Convert km/h to Mach kilometres per hour ↔ Mach numbers Free Online Secure
Type a value in kilometres per hour and read it in Mach numbers 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 to Mach numbers
Common values — Convert km/h to Mach (kilometres per hour ↔ Mach numbers)
| km/h | Mach |
|---|---|
| 1 | 0.00081628761535 |
| 2 | 0.0016325752307 |
| 3 | 0.00244886284605 |
| 5 | 0.00408143807675 |
| 10 | 0.0081628761535 |
| 20 | 0.016325752307 |
| 50 | 0.0408143807675 |
| 100 | 0.081628761535 |
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.
What speed in km/h means on the flight deck: Mach number for airline passengers
The map screen on a long-haul flight shows ground speed in kilometres per hour, while the captain's announcement and the instruments in front of the pilots talk of Mach. A reading of 900 km/h on the seat-back screen and a cruise of Mach 0.85 on the flight deck describe the same aircraft in two different ways, and the link between them is not a single constant. To convert km/h to Mach for sea-level air, divide by 1,225.06: 600 km/h is Mach 0.49, 900 km/h is Mach 0.73 and 2,450 km/h is Mach 2. The calculator above divides as you type, and the sections below show why an airliner at altitude lands on a different number.
The page gives the rule with worked examples, a profile of each unit, a comparison and many cases from commercial flying, followed by the common mistakes. The calculation runs in your browser and nothing you enter is sent anywhere. Pilots must use their aircraft documents and air-traffic instructions for real operations.
How to convert km/h to Mach: divide by 1,225.06
The arithmetic
Sound moves at 340.294 m/s through standard air at sea level and 15 °C. In one hour that is 1,225,058 metres, or 1,225.06 km. To convert km/h to Mach, take the speed in km/h and divide by that figure. For example, 800 km/h gives Mach 0.65, 1,000 km/h gives Mach 0.82 and 3,000 km/h gives Mach 2.45. For the opposite direction, multiply the Mach number by 1,225.06.
Worked examples
A high-speed train at 320 km/h is at Mach 0.26. A racing car at 360 km/h is at Mach 0.29. An airliner at 850 km/h is at Mach 0.69 by the sea-level factor but Mach 0.80 at its cruise level, and a bullet at 3,060 km/h is at Mach 2.5.
When the answer is valid
The result is right only for air in which sound travels at 1,225 km/h. In colder air sound is slower, so the same km/h gives a higher Mach. That is why 850 km/h at 11,000 metres corresponds to Mach 0.80 and not 0.69.
A quick sanity test
The answer should be more than a thousand times smaller than the number of km/h. If a “convert km/h to Mach” calculation gave a figure bigger than the one you started with, you multiplied instead of dividing.
The kilometre per hour
The unit passengers see
The kilometre per hour is the speed unit shown on flight maps, train displays and road signs. It is easy to feel on the ground and a little abstract in the air, where speeds climb into four digits.
Where it appears
Seat-back maps, timetables, speed limits and vehicle brochures.
The Mach number
Speed as a fraction of the speed of sound
The Mach number is the ratio of an object's speed to the speed of sound in the surrounding air. At Mach 0.5 you are halfway to the sound barrier, at Mach 1 you are on it and at Mach 2 you are twice as fast. Pilots use it for cruise because the behaviour of the wings depends on this ratio.
Where it appears
Cockpit displays, air-traffic instructions, wind-tunnel reports and aircraft handbooks.
Kilometres per hour against Mach
One km/h is 0.000816 Mach, so the figure in Mach is more than a thousand times smaller. A car at 100 km/h is at Mach 0.082 and a jet at 1,000 km/h is at 0.816. Mach is not a fixed speed, since the same Mach number means different km/h in warm and in cold air.
For that reason the conversion is exact only under stated conditions. The commonest error is to use the sea-level factor for an aircraft at cruise altitude.
Where the conversion shows up
The cruise of an airliner
Most jets cruise at Mach 0.78 to 0.85, which is 828 to 903 km/h at 11,000 metres, where the speed of sound is 1,062 km/h. If you apply the sea-level factor to 850 km/h you get 0.69, which is far from the real 0.80. A “convert km/h to Mach” calculation for airliners must therefore state the altitude.
Ground speed against airspeed
The seat-back map shows speed over the ground. A jet at Mach 0.85, about 903 km/h through the air, can show 1,100 km/h with a 200 km/h tailwind. Its Mach number is still 0.85, because Mach compares airspeed with the speed of sound, not speed with respect to the ground.
Supersonic flight
A fighter at 2,450 km/h is at Mach 2.0 near the ground and Mach 2.3 at 11,000 metres. Concorde cruised at 2,140 km/h, which was Mach 2.02 in the cold stratosphere. The same ground speed in warm air at sea level would have been just Mach 1.75.
The speed of sound by altitude
In the standard atmosphere, the speed of sound falls as the air cools: 1,225 km/h at sea level, 1,204 km/h at 5,000 feet, 1,182 km/h at 10,000 feet, 1,138 km/h at 20,000 feet, 1,091 km/h at 30,000 feet and 1,062 km/h from 36,000 feet to about 65,000 feet. Above the tropopause the temperature stays constant for a while, so the speed of sound does too.
