From mph to Mach: Why Do We Measure Speed Differently?

Glance at a car's speedometer and it says mph, or km/h. Check a ship's instruments and it says knots. Ask how fast a fighter jet is going and the answer comes back as a Mach number, not a speed at all. Track a rocket leaving the atmosphere and suddenly everyone's talking in kilometres per second. All four are answering the exact same question — how much distance, in how much time? — so why don't we just pick one unit and use it everywhere?

The honest answer splits into two very different stories. The mph-vs-km/h split on ordinary road signs is mostly history — Britain and the US kept imperial units, most of the world went metric, and a car doesn't care which one you use. But the switch to knots, then to Mach, then to km/s isn't history at all. Each one exists because the physics actually changes once you're going fast enough, and the old unit stops being the most useful number on the dashboard. That's the real story this article is about.

The one formula everything else builds on

Every single unit below is just a different way of answering the same basic equation. Get comfortable with this first, because nothing that follows is more complicated than it — it's the same relationship, over and over, at very different scales.

Speed = Distance ÷ Time

A car covering 60 miles in exactly 1 hour is doing 60 mph, by definition — that's literally what "miles per hour" means. Swap the units for kilometres and hours and you get km/h instead; swap distance for metres and time for seconds and you get the SI unit, metres per second (m/s), which is what physicists actually calculate with before converting to whatever unit the audience expects.

Cars: mph and km/h — a units choice, not a physics one

A car at 100 mph and a car at 160 km/h are travelling at genuinely the same speed — nothing about the physics of driving cares which number is on the sign. The conversion is a fixed multiplier:

1 mph = 1.60934 km/h   |   1 km/h = 0.62137 mph

Worked example: a UK motorway limit of 70 mph, in km/h: 70 × 1.60934 = 112.65 km/h — which is why continental European signs near the Channel sometimes show "113" as the rough equivalent. There's no deeper reason cars split this way beyond which measurement system a country adopted; it's the one entry on this list that's genuinely just a units conversion, not a different physical idea.

Ships: why "knots," and why nautical miles exist at all

"Knot" sounds like an odd word for a speed, and it's odd for a very literal historical reason. Sailors used to measure speed with a "chip log" — a wooden panel tied to a rope with knots tied into it at regular intervals — thrown overboard off the stern. As the ship pulled away from the floating panel, a sailor counted how many knots slipped through their hands while a 30-second sandglass ran out. Count the knots, and you had the ship's speed directly, in a unit that was quite literally named after knots in a rope.

The unit stuck, but the modern definition is precise: 1 knot = 1 nautical mile per hour. The genuinely useful part is what a nautical mile actually is — and it's not an old, vague version of a normal mile.

A nautical mile is fixed at exactly 1,852 metres, defined as the distance covered by 1 minute of latitude along a great circle of the Earth (there are 60 minutes in each of the 360 degrees around the planet). That single design choice is what makes it genuinely useful for navigation, not just a quirky alternative: a navigator reading their latitude change straight off a chart or a sextant sighting can convert it directly into nautical miles travelled, with no separate conversion step at all. A statute mile (1,609.344 m) was never built to relate to the Earth's geometry in that way, so it doesn't offer the same shortcut.

1 knot = 1.852 km/h   |   1 km/h = 0.53996 knots

Worked example: a container ship cruising at 22 knots is doing 22 × 1.852 = 40.7 km/h — slow next to a car, but genuinely fast for a vessel the length of several football pitches pushing through water rather than air.

Aircraft: why speed suddenly means Mach, not mph

Once an aircraft gets fast enough, something changes that has nothing to do with the aircraft itself: the air around it starts behaving completely differently depending on how its speed compares to the speed of sound, not to the ground below. That comparison is what Mach number actually measures:

Mach number (M) = aircraft's speed ÷ local speed of sound

The phrase "local speed of sound" is doing real work in that sentence. Sound doesn't travel at one fixed speed — it travels faster through warmer air and slower through colder air, so the speed of sound actually falls the higher an aircraft climbs (it drops from about 343 m/s at sea level on a mild day to around 295 m/s at typical airliner cruise altitude, 11 km up, where it's a bone-chilling −56.5°C). An aircraft flying at a perfectly constant airspeed can cross from subsonic to supersonic purely by climbing into colder air — its Mach number changes even though its actual speed hasn't.

This is the actual reason pilots and engineers care about Mach number rather than plain speed: it directly predicts what the air is doing. Below Mach 1, pressure waves from the aircraft can spread out ahead of it, warning the air to move out of the way smoothly. At Mach 1, the aircraft is moving exactly as fast as those warning waves — they can no longer outrun it, and pile up directly against the aircraft as a wall of compressed air, which is what actually produces a sonic boom. Past Mach 1, the aircraft leaves those waves behind entirely, trailing a cone-shaped shockwave whose angle narrows the faster it goes — exactly what the diagram above is showing, not just illustrating.

Worked example: Concorde cruised at Mach 2.04 at around 18 km altitude, where the local speed of sound is about 295 m/s. Its actual airspeed was therefore 2.04 × 295 ≈ 602 m/s — about 2,168 km/h, or 1,347 mph. Quoting "Mach 2.04" tells an engineer something a raw speed never could: exactly how the shockwave behaviour around the aircraft's nose and wings would change at that speed, at that altitude.

