How does your phone's map know
where you are?
The blue dot on your screen pinpoints you to within a few metres. Your phone isn't sending out any signal. It's only listening. It can still work out where you are because it listens to a clock 20,000 km overhead and measures how long the signal took to arrive. And this whole system only works because it corrects for relativity.
Imagine a wide field with several distant towers. Each tower is set to ring its bell exactly on the hour.
You have an accurate clock, and can measure how many seconds late the sound of each bell arrives. Since you know the speed of sound, the delay tells you the distance to that tower.
If one tower comes out at "3 km," you're somewhere on a circle of radius 3 km centred on that tower. Measure a second and third tower, and the circles cross at exactly one point.
That's exactly what your phone is doing. Instead of towers it uses satellites, and instead of sound it uses radio waves.
Each satellite carries an extremely accurate clock. It keeps broadcasting that time and its own position over radio. The phone just receives it.
Radio waves travel at the speed of light. Multiply the gap between send time and receive time by the speed of light, and you get the distance. Do this with several satellites and the position is pinned to a single point.
But there's a big problem here. Your phone doesn't have an accurate clock. How it gets around that is the cleverest part of the whole system. Let's go through it step by step.
Radio waves are "slower" than you'd think
Radio waves travel at the speed of light — seven and a half times around the Earth in one second. Incredibly fast, but for this job, it's actually "just slow enough" to be useful.
Satellites orbit at roughly 20,000 kilometres up. A radio signal takes about 0.07 seconds to arrive. Measure that time, and you get the distance.
The catch is the precision needed. Light travels 300 metres in a millionth of a second (one microsecond). A timing error of one microsecond means a position error of 300 metres. To get accuracy of a few metres, you need to measure time to a precision of one hundred-millionth of a second.
That's why satellites carry atomic clocks — clocks that drift by no more than one second every few tens of thousands of years.
Your phone doesn't have that clock
Here's the problem. Atomic clocks are big, expensive, and don't fit in a phone. A phone's clock is only accurate to within a few seconds a day. A one-second error works out to 300,000 kilometres of distance. Useless.
So what's the fix? Treat the clock error itself as one more unknown, and solve for it along with everything else.
Let's count what we want to know: east-west position, north-south position, height. That's three. Add "how far off is my own clock," and that's four.
Four unknowns means you need four clues. So you need at least four satellites. Three isn't enough to pin down a position.
And there's an unexpected bonus. By solving for the clock error, the phone can set its own clock to near atomic-clock accuracy. Your phone's clock is so accurate as a side effect of measuring position.
They're only telling you the accurate time.
Here's where something unexpected shows up: relativity. It looks like textbook stuff, but this system corrects for it every single day.
- Satellites move fast, so their clocks run slow compared to the ground. About 7 microseconds a day
- Satellites sit where gravity is weaker, so their clocks run fast compared to the ground. About 45 microseconds a day
- Net result: the satellite's clock runs about 38 microseconds a day fast
Convert 38 microseconds to distance and you get about 11 kilometres. Without correction, your position would drift by that much in a single day. 22 km by the next day. Unusable.
In practice, satellite clocks are launched already slowed down by this exact amount. The plain fact that your map app works is itself a daily confirmation that relativity is correct.
Still off ― where the errors come from
- Air and the ionosphere ― Radio waves travel at the speed of light in space, but slow down slightly in the atmosphere. The upper ionosphere has an especially large effect, and it's considered one of the biggest sources of error
- Reflections off buildings ― In cities, a signal can reach you after bouncing off a building. That detour makes the distance look longer than it is. This is the main reason your position jumps around downtown
- Satellite geometry ― Accuracy drops if the satellites are bunched on one side of the sky, and improves the more spread out they are. It's a bit like a tripod being more stable with its legs spread wide
- Indoors ― The signal can't get through. If a position still shows up, that's because other methods are being used too (see next section)
The blue dot still appears indoors or underground because the phone combines several different clues.
- Nearby Wi-Fi signals ― It checks which wireless networks are visible against a pre-collected map
- Mobile phone towers ― Which tower it's connected to gives a rough area
- Motion and direction sensors ― From the last known position, it estimates direction walked and step count
One common misunderstanding is worth addressing. Satellite positioning itself is receive-only. The phone never sends a signal to the satellite, and the satellite isn't tracking the phone. If your location does get shared externally, that's because an app is sending it over the network. It helps to keep the mechanism separate from the question of who your data goes to.
Something you can check outdoors
- Open a map app in a wide-open park or riverbank and watch the blue dot. Stay still for a minute
- Now move to a narrow street between buildings and wait the same way. The blue circle around the dot (the accuracy estimate) should grow larger
- Go indoors and it may grow further, or the position may jump around
- Some apps can show the number of satellites being received. Try checking how that number changes by location
The more open sky you can see, the better the accuracy. This is the principle itself at work: "more satellites, spread out across the sky, is better." Accuracy gets worse downtown both because fewer satellites are visible and because reflected signals get mixed in. Operating your phone while walking is dangerous. Stop and stay aware of your surroundings.
