Convert m/s to Mach metres per second ↔ Mach numbers Free Online Secure
Type a value in metres per second 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 m/s to Mach (metres per second ↔ Mach numbers)
| m/s | Mach |
|---|---|
| 1 | 0.00293863541526 |
| 2 | 0.00587727083052 |
| 3 | 0.00881590624578 |
| 5 | 0.0146931770763 |
| 10 | 0.0293863541526 |
| 20 | 0.0587727083052 |
| 50 | 0.146931770763 |
| 100 | 0.293863541526 |
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 the physics lab to Mach: reading a velocity against the speed of sound
A student times a pulse between two microphones, a researcher logs the air velocity in a test section, and a reader of space news learns that a probe is moving at 17 km/s. Each of them has a speed in metres per second and a natural follow-up question: how does it compare with sound? The Mach number is the answer. To convert m/s to Mach in air at 15 °C, divide by 340.294. So 100 m/s is Mach 0.294, 340 m/s is Mach 1 and 1,000 m/s is Mach 2.94. The calculator above divides while you type, and the sections below put the figures in the context of a school lab, of orbit and of the news.
Below there are worked examples, a profile of each unit, a comparison, many examples from experiments and nature, and the usual slips. Everything is computed in your browser and nothing is sent to a server. In a lab report, say which temperature you used for the speed of sound.
How to convert m/s to Mach: divide by 340.294
The calculation
The speed of sound in air at 15 °C is 340.294 m/s. The Mach number is a velocity divided by that figure, so a “convert m/s to Mach” calculation is a division: 50 m/s gives Mach 0.147, 250 m/s gives Mach 0.735 and 800 m/s gives Mach 2.35. The same can be done by multiplying by 0.0029386. To go the other way, multiply the Mach number by 340.294.
Worked examples
A gale of 30 m/s is at Mach 0.088. An airliner at 250 m/s is at Mach 0.735 near the ground and Mach 0.85 at 11 km. A projectile at 900 m/s is at Mach 2.64, and a capsule at 7,800 m/s at Mach 22.9 by the sea-level factor.
How far to trust the result
The answer is right only for air at 15 °C. In colder air sound is slower and the same velocity gives a higher Mach number: 250 m/s is Mach 0.85 at −56.5 °C against 0.735 at 15 °C.
A quick sanity test
The result must be more than three hundred times smaller than the number of m/s. If a “convert m/s to Mach” calculation gave a larger figure than you started with, you multiplied by 340 instead of dividing.
The metre per second
The unit of measurement
The metre per second is the SI unit of speed. Lab sensors, research anemometers and simulation codes deliver results in m/s, since the equations of physics are written for it.
Where it appears
Data files, lab reports, numerical simulations and physics textbooks.
The Mach number
The ratio to the speed of sound
The Mach number compares an object's speed with the speed of sound in its surroundings. It has no unit. A value of 0.3 marks the start of compressibility effects, 1 the sound barrier and 5 the start of the hypersonic regime.
Where it appears
Aerodynamics, ballistics, wind tunnels and space research.
Metre per second or Mach?
One m/s equals Mach 0.00294, so the Mach figure is over three hundred times smaller. A velocity of 100 m/s is Mach 0.294, and 1,000 m/s is Mach 2.94. The main difference is that Mach depends on the gas and its temperature while m/s does not.
For this reason the conversion holds exactly only under stated conditions. A frequent trap is using 340.294 for air that is not at 15 °C.
Where the conversion shows up
Measuring the speed of sound in class
To convert m/s to Mach in a classroom, a classic experiment times a pulse over a distance of 1.5 m with two microphones, and finds about 4.4 ms, which gives 343 m/s at 20 °C. Students then use that figure to convert m/s to Mach on their own test speeds. A “convert m/s to Mach” calculation for a rolling trolley at 1.2 m/s gives Mach 0.0035.
Escape and orbit
Earth's escape velocity is 11,186 m/s, Mach 32.9 by the sea-level factor. Orbital velocity near the surface is about 7,800 m/s, Mach 22.9. The Moon's escape velocity is 2,380 m/s, Mach 7.0. Space engineers speak in m/s and km/s; the Mach comparison is rhetorical, because there is little air at orbital height.
Flow experiments
A flow of 100 m/s through a test section is at Mach 0.294, at the edge of where compressibility matters. At 200 m/s, Mach 0.588, the effect is clear, and at 300 m/s, Mach 0.88, local supersonic pockets appear on bodies. A “convert m/s to Mach” calculation tells the researcher which equations to use.
The resonance tube
A tube closed at one end resonates when its length is a quarter of the wavelength. For a tuning fork of 440 Hz in air at 20 °C, the wavelength is 0.78 m and the tube length 0.195 m. Measuring that length lets students compute the speed of sound, 4 × L × f, and compare it with the Mach reference.
