
- 15 Mach = 18,375.876 km/h
- 20 Mach = 24,501.168 km/h
- 75 Mach = 91,879.38 km/h
- 200 Mach = 245,011.68 km/h
- 500 Mach = 612,529.2 km/h
- 2,000 Mach = 2,450,116.8 km/h
- 10,000 Mach = 12,250,584 km/h
Common slips when you convert Mach to km/h
Dividing instead of multiplying
From Mach to km/h the number grows. If Mach 2 turned into 0.0016, you used the factor for the opposite direction.
Ignoring altitude
The factor 1,225.06 holds at sea level. At cruise altitude one Mach is about 1,062 km/h, so using it by mistake gives an error of 13 per cent.
Treating Mach as a fixed speed
Mach is a ratio, so the same Mach number means different speeds at different temperatures and on different planets.
Short answers
How do I convert Mach to km/h?
Multiply the Mach number by 1,225.06.
How many km/h is Mach 1?
1,225.06 km/h at sea level.
How many km/h is Mach 2?
2,450.12 km/h.
How many km/h is Mach 1 at altitude?
About 1,062 km/h at 11 km.
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 Mach to mph, Convert mph to km/h, Convert ft/s to km/h, Convert km/h to knots, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. The reverse direction is Convert km/h to Mach.
In short, a “convert Mach to km/h” calculation means multiplying by 1,225.06 under sea-level conditions and writing the unit beside the answer. Your number is computed locally, with no account and no upload.