Find the Mach number of an object from its speed and the local speed of sound, derive the speed of sound from air temperature, or classify a Mach number by flow regime — M = v/a.
Speed and speed of sound
343 m/s is standard for dry air at 20°C. Use the From Temperature tab to derive it for other conditions.
Mach number
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Enter speed and the local speed of sound to compute.
Flow regime—
Speed of sound used—
Derive speed of sound from air temperature
Colder air slows the speed of sound, which raises the Mach number for the same object speed — this is why aircraft reach a given Mach number more easily at high, cold altitude.
Mach number from temperature
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Enter speed and air temperature to compute.
Speed of sound—
Flow regime—
Classify by Mach number
Paste a Mach value from the first tab, or type one directly.
Flow regime convention: below Mach 0.8 is subsonic, 0.8–1.2 is transonic, 1.2–5 is supersonic, and above Mach 5 is hypersonic.
Flow regime
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Enter a Mach number to classify the flow.
Regime thresholds
Regime
Mach range
Subsonic
M < 0.8
Transonic
0.8 – 1.2
Supersonic
1.2 – 5
Hypersonic
M > 5
Thresholds follow the standard aerodynamics convention; exact transition points vary with vehicle shape and altitude.
3 min read3 steps7 terms3 examples6 FAQsM = v / a
The Mach number tells you how fast something is moving relative to the speed of sound in the surrounding air — a single dimensionless number that governs whether airflow behaves smoothly or violently.
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Walk-through
How to Use This Calculator
3 steps▸
1
Enter speed and speed of sound
On the Mach Number tab, type the object's speed and the local speed of sound. If you don't know the speed of sound for your conditions, use 343 m/s (dry air, 20°C) as a reasonable default, or switch to the From Temperature tab.
2
Or derive it from air temperature
On the From Temperature tab, enter the object's speed plus the air temperature. The calculator derives the local speed of sound from temperature first, then computes the Mach number from that.
3
Read the Mach number and flow regime
The result card shows the Mach number and labels the flow as subsonic, transonic, supersonic, or hypersonic. Use the Flow Regime tab to classify a Mach number you already have without re-entering speed.
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Reference
Formula & Methodology
2 formulas▸
Mach number
M = v / a
The Mach number M is the ratio of an object's speed v to the local speed of sound a. Both v and a must be in the same units (typically m/s); M is dimensionless.
Speed of sound from temperature
a ≈ 331.3 + 0.606 · T(°C)
This linear approximation gives the speed of sound in dry air near sea-level pressure, where T is the air temperature in degrees Celsius. The exact relationship is a = √(γRT) for an ideal gas, but this approximation is accurate to within about 0.5% over typical atmospheric temperatures.
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Glossary
Key Terms Explained
7 terms▸
Mach number ↗A dimensionless ratio of an object's speed to the local speed of sound, written M = v/a. Mach 1 means the object is moving exactly at the speed of sound.
Speed of sound ↗The speed at which sound waves travel through a medium. In air it depends primarily on temperature, roughly 343 m/s at 20°C and slower in colder air.
Subsonic ↗Flow or motion at a Mach number below about 0.8, where air behaves as an incompressible fluid and compressibility effects are negligible.
Transonic ↗The Mach range roughly between 0.8 and 1.2, where airflow over parts of an object can be locally supersonic even though the object's overall speed is near Mach 1.
Supersonic ↗Motion at a Mach number greater than 1, meaning the object outruns the sound waves it generates, producing shock waves and a sonic boom.
Hypersonic ↗Motion at a Mach number greater than about 5, where aerodynamic heating and air chemistry effects become dominant design concerns.
Compressible flow ↗Fluid flow in which density changes significantly with pressure, becoming important as Mach number approaches and exceeds 1.
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Scenarios
Real-World Examples
3 worked examples▸
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Commercial jet
Cruising airliner
Speed 343 m/sSpeed of sound 343 m/s
At 343 m/s against a speed of sound of 343 m/s, M = 343/343 = 1.00 — exactly Mach 1, the transonic boundary. A real airliner cruises a bit below this, around Mach 0.78–0.85, to stay comfortably subsonic.
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High-altitude flight
From air temperature
Speed 250 m/sAir temperature 15°C
At 15°C the speed of sound is about 340.4 m/s (331.3 + 0.606 × 15). Mach number = 250/340.4 ≈ 0.73 — subsonic, just below the transonic boundary. Colder air at altitude lowers the speed of sound, which raises the Mach number for the same true airspeed.
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Fighter jet
Supersonic dash
Mach number 1.8
A Mach number of 1.8 falls in the supersonic range (1.2–5). The aircraft is moving 1.8 times faster than sound, generating a sonic boom and shock waves along its airframe.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
The Mach number tells you how fast something is moving relative to the speed of sound in the surrounding air — a single dimensionless number that governs whether airflow behaves smoothly or violently. This calculator finds Mach number from speed and speed of sound, derives speed of sound from air temperature, and classifies any Mach number into a flow regime.
How the Mach Number Calculator works
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The Mach number is simply M = v/a, the object's speed divided by the local speed of sound. Because the speed of sound in air is not constant — it depends on temperature — the same physical speed corresponds to different Mach numbers in different conditions. Cold, high-altitude air has a lower speed of sound than warm air at sea level, so an aircraft flying the same true airspeed reaches a higher Mach number at altitude.
The calculator uses the standard linear approximation a ≈ 331.3 + 0.606·T(°C) for the speed of sound in dry air, which tracks the exact ideal-gas relationship a = √(γRT) closely across the temperature ranges relevant to aviation and everyday physics.
Inputs and what they mean
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Speed can be entered in meters per second or kilometers per hour. Speed of sound is in meters per second — 343 m/s is the commonly cited value for dry air at 20°C, but it drops to around 295 m/s at -40°C, a difference that matters for high-altitude flight. Air temperature accepts Celsius or Fahrenheit and feeds directly into the speed-of-sound approximation on the From Temperature tab.
Limits and edge cases
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The temperature-based approximation assumes dry air near standard atmospheric pressure; humidity and altitude-driven pressure changes shift the true speed of sound slightly. The linear formula also loses accuracy at extreme temperatures far outside typical atmospheric ranges. For precise aerospace engineering work, use the full a = √(γRT) relationship with the appropriate values of γ and the specific gas constant R for the actual atmosphere, or consult a standard atmosphere model.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for Mach number?+
Mach number is M = v/a, where v is the object's speed and a is the local speed of sound, both in the same units. It's a plain ratio, so it carries no units of its own.
What does Mach 1 mean?+
Mach 1 means an object is moving at exactly the local speed of sound. Below Mach 1 is subsonic, and above Mach 1 is supersonic; the region right around Mach 1 (roughly 0.8 to 1.2) is called transonic.
Why does the speed of sound change?+
The speed of sound in air depends mainly on temperature, not pressure or altitude directly. Warmer air has faster-moving, more energetic molecules, so sound travels through it faster. That's why the speed of sound drops in the cold air at high altitude.
What counts as supersonic?+
Supersonic means a Mach number greater than 1 — the object is moving faster than the sound waves it produces, which is what creates a sonic boom.
Does altitude affect the Mach number for the same speed?+
Yes. Because higher altitudes are typically colder, the speed of sound is lower up there. Flying at the same true airspeed at a higher, colder altitude results in a higher Mach number than flying at sea level.
What units does the Mach number use?+
Mach number is dimensionless — it has no units, since it's a ratio of two speeds. Enter speed in m/s or km/h and the calculator handles the conversion internally.
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