Re-entry capsules
A returning capsule meets the atmosphere at roughly 7,800 m/s. Where the heating peaks, sound travels at about 300 m/s, so the capsule is at Mach 26 there. The ground factor would suggest only Mach 22.9, a clear sign of how strongly the answer depends on the temperature of the air.
The mental shortcut
To convert m/s to Mach in your head, divide by 340 and take off 0.1 per cent. For 680 m/s: 2.0 less 0.002 gives 1.998. For 250 m/s: 0.735. At altitude divide by 295 instead.
Spreadsheet formulas
To convert m/s to Mach in a spreadsheet, put the velocities in m/s in column A and enter =A2/340.294 in column B. For another temperature T in °C use =A2/(20.0468*SQRT(273.15+T)). You will see how the Mach number shifts with temperature.
Rounding and precision
If you measure 250 m/s to within 1 per cent, the result Mach 0.7347 should not be quoted with four decimals. Write 0.73. Keep the full digits in intermediate steps, especially where the air temperature has been measured separately.
Landmarks to memorise
34 m/s is Mach 0.1. 102 m/s is Mach 0.3. 170 m/s is Mach 0.5. 340 m/s is Mach 1. 680 m/s is Mach 2. 1,000 m/s is Mach 2.94. 1,700 m/s is Mach 5. With these values you can convert m/s to Mach by eye.
Quick lookup table
10 m/s equals Mach 0.029, 30 m/s Mach 0.088, 60 m/s Mach 0.176, 150 m/s Mach 0.441, 330 m/s Mach 0.970, 500 m/s Mach 1.469, 1,500 m/s Mach 4.408 and 3,000 m/s Mach 8.816. A short table makes every “convert m/s to Mach” calculation check immediate.
Checking by reversing
To check a “convert m/s to Mach” calculation result, multiply the answer by 340.294. If 250 m/s became Mach 0.735, then 0.735 times 340.294 comes to nearly 250. A second test is size: Mach 1 should land just above 340 m/s.
Link to km/h and mph
One m/s is 3.6 km/h and 2.237 mph. Mach 1 is 340.3 m/s, 1,225 km/h and 761.2 mph. Going via km/h means multiplying by 3.6 and dividing by 1,225.06, which gives the same as dividing directly by 340.294.
A worked example
To convert m/s to Mach correctly: a sensor in a tunnel records a flow of 272 m/s at 20 °C. At that temperature sound moves at 343.2 m/s, so the Mach number is 0.79. With the factor for 15 °C you would get 0.80. The 1 per cent difference can matter for an experiment on the transonic boundary.
Shock cone from a photograph
A body at 510 m/s is at Mach 1.5, and its shock cone has half angle arcsin(1 / 1.5), which is 41.8°. At 680 m/s, Mach 2, the angle is 30°. By measuring the angle on a photograph you can find the Mach number without any other instrument.
Timing an echo
A hand clap that comes back from a wall after 0.4 s means the wall is 68.6 m away at 20 °C, since the sound covers 343.2 m/s and travels there and back. If the temperature is 5 °C instead, the speed is 334.3 m/s, and the same delay means 66.9 m. A good result needs the air temperature.
Schlieren photography
Schlieren pictures make the shock waves around a projectile visible. The cone angle gives the Mach number through sin(angle) = 1 / Mach. Ernst Mach used a similar method in 1887 to photograph the shock waves of a projectile moving faster than sound.
Heating by the air
At Mach 1 the stagnation temperature rise is about 58 K, at Mach 2 about 230 K and at Mach 3 about 518 K. A body moving at 680 m/s through air at 15 °C has surfaces reaching over 240 °C. Materials must be chosen to survive these temperatures.
Energy per kilogram
At 340 m/s a kilogram of material has 57.8 kJ of kinetic energy; at 680 m/s it has 231 kJ, four times as much. The impact energy of a supersonic projectile grows with the square of speed, so Mach 2 is far more dangerous than Mach 1.
Echo-ranging
An echo returning after 0.5 s comes from 85 m. Sonar and acoustic rangefinders use this. Because sound moves at 340 m/s, an error of 1 °C in the air temperature gives an error of 0.17 per cent in the distance.
Ultrasound
A 40 kHz transducer produces waves of 8.6 mm wavelength in air. If the source moves at 3.4 m/s, Mach 0.01, the Doppler effect shifts the frequency by 1 per cent. Ultrasonic speed meters rely on this proportion.
Car and aircraft tests
Racing cars are tested in tunnels at 40 to 70 m/s, Mach 0.12 to 0.21, where compressibility can be ignored. Airliners are tested at Mach 0.7 to 0.9, 238 to 306 m/s, where compressibility is essential.
Very thin air
At 80 km altitude the air is so thin that the ordinary notion of the speed of sound loses meaning. For bodies moving at 7,000 m/s the Mach number becomes a formal quantity, and physicists use the Knudsen number and other parameters instead.