Spreadsheet formulas
To convert km/h to Mach in a spreadsheet, put the speeds in km/h in column A and enter =A2/1225.0584 in column B. For flight level use =A2/1062.25. For any temperature T in °C compute the sound speed with =20.0468*SQRT(273.15+T)*3.6 and divide by that instead.
Rounding and precision
On a screen, Mach 0.80 is enough. If you need to convert km/h to Mach for performance work, use three decimals, 0.803. Precision in the temperature matters more than extra digits in the arithmetic, because one degree changes the speed of sound by about 0.6 m/s.
Landmarks to memorise
100 km/h is Mach 0.08. 300 km/h is Mach 0.24. 600 km/h is Mach 0.49. 900 km/h is Mach 0.73. 1,225 km/h is Mach 1. 2,450 km/h is Mach 2. These sea-level values give a basis from which to scale.
Reference ladder
50 km/h is Mach 0.041. 130 km/h is Mach 0.106. 200 km/h is Mach 0.163. 320 km/h is Mach 0.261. 431 km/h is Mach 0.352. 800 km/h is Mach 0.653. 1,500 km/h is Mach 1.224. 3,000 km/h is Mach 2.449. 10,000 km/h is Mach 8.163. A ladder like this speeds up any convert km/h to Mach check.
Checking by reversing
To check a “convert km/h to Mach” calculation result, multiply the answer by 1,225.06. If 600 km/h gave Mach 0.49, then 0.49 times 1,225.06 comes to about 600. A second test is size: Mach 1 should land a little above 1,200 km/h.
Link to m/s and mph
One km/h is 0.2778 m/s and 0.6214 mph. Mach 1 is 340.3 m/s, 1,225 km/h and 761 mph. You can go through m/s by dividing by 3.6 and then by 340.294. The answer matches the direct division by 1,225.06.
A worked example
A maglev train runs at 603 km/h, which is 167.5 m/s. Divided by the speed of sound, 340.294 m/s, this gives Mach 0.492. The direct route to convert km/h to Mach, 603 / 1,225.06, gives the same figure. In a tunnel 10 km long, the train needs 60 seconds.
Distance per second
At Mach 0.1, 122.5 km/h, you cover 34 metres each second. At Mach 0.5, 612.5 km/h, 170 metres. At Mach 2, 2,450 km/h, 680 metres. A small Mach number can still mean a vehicle moving at a very high speed in daily terms.
Records on the ground
The fastest production car has passed 490 km/h, which is Mach 0.40. The Thrust SSC exceeded Mach 1 on the ground at 1,228 km/h in 1997. A Formula One car on a straight reaches 360 km/h, Mach 0.29. A “convert km/h to Mach” calculation puts these on one scale.
Trains
The record for a magnetic levitation train is 603 km/h, Mach 0.49, and for a wheeled train 574.8 km/h, Mach 0.47. Commercial high-speed services run at 300 to 350 km/h, which is Mach 0.24 to 0.29. Air resistance becomes the main issue, and tunnels create pressure waves.
Why pilots fly by Mach at height
At high altitude the dangers are set by Mach, not by km/h: the wing begins to form shock waves at its critical Mach number, and a limit called MMO, often 0.82 or 0.89 depending on the aircraft, protects the structure and the controls. Below a crossover altitude the limit is expressed as an indicated airspeed, above it as a Mach number.
Birds and animals
A peregrine falcon in a dive reaches 389 km/h, Mach 0.32. A cheetah sprints at 110 km/h, Mach 0.09, and an elite human sprinter at 45 km/h, Mach 0.037. All are far below the speed of sound.
Weather extremes
The strongest gust measured at the surface, 408 km/h, is Mach 0.33. A violent tornado at 322 km/h is Mach 0.26. Even the worst weather is well below the sound barrier.
Why the number is a fraction
Mach numbers below one are fractions of the speed of sound. Mach 0.85 means 85 per cent of the speed of sound, and Mach 0.1 means 10 per cent. Reading it as a percentage helps to see how close the aircraft is to the limit.
Pressure waves and tunnels
At 320 km/h, Mach 0.26, air can no longer be treated as incompressible in tunnel design. A train entering a tunnel pushes a pressure wave ahead of it, and the wave can emerge as a boom. Entrances are shaped to soften the effect.
Mach on another planet
On Mars sound travels at about 240 m/s, 864 km/h. A vehicle moving at 100 km/h there is at Mach 0.12, compared with 0.082 on Earth. Probes bound for Mars are designed with the local speed of sound.
Rockets and re-entry
A rocket passes Mach 1 about a minute after lift-off at around 1,300 km/h, and a capsule returning from orbit enters the atmosphere at nearly 28,000 km/h, Mach 23 by the sea-level factor. At the real altitude of peak heating Mach is a little higher.
Flight simulators
Flight simulators display Mach but calculate motion in m/s or knots. For an airliner moving at 250 m/s at 11 km, the Mach number is 0.85. Developers convert km/h to Mach using the speed-of-sound formula and the standard atmosphere model.
