[{"data":1,"prerenderedAt":345},["ShallowReactive",2],{"learn-\u002Flearn\u002Fmach-number-and-true-airspeed":3,"learn-nav-\u002Flearn\u002Fmach-number-and-true-airspeed":317},{"id":4,"title":5,"body":6,"date":244,"description":245,"draft":246,"extension":247,"faqs":248,"howTo":258,"keyTakeaways":265,"meta":270,"navigation":271,"path":272,"quiz":273,"seo":299,"series":300,"seriesOrder":300,"sources":301,"stem":314,"topic":315,"__hash__":316},"learn\u002Flearn\u002Fmach-number-and-true-airspeed.md","Mach number, true airspeed and the speed of sound",{"type":7,"value":8,"toc":235},"minimark",[9,19,25,30,49,52,82,85,89,116,119,143,150,154,163,193,200,204,224,228],[10,11,12,13,18],"p",{},"High and fast, a pilot stops thinking in knots and starts thinking in Mach, and the reason is the same physics that makes the ",[14,15,17],"a",{"href":16},"\u002Flearn\u002Fthe-international-standard-atmosphere","standard atmosphere"," so useful: the speed of sound is set by temperature alone.",[20,21,22],"blockquote",{},[10,23,24],{},"This is general educational information, not operational, legal, or regulatory advice. Rules differ by authority and change over time. Always verify against current official sources and follow your operator's approved procedures.",[26,27,29],"h2",{"id":28},"the-speed-of-sound-follows-temperature","The speed of sound follows temperature",[10,31,32,33,37,38,44,45,48],{},"In the standard atmosphere, the ",[34,35,36],"strong",{},"speed of sound depends only on the temperature"," of the air, not on its pressure or density on their own. Colder air carries sound more slowly. As the ",[14,39,43],{"href":40,"rel":41},"https:\u002F\u002Fwww.grc.nasa.gov\u002Fwww\u002FBGH\u002Fsound.html",[42],"nofollow","NASA Glenn Research Center"," sets out, it varies with the square root of the absolute temperature, which gives a handy approximation: the local speed of sound in knots is ",[34,46,47],{},"roughly 39 times the square root of the temperature in kelvin",".",[10,50,51],{},"Run that down the standard atmosphere:",[53,54,55,72],"ul",{},[56,57,58,59,68,69,48],"li",{},"At ",[34,60,61,67],{},[14,62,66],{"href":63,"className":64},"\u002Flearn\u002Fglossary#gt-isa",[65],"glossary-link","ISA"," sea level",", 15 degrees Celsius (288 K), the speed of sound is about ",[34,70,71],{},"661 knots",[56,73,74,75,78,79,48],{},"At the ",[34,76,77],{},"standard tropopause",", about minus 56.5 degrees Celsius (217 K), it has fallen to about ",[34,80,81],{},"573 knots",[10,83,84],{},"So a wing climbing into the cold upper air meets a steadily falling speed of sound, and that is what makes Mach matter up high.",[26,86,88],{"id":87},"what-mach-number-actually-is","What Mach number actually is",[10,90,91,105,106,109,110,115],{},[34,92,93,98,99,104],{},[14,94,97],{"href":95,"className":96},"\u002Flearn\u002Fglossary#gt-mach-number",[65],"Mach number"," is ",[14,100,103],{"href":101,"className":102},"\u002Flearn\u002Fglossary#gt-true-airspeed",[65],"true airspeed"," divided by the local speed of sound."," It is a ratio, so it has no units: Mach 0.80 means flying at 80 per cent of the speed of sound in the air you are actually in. Because the speed of sound changes with temperature, ",[34,107,108],{},"the same true airspeed is a different Mach number at a different level",", as ",[14,111,114],{"href":112,"rel":113},"https:\u002F\u002Fskybrary.aero\u002Farticles\u002Fmach-number",[42],"SKYbrary"," describes.",[10,117,118],{},"A worked example, using the rounded standard temperatures:",[53,120,121,127,133],{},[56,122,58,123,126],{},[34,124,125],{},"FL350"," on a standard day, the temperature is about minus 54 degrees Celsius (219 K).",[56,128,129,130,48],{},"The speed of sound is about 39 times the square root of 219, which is about ",[34,131,132],{},"577 knots",[56,134,135,136,139,140,48],{},"A ",[34,137,138],{},"true airspeed of 480 knots"," is then 480 divided by 577, or about ",[34,141,142],{},"Mach 0.83",[10,144,145,146,149],{},"Climb higher into colder air, hold 480 knots true, and that Mach number creeps up, which is exactly why a jet transitions from holding a constant indicated speed lower down to holding a ",[34,147,148],{},"constant Mach"," higher up.",[26,151,153],{"id":152},"the-speed-chain-ias-cas-tas-mach","The speed chain: IAS, CAS, TAS, Mach",[10,155,156,157,162],{},"These are four different things, and mixing them up is a classic