Sprinters and animals
An elite sprinter at 12.4 m/s is at Mach 0.036, a cheetah at 29 m/s at Mach 0.085 and a peregrine falcon in a dive at 108 m/s at Mach 0.32. No living creature approaches Mach 1, apart from the tip of a whip.
The whip crack
The crack of a whip is a tiny sonic boom. As the loop of the whip travels towards the tip it accelerates past 340 m/s. It is one of the few everyday objects that exceed Mach 1.
Probes of the solar system
The Voyager 1 probe travels at about 17,000 m/s, which is Mach 50 by the ground factor, and the Parker Solar Probe has reached about 192,000 m/s, Mach 565. There is no air in space, so these Mach numbers are only for comparison, but they give a vivid sense of scale.
Starting-pistol delay
At a sprint, the sound of the starting gun takes 0.29 seconds to reach a runner 100 metres away. Timers at the finish line therefore start their clocks on the flash and not on the bang. The 0.29 s is nearly three times the reaction time threshold allowed in a legal start, which is 0.1 s.
Two routes to one answer
You can go from m/s to Mach directly, dividing by 340.294, or in two steps: compute the speed of sound from the temperature and divide by that. At 15 °C the routes coincide. At other temperatures the second is the right one.
Meteorological data
A research anemometer records wind in m/s. The strongest gust ever measured, 113 m/s, is Mach 0.33. A hurricane of 70 m/s is Mach 0.21 and a jet stream of 60 m/s Mach 0.18. Even the most violent wind comes nowhere near the sound barrier.
Wind tunnels
A subsonic tunnel works below 270 m/s, Mach 0.8. A transonic one covers 270 to 410 m/s, Mach 0.8 to 1.2, a supersonic one 410 to 1,700 m/s, Mach 1.2 to 5, and a hypersonic one from 1,700 m/s. Test reports are labelled with Mach number, not with m/s.
Aircraft at altitude
An airliner flying at 250 m/s at 11 km, where sound travels at 295 m/s, is at Mach 0.85. Using the ground figure, 340 m/s, you would get 0.735. Pilots work in Mach at altitude because the aerodynamic limits are set in Mach.
Other gases
In helium sound travels at 1,007 m/s, so a body at 340 m/s is at Mach 0.34. In carbon dioxide sound travels at 268 m/s, and the same body is at Mach 1.27. The Mach number must always be computed with the speed of sound of the gas concerned.
Mars and Venus
On Mars sound travels at about 240 m/s, so a vehicle at 100 m/s is at Mach 0.42 there, against 0.29 on Earth. On Venus, where sound travels at about 410 m/s, the same vehicle is at Mach 0.24. Probes are designed with the local values.
Meteors
A meteoroid enters the atmosphere at 11 to 72 km/s. At 20 km/s, 20,000 m/s, it is at Mach 59 by the sea-level factor. In the colder, thinner air where it burns the real Mach number is higher still, but the effects are the same: a strong shock wave and intense heating.
More values for convert m/s 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 m/s = 0.000293864 Mach
- 0.5 m/s = 0.00146932 Mach
- 3 m/s = 0.00881591 Mach
- 4 m/s = 0.0117545 Mach
- 7 m/s = 0.0205704 Mach
- 15 m/s = 0.0440795 Mach
- 20 m/s = 0.0587727 Mach
- 75 m/s = 0.220398 Mach
- 200 m/s = 0.587727 Mach
- 500 m/s = 1.46932 Mach
- 2,000 m/s = 5.87727 Mach
- 10,000 m/s = 29.3864 Mach
Mistakes to avoid with a “convert m/s to Mach” calculation
The wrong operation
From m/s to Mach you divide. If 250 m/s came out as 85,000, you multiplied by 340.
Temperature forgotten
340.294 is for 15 °C air. At −56.5 °C, 250 m/s is Mach 0.85 and not 0.735, which is 15 per cent apart.
Another gas
Helium or carbon dioxide carry sound at other speeds. Use the speed of sound of the gas you actually have.
Questions in brief
What is the rule for a “convert m/s to Mach” calculation?
Divide the m/s figure by 340.294.
What Mach number is 100 m/s?
Mach 0.294.
What Mach number is 680 m/s?
Mach 2.00.
What is Mach 1 in m/s?
340.294 m/s at 15 °C.
Does the page upload what I type?
No, it is all computed in your browser.
More converters and a short summary
Other speed pages: Convert m/s to km/h, Convert m/s to mph, Convert mph to Mach, Convert km/h to Mach, Convert Mach to mph, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. The opposite direction is Convert Mach to m/s.
In brief, to turn m/s into Mach divide by 340.294 for 15 °C air and keep the unit with the number. Nothing you enter leaves your own device, and no account is needed.