Fighter jets and missiles: still Mach, for the same reason

Military aircraft and missiles stay in Mach-number territory for exactly the reasons above, just pushed further. The SR-71 Blackbird, a Cold War reconnaissance aircraft built almost entirely around outrunning threats, cruised around Mach 3.2 — recorded at 3,529 km/h (2,193 mph) on its fastest verified run. Modern hypersonic weapons are generally defined as anything above Mach 5, a threshold chosen because that's roughly where the aerodynamics and heating effects on a vehicle change character yet again. News reports often translate these into km/h or mph for a general audience, but the number engineers actually design around is still the Mach figure — it's the one that tells you what's physically happening to the vehicle.

Rockets: why the units jump to km/s

Once a rocket climbs high enough, Mach number doesn't just become inconvenient — it stops meaning anything at all. Mach number is a ratio to the local speed of sound, and sound needs air to travel through. Above roughly 100 km altitude there's essentially no atmosphere left, so there's no local speed of sound to compare against — "Mach" simply has nothing left to measure. From that point on, the only number that matters is outright speed, and at these scales that means kilometres per second.

The speed a rocket needs depends on what it's trying to do. To stay in a stable circular orbit rather than fall back down, it needs exactly enough sideways speed that the curve of its fall matches the curve of the Earth falling away beneath it:

Orbital speed: v = √(GM ÷ r)

where G is the gravitational constant, M is Earth's mass, and r is the distance from Earth's centre to the orbit. You don't need to memorise G or M to see what the formula is saying: a smaller r (a lower orbit) needs a higher speed to balance it, which is exactly why low satellites like the ISS move faster than higher ones like geostationary communication satellites.

Worked example: for a low orbit just above Earth's surface (r ≈ 6,371 km), the formula gives v ≈ 7.9 km/s — the famous "first cosmic velocity." The International Space Station orbits a bit higher, at around 400 km altitude (r ≈ 6,771 km), which the same formula predicts should be slightly slower — and it is: the ISS's real orbital speed is about 7.66 km/s, circling the planet roughly every 93 minutes. Go fast enough — about 11.2 km/s from the surface, the "escape velocity" — and gravity can no longer pull the object back into orbit at all; it leaves Earth's gravity behind entirely, which is the speed real interplanetary missions have to reach.

All five units, side by side

Notice how the mph/km/h/knots columns become almost meaningless for the last two rows — nobody describes the SR-71 or the ISS that way in practice. That's the table making the same point the whole article's been building to: past a certain speed, the unit that actually gets used stops being about tradition and starts being about which number tells you something useful.

A few things worth knowing

• The 30-second sandglass used with a ship's chip log is the direct ancestor of "knots" — the interval between knots on the rope was deliberately chosen so that counting knots in 30 seconds gave speed in nautical miles per hour without any further maths.
• Chuck Yeager became the first person confirmed to fly faster than sound in 1947, in the Bell X-1 — reaching Mach 1.06. The aircraft's designers built it shaped like a .50-calibre bullet, since bullets were already known to fly stably at supersonic speeds.
• A commercial airliner cruising at "only" Mach 0.85 is still travelling at roughly 900 km/h — deliberately kept below Mach 1 partly because transonic drag rises sharply as you approach the sound barrier, making Mach 1 itself expensive to sustain in fuel.
• Geostationary satellites, much higher than the ISS (about 35,786 km up), only need to travel about 3.07 km/s to stay in orbit — slower than the ISS, exactly as the orbital speed formula predicts for a larger r.

Try it yourself

• A ferry is logged doing 18 knots. What's that in km/h, and in mph? (Use 1 knot = 1.852 km/h and 1 km/h = 0.62137 mph.)
• An aircraft is flying at 850 km/h at an altitude where the local speed of sound is 300 m/s. First convert 850 km/h into m/s, then work out its Mach number. Is it subsonic or supersonic?
• Using v = √(GM ÷ r) with GM ≈ 3.986 × 10¹⁴ m³/s² for Earth, estimate the orbital speed for a satellite at r = 7,000 km from Earth's centre. Is it faster or slower than the ISS, and does that match what the formula predicts about lower vs higher orbits?
• Explain, in your own words, why it's meaningless to describe a rocket in deep space as travelling at "Mach 20." What would you say instead?

Suggested visuals for this article

The Mach cone and nautical mile diagrams above are already built into the page. A few more would make this even stronger as a standalone visual piece:

• A single scaled illustration showing a car, a ship, an airliner, a fighter jet and a rocket in a row, each labelled with its typical speed in every unit from the table — makes the scale jump across the whole article visible at a glance rather than read in numbers.
• A short looped animation of the chip log in use — a rope with knots paying out over a ship's stern as a sandglass empties, ending on a speed readout in knots — to make the etymology genuinely land rather than just be a fun fact.
• An animated speed-of-sound-vs-altitude graph, with a marker aircraft climbing through it, showing its Mach number ticking upward at constant airspeed purely because the air gets colder — the clearest possible demonstration that Mach isn't just relabelled speed.
• A side-view cutaway of Earth showing the ISS, a geostationary satellite, and their respective orbital radii and speeds drawn to scale, to make the v = √(GM ÷ r) relationship visually obvious (smaller radius, tighter and faster orbit) rather than only algebraic.

If speed, forces, or any other GCSE or A-Level physics topic needs explaining with the actual reasoning behind the formula rather than a number to memorise, that's exactly what our GCSE physics tutoring and A-Level physics tutoring are for — see the full learning pathway here.