trap. In order, as the ",[14,158,161],{"href":159,"rel":160},"https:\u002F\u002Fwww.faa.gov\u002Fregulations_policies\u002Fhandbooks_manuals\u002Faviation\u002Fphak",[42],"FAA Pilot's Handbook"," lays them out:",[53,164,165,171,177,187],{},[56,166,167,170],{},[34,168,169],{},"Indicated airspeed (IAS):"," what the airspeed indicator reads.",[56,172,173,176],{},[34,174,175],{},"Calibrated airspeed (CAS):"," IAS corrected for instrument and position error.",[56,178,179,182,183,186],{},[34,180,181],{},"True airspeed (TAS):"," CAS corrected for air density. Because density falls with altitude, ",[34,184,185],{},"TAS is higher than CAS up high",", by very roughly 2 per cent per 1000 feet as a rule of thumb.",[56,188,189,192],{},[34,190,191],{},"Mach number:"," TAS as a fraction of the local speed of sound, which depends on temperature.",[10,194,195,196,199],{},"The instrument measures dynamic pressure, so the indicator reads close to true at sea level on a standard day, and increasingly ",[34,197,198],{},"under","-reads your true speed as you climb.",[26,201,203],{"id":202},"common-pitfalls","Common pitfalls",[53,205,206,212,218],{},[56,207,208,211],{},[34,209,210],{},"Speed of sound is about temperature, not pressure."," Two levels at the same temperature have the same speed of sound, whatever their pressure.",[56,213,214,217],{},[34,215,216],{},"Mach rises in the climb at constant TAS."," It is the falling speed of sound, not a change in your speed, that does it.",[56,219,220,223],{},[34,221,222],{},"TAS is not what the dial shows."," At altitude your true speed is well above the indicated figure, so use TAS for navigation and flight planning, not IAS.",[26,225,227],{"id":226},"in-pilot-efb","In Pilot EFB",[10,229,230,231,234],{},"Pilot EFB includes ",[34,232,233],{},"true airspeed and Mach"," among its built-in flight calculators, with the working shown so you can follow how temperature and altitude feed the answer. The figures are for your own planning and reference; Pilot EFB is offline-first and is not a certified Electronic Flight Bag, so check them against your aircraft's approved data and instruments before you act on them.",{"title":236,"searchDepth":237,"depth":237,"links":238},"",2,[239,240,241,242,243],{"id":28,"depth":237,"text":29},{"id":87,"depth":237,"text":88},{"id":152,"depth":237,"text":153},{"id":202,"depth":237,"text":203},{"id":226,"depth":237,"text":227},"2026-06-20","How the speed of sound depends on temperature, why Mach number rises as you climb at a constant true airspeed, and how indicated, calibrated, true airspeed and Mach relate.",false,"md",[249,252,255],{"q":250,"a":251},"What does the speed of sound depend on?","In the standard atmosphere the speed of sound depends only on temperature: the colder the air, the slower sound travels. It does not depend on pressure or density on their own. At ISA sea level (15 degrees Celsius) it is about 661 knots; at the standard tropopause (about minus 56.5 degrees Celsius) it has fallen to about 573 knots.",{"q":253,"a":254},"Why does Mach number increase as you climb at a constant true airspeed?","Because Mach number is true airspeed divided by the local speed of sound, and the speed of sound falls as the air gets colder with height. Hold the true airspeed constant and climb into colder air and the same speed becomes a higher fraction of the speed of sound, so the Mach number rises.",{"q":256,"a":257},"What is the difference between true airspeed and Mach number?","True airspeed is the aircraft's actual speed through the air, in knots. Mach number is that speed expressed as a fraction of the local speed of sound, so it has no units. The same true airspeed is a higher Mach number up high, where the air is colder and sound travels more slowly.",{"name":259,"steps":260},"Work out the Mach number from true airspeed at altitude",[261,262,263,264],"Find the air temperature at your level, in kelvin (degrees Celsius plus 273).","Estimate the local speed of sound: roughly 39 times the square root of the temperature in kelvin gives knots (an approximation).","Divide your true airspeed by that speed of sound to get the Mach number.","Sense-check it: the same true airspeed gives a higher Mach number the colder and higher you are.",[266,267,268,269],"In the standard atmosphere the speed of sound depends only on temperature: about 661 knots at ISA sea level, falling to