Convert Mach to mph Mach numbers ↔ miles per hour Free Online Secure
Type a value in Mach numbers and read it in miles 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 miles per hour
Common values — Convert Mach to mph (Mach numbers ↔ miles per hour)
| Mach | mph |
|---|---|
| 0.5 | 380.607999284 |
| 0.8 | 608.972798855 |
| 1 | 761.215998568 |
| 1.5 | 1141.82399785 |
| 2 | 1522.43199714 |
| 3 | 2283.64799571 |
| 5 | 3806.07999284 |
| 10 | 7612.15998568 |
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 miles per hour: fighter jets, air shows and the sound barrier over America
American press releases about fighter jets give top speed as a Mach number, air-show announcers shout speeds in miles per hour, and the average listener has to carry the figures between the two. Mach is a ratio, the speed of an object divided by the speed of sound around it, so turning it into mph needs one assumption about the air. To convert Mach to mph under standard sea-level conditions, multiply by 761.2: Mach 1 is 761 mph, Mach 2 is 1,522 mph and Mach 0.85 is 647 mph. The calculator above uses the speed of sound at 15 °C, 340.294 m/s, and the sections below explain how much the answer changes at altitude, where the jets actually fly.
The page gives the rule with worked examples, a profile of each unit, a comparison and a long run of cases from military and civil aviation, followed by the usual mistakes. The calculation runs in your browser and nothing you enter is sent anywhere. For real operations, use the official figures for each aircraft.
How to convert Mach to mph: one number, 761.2
Where 761.2 comes from
Sound covers 340.294 metres each second in standard air at 15 °C. One metre per second is 2.23694 mph, so 340.294 × 2.23694 gives 761.2 mph. That is the whole rule behind a “convert Mach to mph” calculation: take the Mach number and multiply by 761.2. Mach 0.5 comes to 380.6 mph, Mach 1.5 to 1,141.8 mph and Mach 3 to 2,283.6 mph.
Worked examples
An airliner at Mach 0.8 is going 609 mph at sea level. A supersonic jet at Mach 2 is going 1,522 mph. Mach 5, the hypersonic threshold, is 3,806 mph, and Mach 25, the order of a returning spacecraft, is 19,030 mph. To go back, divide mph by 761.2.
The conditions behind the factor
Mach is a ratio and not a speed, and the factor 761.2 assumes 15 °C air. At 36,000 feet, at −56.5 °C, sound moves at 660 mph, so Mach 1 there is 13 per cent fewer miles per hour than on the ground.
A quick sanity test
The figure in mph must be hundreds of times larger than the Mach number. If you ended with a smaller number than you began with, you divided where you should have multiplied.
The Mach number
A ratio to the speed of sound
The Mach number is the speed of an object relative to the speed of sound in the medium. It is named after the physicist Ernst Mach. Flight below Mach 1 is subsonic, around it transonic, above it supersonic and beyond Mach 5 hypersonic.
Where it appears
Fighter and bomber specifications, air-show commentary, rocket reports and wind-tunnel data.
The mile per hour
The unit of the American public
The mile per hour is the unit in which speeds are described to the general public in the United States and the United Kingdom, whether for cars or for aircraft. Numbers such as "1,500 mph" are those people remember.
Where it appears
Press releases, air-show commentary, documentaries and record books.
Mach against miles per hour
One Mach is 761 mph at sea level, so the figure in mph is more than seven hundred times larger. Mach 2 is 1,522 mph and Mach 0.85 is 647 mph. Mach depends on the temperature of the air, while mph does not.
For that reason the conversion is exact only when the conditions are stated. The standard trap is to apply the sea-level factor to a jet at 40,000 feet.
Where the conversion shows up
Fighter jets
An F-15 is rated at about Mach 2.5, an F-16 at Mach 2 and an F-22 at Mach 2.25. At altitude, where Mach 1 is 660 mph, a “convert Mach to mph” calculation gives 1,650, 1,320 and 1,485 mph. With the sea-level factor you would get 1,903, 1,522 and 1,713 mph, which is 15 per cent too much. A “convert Mach to mph” calculation must therefore state where the jet is flying.
Air shows
At air shows, jets fly low and stay subsonic. A demonstration pass at 500 mph is Mach 0.66 at sea level. In the United States, civil rules prohibit supersonic flight over land, and military aircraft are restricted to special areas, so spectators almost never hear a sonic boom.
Strategic aircraft
A heavy bomber such as the B-52 cruises at about Mach 0.77, 508 mph at altitude, and the supersonic B-1B can dash at Mach 1.25, 825 mph. Crews think in Mach at height and in knots near the ground.
The F-22 and supercruise
The F-22 can cruise supersonically without afterburner, a trait called supercruise, at about Mach 1.5. At altitude that is 990 mph. With afterburner it reaches Mach 2.25. Without needing the fuel-hungry afterburner, it saves fuel and keeps its infra-red signature low.