Reporting in the press
An article that speaks of "Mach 5" without more detail is vague. A careful reader can convert km/h to Mach twice: 6,125 km/h at sea level, 5,300 km/h in the stratosphere. If the article gives altitude, you can do the calculation yourself. If not, treat the figure as approximate.
Two routes to one answer
You can go from km/h to Mach directly by dividing by 1,225.06, or via m/s by dividing by 3.6 and then by 340.294. If they disagree, one of the digits was copied wrongly.
Echo and distance
A shout towards a wall 170 metres away returns after one second, since sound covers 340 metres there and back. Sailors and climbers use this to judge distance. As the air temperature changes, the speed of sound varies by 0.6 m/s per degree, and so does the Mach number of anything moving at a fixed speed.
Air-traffic instructions
Controllers sometimes tell crews to "maintain Mach point eight zero". At cruise level this is 850 km/h. Using the sea-level factor, the instruction would seem to mean 980 km/h, which could mislead. The conversion is made by flight computers, but pilots keep the sense of the numbers.
Underwater
In water, Mach 1 is 5,328 km/h. A submarine at 70 km/h is at Mach 0.013 relative to the water, and a supercavitating torpedo at about 370 km/h at Mach 0.07. Speeds near Mach 1 are practically out of reach in water, so the Mach number is rarely used there.
Mach tuck and buffet
If a jet goes beyond its critical Mach number, the centre of pressure moves back and the nose tends to pitch down, an effect called Mach tuck. Modern aircraft prevent it with an automatic trim system. For a jet whose critical Mach is 0.82, the limit at cruise altitude is about 871 km/h of airspeed.
Total air temperature
The sensor on the nose reads a temperature higher than the real air, because the airflow is stopped on the probe. The rise is T × 0.2 × M². At Mach 0.85 in air at −56.5 °C this adds about 31 °C, giving a reading of −25 °C. Flight computers correct it, using Mach number to find the true air temperature.
The coffin corner
At very high altitude, the margin between the speed at which the wing stalls and the Mach limit shrinks, until a small error would put the aircraft in trouble on both sides. Pilots call this the coffin corner. Because the speed of sound has dropped to 1,062 km/h, the margin in km/h is much smaller than at sea level.
Time and fuel at different Mach numbers
On a 5,570 km Atlantic crossing, a jet at Mach 0.80, about 850 km/h, takes 6 h 33 min, and at Mach 0.85, 903 km/h, takes 6 h 10 min. The 23 minutes saved need a good deal more fuel. Airlines usually fly a "long range cruise" Mach chosen to balance time and cost.
Jet streams
A jet stream of 200 km/h can add or subtract from the ground speed. Eastbound with that tailwind the ground speed is 1,103 km/h and the 5,570 km crossing takes about 5 h 3 min. Westbound with a 150 km/h headwind it is 753 km/h and takes 7 h 24 min. The Mach number stays the same, 0.85, in both directions.
The mental shortcut
To convert km/h to Mach in your head at sea level, divide by 1,200 and remove 2 per cent. For 2,450 km/h: 2.04 less 0.04 gives 2.0. For 850 km/h: 0.708 less 0.014 gives 0.694. At cruise altitude divide by 1,060 instead.
More values for convert km/h to Mach
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 km/h = 0.0000816288 Mach
- 0.5 km/h = 0.000408144 Mach
- 3 km/h = 0.00244886 Mach
- 4 km/h = 0.00326515 Mach
- 7 km/h = 0.00571401 Mach
- 15 km/h = 0.0122443 Mach
- 20 km/h = 0.0163258 Mach
- 75 km/h = 0.0612216 Mach
- 200 km/h = 0.163258 Mach
- 500 km/h = 0.408144 Mach
- 2,000 km/h = 1.63258 Mach
- 10,000 km/h = 8.16288 Mach
Common slips when you convert km/h to Mach
Multiplying instead of dividing
From km/h to Mach you divide. If 600 km/h turned into 735,000, you multiplied instead.
Forgetting altitude
The factor 1,225.06 holds at sea level. At 11 kilometres, 850 km/h is Mach 0.80 and not 0.69, a difference of 15 per cent.
Treating Mach as a speed
Mach is a ratio. In air at different temperatures the same km/h gives different Mach numbers.
Quick questions
What is the formula to convert km/h to Mach?
Mach equals km/h divided by 1,225.06.
What is 600 km/h in Mach?
Mach 0.49.
What is 2,450 km/h in Mach?
Mach 2.00.
What is one Mach in km/h?
1,225.06 km/h at sea level.
Is my number uploaded?
No, everything is calculated in your browser.
Where to go next
Other speed converters are listed here: Convert km/h to ft/s, Convert km/h to mph, Convert m/s to Mach, Convert mph to Mach, Convert Mach to m/s, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. If you need the opposite direction, go to Convert Mach to km/h.
To sum up: km/h become Mach when you divide by 1,225.06 under sea-level conditions, and the unit always goes beside the answer. What you type is processed on your own device, with no sign-up and no upload.