about 573 knots at the tropopause.","Mach number is true airspeed divided by the local speed of sound, so it is a unitless fraction.","Climbing at a constant true airspeed, the Mach number rises, because the colder air aloft has a lower speed of sound.","The speed chain runs indicated to calibrated (instrument and position error) to true (air density) to Mach (temperature).",{},true,"\u002Flearn\u002Fmach-number-and-true-airspeed",[274,283,291],{"q":275,"options":276,"answer":281,"explanation":282},"The speed of sound in the atmosphere depends mainly on what?",[277,278,279,280],"Pressure","Temperature","Density altitude","Humidity",1,"In the standard atmosphere the speed of sound depends only on temperature: colder air means a slower speed of sound. It is about 661 knots at ISA sea level.",{"q":284,"options":285,"answer":281,"explanation":290},"You hold a constant true airspeed and climb into colder air. What happens to your Mach number?",[286,287,288,289],"It falls","It rises","It stays the same","It depends on the pressure","Mach is TAS divided by the local speed of sound. As you climb the air gets colder, the speed of sound falls, so the same TAS becomes a higher Mach number.",{"q":292,"options":293,"answer":281,"explanation":298},"What is Mach number?",[294,295,296,297],"Speed in knots through the air","True airspeed as a fraction of the local speed of sound","The aircraft's maximum speed","Indicated airspeed corrected for instrument error","Mach number is true airspeed divided by the local speed of sound, so it is a unitless fraction, not a speed in knots.",{"title":5,"description":245},null,[302,304,307,309,311],{"label":303,"url":159},"FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C)",{"label":305,"url":306},"FAA Airplane Flying Handbook (FAA-H-8083-3C)","https:\u002F\u002Fwww.faa.gov\u002Fregulations_policies\u002Fhandbooks_manuals\u002Faviation\u002Fairplane_handbook",{"label":308,"url":40},"NASA Glenn Research Center: speed of sound",{"label":310,"url":112},"SKYbrary: Mach Number",{"label":312,"url":313},"SKYbrary: True Airspeed","https:\u002F\u002Fskybrary.aero\u002Farticles\u002Ftrue-airspeed","learn\u002Fmach-number-and-true-airspeed","Operations","CsXZLz7SpMOVc7ANqbucZmcRr2vCwcbSBIyWtHzhX6Y",{"related":318,"newer":334,"older":340,"series":300},[319,325,329],{"path":320,"title":321,"description":322,"date":323,"topic":315,"draft":246,"minutes":324,"series":300,"seriesOrder":300},"\u002Flearn\u002Fcold-temperature-altimeter-corrections","Cold-temperature altimeter corrections","Why a pressure altimeter over-reads in cold air, leaving you lower than indicated, and how to correct minimum altitudes for temperature on an approach in mountainous or freezing conditions.","2026-06-21",4,{"path":326,"title":327,"description":328,"date":323,"topic":315,"draft":246,"minutes":324,"series":300,"seriesOrder":300},"\u002Flearn\u002Fmode-s-and-ads-b-explained","Mode S and ADS-B explained","How Mode S adds a 24-bit address, selective interrogation and a data link to the transponder, the difference between elementary and enhanced surveillance, and how ADS-B broadcasts your GPS position.",{"path":330,"title":331,"description":332,"date":323,"topic":315,"draft":246,"minutes":333,"series":300,"seriesOrder":300},"\u002Flearn\u002Fthe-global-reporting-format-for-runway-conditions","The Global Reporting Format for runway conditions","How the Global Reporting Format (GRF) describes a contaminated runway, including the runway condition code (RWYCC) from 6 to 0, the assessment matrix (RCAM), and how the report is split into thirds.",5,{"path":335,"title":336,"description":337,"date":244,"topic":338,"draft":246,"minutes":339,"series":300,"seriesOrder":300},"\u002Flearn\u002Ficao-vs-iata-codes","ICAO vs IATA codes explained","The difference between the 4-letter ICAO location indicators used for flight planning and weather and the 3-letter IATA codes on your boarding pass, plus airline codes and callsigns.","Briefing",3,{"path":341,"title":342,"description":343,"date":244,"topic":344,"draft":246,"minutes":339,"series":300,"seriesOrder":300},"\u002Flearn\u002Freading-a-surface-analysis-chart","How to read a surface analysis chart","Decode a surface analysis chart: isobars and the pressure gradient, highs and lows, warm, cold and occluded fronts, and what the big picture tells you before you read the METAR.","Weather",1781989192087]