Convert Mach to m/s Mach numbers ↔ metres per second Free Online Secure
Type a value in Mach numbers and read it in metres per second 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.
Nothing uploaded
Convert from Mach numbers
Convert to metres per second
Common values — Convert Mach to m/s (Mach numbers ↔ metres per second)
| Mach | m/s |
|---|---|
| 0.5 | 170.147 |
| 0.8 | 272.2352 |
| 1 | 340.294 |
| 1.5 | 510.441 |
| 2 | 680.588 |
| 3 | 1020.882 |
| 5 | 1701.47 |
| 10 | 3402.94 |
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.
From Mach number to metres per second in engineering: nozzles, tunnels, turbines and simulations
An engineer who sets up a supersonic nozzle, a wind-tunnel run or a computational model works in SI units, yet the specification often says "Mach 2.5". Turning that number into metres per second is a small calculation with one big assumption: the temperature of the gas. To convert Mach to m/s for standard air at 15 °C, multiply by 340.294: Mach 0.5 is 170.1 m/s, Mach 1 is 340.3 m/s and Mach 2 is 680.6 m/s. The calculator above does the multiplication as you type, and the sections below show where the number comes from and when it does not apply.
The page covers the rule with worked examples, a profile of each unit, a comparison and a long series of engineering settings, followed by the usual pitfalls. The calculation runs in your browser and nothing you type is sent anywhere. In technical reports, always state the gas and the temperature you assumed.
How to convert Mach to m/s: multiply by 340.294
The rule
The speed of sound in an ideal gas is the square root of γRT/M, with γ the heat capacity ratio, R the gas constant, T the absolute temperature and M the molar mass. For air, γ = 1.4 and M = 0.028965 kg/mol, so at 288.15 K the formula gives 340.29 m/s. To convert Mach to m/s, multiply the Mach number by that figure. Mach 0.8 gives 272.2 m/s, Mach 3 gives 1,020.9 m/s and Mach 10 gives 3,402.9 m/s. To go back, divide m/s by 340.294.
Worked examples
A “convert Mach to m/s” calculation for a transonic test at Mach 0.85 in air at 15 °C gives 289.2 m/s. A supersonic tunnel at Mach 2.5 runs at 850.7 m/s. A hypersonic facility at Mach 6.7 runs at 2,280 m/s and a re-entry condition of Mach 25 corresponds to 8,507 m/s by the sea-level factor.
What the factor leaves out
Mach is a ratio, so 340.294 applies only to air at 15 °C. At −56.5 °C, the temperature at 11 km, sound travels at 295.1 m/s, and Mach 2 is then 590 m/s and not 681 m/s.
A quick sanity test
The answer in m/s should be more than three hundred times the Mach number. If a “convert Mach to m/s” calculation gave a smaller figure than you started with, you divided by mistake.
The Mach number
A dimensionless ratio
The Mach number is the ratio of a speed to the local speed of sound. As a ratio of two speeds, it has no unit. It is named after Ernst Mach, who photographed the shock waves around supersonic projectiles in the 1880s.
Where it appears
Aerodynamics, gas dynamics, propulsion, ballistics and acoustics.
The metre per second
The SI unit of speed
The metre per second is the coherent SI unit of speed. Equations of gas dynamics, such as the isentropic relations and the mass-flow formulas, are written in it, and test reports usually give velocities in m/s.
Where it appears
Engineering textbooks, test reports, standards and simulation outputs.
Mach against metres per second
One Mach is 340.3 m/s at 15 °C, so the figure in m/s is more than three hundred times larger. Mach 0.1 is 34 m/s and Mach 10 is 3,403 m/s. Unlike m/s, Mach depends on the gas and on its temperature.
The conversion is exact only for stated conditions. The typical error is to apply 340.294 to a gas or a temperature it was not computed for.
Where the conversion shows up
Wind tunnels
A tunnel at Mach 0.3 has a stream of 102 m/s, one at Mach 0.8 a stream of 272 m/s and a supersonic one at Mach 2 a stream of 681 m/s, at 15 °C. The actual speed follows from the temperature in the test section. A “convert Mach to m/s” calculation is the first line of any test plan.
Rocket nozzles
In a rocket nozzle the gas leaves at 2,500 to 3,500 m/s. The local speed of sound in the hot exhaust is about 1,000 m/s, so the exit Mach number is typically 3 to 4. The engineer quotes performance as exhaust velocity in m/s and as Mach number, according to the audience.
Simulations
Computational fluid dynamics codes can be fed either a Mach number and a temperature, or a velocity. Converting between them is a routine step, and a mistake in the temperature gives a velocity error of about 0.17 per cent for every degree.
Isentropic relations
The ratio of stagnation to static temperature in a flow is 1 + 0.2 M² for air. At Mach 2 in air of 288 K that is a temperature rise of 230 K, and at Mach 3 of 518 K. These formulas use Mach as the main variable, and the velocity in m/s follows when the static temperature is known.