Spreadsheet formulas
To convert Mach to mph in a spreadsheet, put the Mach numbers in column A and enter =A2*761.216 in column B. For cruise altitude multiply by 660.05. For any temperature T in °C, the speed of sound in mph is =20.0468*SQRT(273.15+T)*2.23694.
Rounding and honesty
When you convert Mach to mph for a poster, Mach 3.3 means "about 2,500 mph" by the sea-level factor or 2,178 mph at altitude. In a technical note, state the altitude. The uncertainty in the speed of sound is bigger than any rounding in the multiplication.
Landmarks to memorise
To convert Mach to mph at a glance, recall that Mach 0.5 is 381 mph. Mach 0.8 is 609 mph. Mach 1 is 761 mph. Mach 2 is 1,522 mph. Mach 3 is 2,284 mph. Mach 5 is 3,806 mph. Mach 10 is 7,612 mph. When you convert Mach to mph by eye, these seven values are enough to estimate any headline.
Reference ladder
Mach 0.3 is 228 mph. Mach 0.75 is 571 mph. Mach 0.9 is 685 mph. Mach 1.2 is 913 mph. Mach 1.5 is 1,142 mph. Mach 2.5 is 1,903 mph. Mach 6 is 4,567 mph. Mach 20 is 15,224 mph. With a ladder like this, quick checks are easy.
Checking by reversing
To check a “convert Mach to mph” calculation result, divide the answer by 761.2. If Mach 2 became 1,522 mph, then 1,522 divided by 761.2 returns 2. A second check concerns size: the figure in mph should be more than seven hundred times larger.
Link to km/h and m/s
Mach 1 is 340.3 m/s, 1,225 km/h and 761.2 mph. You can go via km/h by multiplying Mach by 1,225.06 and then by 0.6214. The result is the same as a direct multiplication by 761.2.
A worked example
A supersonic airliner cruises at Mach 2 at 60,000 feet, where the speed of sound is 660 mph. Its true speed is 1,320 mph. On a route from New York to Los Angeles of about 2,450 miles, the flight lasts 1 h 51 min. With the sea-level figure of 1,522 mph the answer would be 1 h 37 min, which is a wrong promise to passengers.
The shock cone
A supersonic aircraft trails a cone of shock waves whose half angle is arcsin(1 / Mach): 41.8 degrees at Mach 1.5, 30 degrees at Mach 2 and 19.5 degrees at Mach 3. The boom reaches the ground when the cone sweeps over it. At 1,522 mph the aircraft covers a mile in 2.4 seconds.
Distance each second
At Mach 1 on the ground you cover 0.21 miles a second, close to 340 metres. At Mach 2, 0.42 miles. At Mach 3, 0.63 miles. An hour at Mach 2 is 1,522 miles, nearly the distance from Chicago to Los Angeles with some to spare.
Aerodynamic heating
At Mach 2 in air at −56.5 °C, the stagnation temperature is about 117 °C, and at Mach 3 about 240 °C. Ordinary aluminium loses strength at such temperatures, which is why very fast aircraft use titanium or special alloys.
The F-35 family
The F-35 has a top speed of about Mach 1.6, which is roughly 1,056 mph at altitude. Compared with older fighters it trades some speed for stealth and sensors.
Records, briefly
Yeager's first supersonic flight in 1947 was about 700 mph, Mach 1.06 at altitude. The SR-71 reached 2,193 mph in 1976, Mach 3.3. The X-15 flew at 4,520 mph in 1967, Mach 6.7. The Thrust SSC car reached 763 mph on land in 1997.
Bullets and sound
A rifle bullet at 1,900 mph is travelling at Mach 2.5. A slow pistol bullet at 560 mph is at Mach 0.74 and stays subsonic. The crack heard from a supersonic bullet is its shock wave, not the muzzle blast.
Extreme weather in Mach
The strongest gust ever measured at the surface, 253 mph, is Mach 0.33. A category 5 hurricane begins at 157 mph, Mach 0.21. Even the worst weather is far from the speed of sound.
Mach in water
In water, sound travels at 3,310 mph, so Mach 1 in water is that figure. A submarine at 40 mph is at Mach 0.012 relative to the water. Mach is always measured against the medium the object moves through.
Mach on Mars
On Mars sound travels at about 240 m/s, 537 mph. A vehicle at 100 mph there would be at Mach 0.19, against 0.13 on Earth. Probes bound for Mars are designed using the local speed of sound.
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 tunnel at Mach 0.5 has a stream at 381 mph at sea level. Test data are labelled by Mach number, not mph.
The compressibility threshold
Above Mach 0.3, 228 mph at sea level, variations in the density of air can no longer be ignored. Light aircraft stay below that threshold, and airliners pass it soon after take-off, so designers switch from simple to compressible-flow models.
"Mach 1" in movies
Action films use "Mach 1" to mean "very fast". Yet Mach 1 is 761 mph on the ground, 741 mph at 0 °C, 791 mph on a 38 °C day and 660 mph in the stratosphere. A careful report states the conditions, and a careful reader asks.
Records in two units
Record bodies want speeds in the local unit and in km/h. The SR-71 record appears as 2,193 mph and as 3,529.6 km/h. A journalist who wants a “convert Mach to mph” calculation for readers can use 0.6214 on a km/h table or start from Mach.
The man behind the name
Ernst Mach, an Austrian physicist and philosopher, photographed the shock wave of a supersonic bullet in 1887. The number named after him was introduced in 1929 by the engineer Jakob Ackeret. Nowadays almost every figure about aircraft speed is given in Mach and then turned into mph or km/h for the public.
A-10 and other slow flyers
The A-10 attack aircraft cruises at about 340 mph and has a maximum of 439 mph, which is Mach 0.58 at sea level. It was designed to fly low and slow, with a gun, to support troops. Even among military aircraft, speed in Mach is not always the point.
Two routes to the same number
You can go from Mach to mph directly with 761.2, or in two steps: multiply by 340.294 to get m/s, then by 2.23694. If the routes disagree, a digit was copied wrongly.
Carrier landings
A naval jet approaches the deck at about 145 knots, 167 mph, which is Mach 0.22 at sea level. At that speed it is caught by an arresting wire and stopped in around 100 metres. The same airframe is capable of Mach 1.7 at altitude, so the difference between landing and flight speed is a factor of about seven.
Sonic boom rules
Since 1973 civil supersonic flight over the land of the United States has been prohibited by regulation, because of the boom. A supersonic jet at 1,320 mph produces a wave that spreads over a corridor tens of miles wide. Research on quieter designs aims to reduce the boom to the level of a car door slam.
Speed in Mach at altitude
The speed of sound falls as air cools: 761 mph at sea level, 748 mph at 5,000 feet, 735 mph at 10,000 feet, 707 mph at 20,000 feet, 678 mph at 30,000 feet and 660 mph from 36,000 feet up to about 65,000 feet. A pilot reading 600 mph at 30,000 feet is thus at Mach 0.88.
Airliners
An airliner cruising at Mach 0.85 at 36,000 feet flies at 561 mph, and it is that value a “convert Mach to mph” calculation for flight time needs. The sea-level factor would say 647 mph, which is 15 per cent too fast. For accurate flight times, airlines use true airspeed, found by multiplying Mach by the local speed of sound.
The hypersonic frontier
Hypersonic flight begins at Mach 5, 3,806 mph at sea level or 3,300 mph in the stratosphere. An unmanned test vehicle reached Mach 9.6 in 2004, about 7,000 mph. The flight lasted seconds, since its engine could burn only a short time.
The mental shortcut
To convert Mach to mph in your head, multiply by 750 and add 1.5 per cent. For Mach 2: 1,500 plus 22 gives 1,522. For Mach 0.5: 375 plus 5.6 gives 380.6. At cruise altitude use 660 instead of 761.
More values for convert Mach to mph
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 = 76.1216 mph
- 0.5 Mach = 380.608 mph
- 3 Mach = 2,283.65 mph
- 4 Mach = 3,044.86 mph
- 7 Mach = 5,328.51 mph
- 15 Mach = 11,418.2 mph
- 20 Mach = 15,224.3 mph
- 75 Mach = 57,091.2 mph
- 200 Mach = 152,243 mph
- 500 Mach = 380,608 mph
- 2,000 Mach = 1,522,432 mph
- 10,000 Mach = 7,612,160 mph
Common slips with a “convert Mach to mph” calculation
The wrong operation
Mach to mph means multiplying. If Mach 2 came out as 0.0026, you divided by 761.2.
Ground factor used at height
The number 761.2 is for sea level. At cruise altitude one Mach is 660 mph, and forgetting it costs 15 per cent in accuracy.
Mach treated as a fixed speed
Mach is a ratio. The same Mach number means different mph in warm and cold air.
Questions in brief
What is the rule for a “convert Mach to mph” calculation?
Multiply the Mach number by 761.2 to get mph.
What is Mach 1 in mph on the ground?
761.2 mph.
What is Mach 2 in mph on the ground?
1,522.4 mph.
What is Mach 1 at 36,000 feet?
Close to 660 mph.
Does the calculator send my input anywhere?
No, it is all done in your browser.
Related pages and a summary
You may also want Convert Mach to km/h, Convert Mach to m/s, Convert knots to mph, Convert ft/s to mph, Convert mph to km/h, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. For the opposite direction, see Convert mph to Mach.
Summing up: multiply a Mach number by 761.2 to get miles per hour under sea-level conditions, and always write the unit beside the result. Everything stays in your own browser, with no account and no upload.