Spreadsheet formulas
To convert Mach to m/s in a spreadsheet, put the Mach numbers in column A and enter =A2*340.294 in column B. For another temperature T in °C, work out the local speed of sound with =20.0468*SQRT(273.15+T) and multiply the Mach number by it.
Combining with other columns
A third column dividing B by 3.6 or multiplying by 3.6 gives km/h, so you can compare the result with the specification of a vehicle or a facility.
Rounding and precision
When you convert Mach to m/s for classroom work, 340 m/s is enough. For a tunnel, use the exact value from the measured temperature. An error of 1 degree in temperature gives an error of 0.6 m/s in the speed of sound, which is 0.17 per cent.
Landmarks to memorise
Mach 0.1 is 34 m/s. Mach 0.5 is 170 m/s. Mach 1 is 340 m/s. Mach 2 is 681 m/s. Mach 3 is 1,021 m/s. Mach 5 is 1,701 m/s. Mach 10 is 3,403 m/s. To convert Mach to m/s on the fly, scale from these values.
Reference ladder
Mach 0.3 is 102.1 m/s. Mach 0.75 is 255.2 m/s. Mach 0.9 is 306.3 m/s. Mach 1.2 is 408.4 m/s. Mach 1.5 is 510.4 m/s. Mach 2.5 is 850.7 m/s. Mach 6 is 2,042 m/s. Mach 20 is 6,806 m/s. A ladder like this speeds up any convert Mach to m/s check.
Checking by reversing
To check a “convert Mach to m/s” calculation result, divide the answer by 340.294. If Mach 2 became 680.6 m/s, then 680.6 divided by 340.294 returns 2. A second test is size: the m/s figure should be more than three hundred times the Mach number.
Link to km/h and mph
Mach 1 is 340.3 m/s, 1,225 km/h and 761.2 mph. Via km/h you can multiply by 1,225.06 and divide by 3.6. To convert Mach to m/s either way gives the same result as multiplying directly by 340.294.
A worked example
To convert Mach to m/s correctly at altitude: an airliner cruises at Mach 0.85 at 11 km. The temperature is −56.5 °C, so sound travels at 295.1 m/s and the aircraft at 250.8 m/s, which is 903 km/h. In ten minutes the aircraft covers 150.5 km. The sea-level figure of 340.294 m/s would give 289.2 m/s, an error of 15 per cent.
Shock cone angles
A supersonic body trails a cone of shock waves with half angle arcsin(1 / Mach): 41.8° at Mach 1.5, 30° at Mach 2 and 19.5° at Mach 3. At Mach 2 the body moves 681 m each second while the wave front advances 340 m.
Doppler shift
A sound source moving at speed v toward an observer shifts the observed frequency by the factor 1 / (1 − v / c). A siren approaching at 34 m/s, Mach 0.1, rises in pitch by about 11 per cent. Weather radars use the same principle to measure the velocity of raindrops.
Kinetic energy at high speed
At Mach 2, 681 m/s, one kilogram of matter has 232 kJ of kinetic energy, 44 times more than at Mach 0.3, 102 m/s. This is why the impact of a supersonic projectile is so much more destructive than that of a slow one.
Choked flow
When gas flows through a narrowing duct, its velocity at the throat cannot exceed the local speed of sound. For air at 288 K that limit is 340 m/s. Beyond it, only a diverging section can accelerate the flow to supersonic speed. This is the principle of the de Laval nozzle used on rocket engines and steam turbines.
The sonic boom
A supersonic aircraft generates a boom heard on the ground. Its strength depends on altitude, aircraft size and Mach number. At Mach 2, 590 m/s at altitude, the shock cone reaches the ground many kilometres behind the point at which it was produced.
Echo location
An echo returning after a time t comes from a distance 343 t / 2 at 20 °C. For t = 0.5 s the distance is 86 m. Sonar, echo sounders and bats rely on the same relation, correcting for temperature or salinity.
Lightning and thunder
Sound takes 2.94 seconds to cover a kilometre. Counting the seconds between flash and thunder and dividing by three gives the distance in kilometres. The method rests directly on the figure of 340 m/s.
Ultrasound
An ultrasound of 40 kHz has a wavelength of 8.6 mm in air and 37 mm in water. Medical ultrasound uses frequencies of millions of hertz and a speed of sound in tissue of about 1,540 m/s. The conversion helps to compute resolution.
Humidity
Moist air carries sound slightly faster than dry air, because water vapour is lighter than nitrogen and oxygen. At 20 °C and 100 per cent humidity the increase is 0.5 to 1 m/s. The difference is small, yet measurable in precision acoustics.
Hypersonic flow
The hypersonic regime begins at Mach 5, which is 1,701 m/s at 15 °C and 1,475 m/s at altitude. At these speeds the air near the body is heated to thousands of degrees, and oxygen and nitrogen molecules begin to dissociate. The gas can no longer be treated as ideal.
Molecular speeds
The nitrogen molecules in air move at a root-mean-square speed of 507 m/s at 15 °C, faster than sound. The ratio is the square root of 3 / 1.4, or 1.46. Sound travels by collisions between molecules, so it is somewhat slower than the molecules themselves.
Wind speed against sound
The strongest surface gust ever measured, 113 m/s, is Mach 0.33. A violent tornado at 90 m/s is Mach 0.26. Even the most intense wind on Earth is below a third of the speed of sound.
Rockets and spacecraft
A rocket passes Mach 1 about a minute after launch, at roughly 340 m/s. A capsule returning from orbit enters the atmosphere at 7,800 m/s, almost Mach 26 relative to the sound speed at altitude. These speeds are more than twenty times that of sound.
Mach on Mars and Venus
On Mars, in carbon dioxide at about −60 °C, sound travels at roughly 240 m/s, so Mach 1 there is about 70 per cent of Earth's. At the surface of Venus the hot atmosphere carries sound at around 410 m/s.
Gas turbine blades
The tips of the first-stage blades of a large aircraft engine fan move at around 400 m/s, which is above Mach 1 relative to the incoming air. Designers shape the blades to cope with shock waves. Engineers quote tip speeds in m/s or Mach numbers.
Two routes to one result
You can go from Mach to m/s directly with 340.294, or in two steps: work out the speed of sound from the temperature and then multiply by the Mach number. At 15 °C the routes agree. At other temperatures the second is the right one.
Shock tubes
In a shock tube a diaphragm bursts and a shock wave runs down the tube. A wave of Mach 3 in air at 288 K moves at 1,021 m/s. Researchers use these tubes to study combustion and gas chemistry at high temperature, and the shock Mach number sets the conditions behind the wave.
Sound in different gases
At 20 °C sound travels at 343 m/s in air, 1,007 m/s in helium, 1,305 m/s in hydrogen, 319 m/s in argon and 268 m/s in carbon dioxide. Mach 1 therefore means very different velocities in different gases, and wind tunnels that use helium or heavy gases exploit this to reach a particular Mach number at modest velocity.
Heavy gas tunnels
Some facilities use gases heavier than air, such as sulphur hexafluoride, to run at lower speeds with the same Mach number. A gas in which sound travels at 135 m/s needs only 270 m/s to reach Mach 2. The model then experiences less severe loads, and the tunnel needs less power.
Altitude and temperature
At 11 km the speed of sound is 295.1 m/s. A jet at Mach 0.85 is moving at 250.8 m/s there, not at 289.2 m/s. A jet at Mach 2 moves at 590 m/s. The low pressure does not influence the speed of sound, only the temperature does.
A practical formula for air
For air, the speed of sound in m/s is roughly 331.3 + 0.606 T, with T in degrees Celsius. At 0 °C this gives 331.3, at 15 °C 340.4, at 20 °C 343.4 and at 40 °C 355.5. The formula is good enough for ordinary calculations between −40 and 40 °C.
The mental shortcut
To convert Mach to m/s in your head, multiply by 340 and add 0.1 per cent. For Mach 2: 680 plus 0.7 gives 680.7. For Mach 0.5: 170 plus 0.2 gives 170.2. At cruise altitude use 295 instead of 340.
More values for convert Mach 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 Mach = 34.0294 m/s
- 0.5 Mach = 170.147 m/s
- 3 Mach = 1,020.882 m/s
- 4 Mach = 1,361.176 m/s
- 7 Mach = 2,382.058 m/s
- 15 Mach = 5,104.41 m/s
- 20 Mach = 6,805.88 m/s
- 75 Mach = 25,522.05 m/s
- 200 Mach = 68,058.8 m/s
- 500 Mach = 170,147 m/s
- 2,000 Mach = 680,588 m/s
- 10,000 Mach = 3,402,940 m/s
Common slips with a “convert Mach to m/s” calculation
Dividing instead of multiplying
From Mach to m/s the number grows. If Mach 2 turned into 0.006, you divided by mistake.
Ignoring temperature
The value 340.294 holds at 15 °C. At −56.5 °C one Mach is 295 m/s, and forgetting this leads to an error of 15 per cent.
The wrong gas
In helium or carbon dioxide the speed of sound differs. The Mach number must be computed with the speed of sound of the gas in question.
Quick questions
What is the formula to convert Mach to m/s?
Metres per second equal the Mach number times 340.294.
How many m/s is Mach 1?
340.294 m/s in air at 15 °C.
How many m/s is Mach 2?
680.59 m/s.
How fast is sound at 20 °C?
About 343 m/s.
Is anything uploaded?
No, everything is calculated in your browser.
Related pages and a summary
You may also want Convert Mach to mph, Convert Mach to km/h, Convert mph to m/s, Convert ft/s to m/s, Convert m/s to ft/s, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. For the opposite direction, see Convert m/s to Mach.
Summing up: multiply a Mach number by 340.294 for air at 15 °C and write the unit beside the result. Everything stays in your browser, with no account and no upload.