Summary
Your phone can find its position because satellites keep broadcasting "here's the time," and the delay in receiving that tells you the distance. Since the phone lacks an accurate clock, it solves for the clock error as an unknown too. That's why you need four or more satellites — and as a bonus, you get an accurate clock too.
Measuring position means measuring time.
And time is changed by speed and gravity.
Want to know more? ― Terms, equations, and textbook linksLevels are marked, from middle-school science to open research questions
- MSCovered in middle-school science and maths
- HSCovered in high-school "Physics Basics" and maths
- HS+Covered in high-school "Physics," or treated as advanced/sidebar content in textbooks
- UnivNot taught in high school — university-level specialist material (positioning engineering, relativity)
- ResearchNot even settled "textbook fact" at university — an open question researchers are actively working on
MSTerms: the vocabulary of positioning
- GPS: the name of the satellite positioning system run by the United States. There are also ones from Europe, Russia, China, and Japan; together these are called GNSS (Global Navigation Satellite System). Phones use several at once.
- Michibiki (QZSS): Japan's satellite positioning system. It uses an orbit that keeps it over Japan for long stretches, boosting accuracy in Japan's dense cities.
- Atomic clock: an extremely precise clock based on the properties of atoms. Carried aboard satellites.
- Ionosphere: a layer high in the atmosphere rich in charged particles. It affects how radio waves travel.
- Multipath: when a radio signal reflects off buildings and arrives via multiple paths. The main source of error in cities.
HSWorking it out: what a millionth-of-a-second error means in metres
The way your phone finds its own position isn't with a ruler — it measures with a clock. So "how accurate a clock do you need" directly determines the accuracy you get. We can work it out.
distance = speed of light × time
| distance | separation from the satellite [m] |
| speed of light | 3.0 × 10⁸ m/s |
| time | time taken for the signal to arrive [s] |
A satellite keeps broadcasting "here's the time" over radio. The receiver compares that to its own clock and works out how many seconds it took. Multiply, and you get the distance.
The catch is that you're multiplying by the speed of light. A tiny timing error turns into a large distance error. Let's see exactly how large, next.
| If the clock is off by 1 second | 3.0 × 10⁸ = 300000000 m (300,000 km) |
| 1 millisecond (1/1000 s) | 300000000 ÷ 1000 = 300000 m (300 km) |
| 1 microsecond (1/1,000,000 s) | 300000 ÷ 1000 = 300 m |
| 1 nanosecond (1/1,000,000,000 s) | 300 ÷ 1000 = 0.3 m |
A one-microsecond error means a 300 m error. To pin down "the nearby convenience store," you need timing accurate to one billionth of a second.
A wristwatch drifts by a few seconds a day. A clock that loose would put you several laps of the Earth off target. Atomic clocks aboard satellites aren't there for show — this calculation demands them.
Once billionths of a second matter, things normally ignorable start to count. A satellite's clock doesn't run at the same rate as one on the ground. There are two reasons, and they pull in opposite directions.
| Weaker gravity up there → clock runs fast | about +45 microseconds/day |
| Moving fast → clock runs slow | about −7 microseconds/day |
| Net | 45 − 7 = 38 microseconds/day fast |
Using the table from ②, converting this to metres is quick. One microsecond is 300 m, so:
| Error per day | 300 × 38 = 11400 m |
| In kilometres | 11400 ÷ 1000 = 11.4 km |
Without correction, you'd drift 11 km in a day. Leave it two days and it's over 20 km. Relativity isn't "just cosmology" here — it's a practical requirement, or today's map app wouldn't work.
A theory that feels distant in a textbook turns out to be a working condition for the map app in your hand. That sinks in properly only once you've done this multiplication yourself.
Since position is fixed by three numbers — east-west, north-south, height — three satellites might look like enough. They aren't. Counting the equations shows why.
| Unknowns to solve for | east-west, north-south, height, and your clock's error — 4 total |
| Equations from one satellite | 1 |
| Satellites needed | 4 |
Four unknowns need four equations. That's exactly the same counting rule as the simultaneous equations you learn at school.
And the fourth satellite is what solves for your clock's error. That's why the phone doesn't need an atomic clock. Instead of carrying a precise clock, it watches one extra satellite. That's the clever part of this system.
Positions going astray between tall buildings happen because fewer satellites are visible, or because a signal bounces off a wall and takes a longer route to arrive. A signal that took a detour gets read as "farther away" in the calculation from ①.
HSThe numbers behind the required precision
| Speed of radio waves (light) | about 300,000 km/s = 3×10⁸ m/s |
| Distance travelled in 1 microsecond (1/1,000,000 s) | 3×10⁸ ÷ 1,000,000 = 300 m |
| Timing precision needed for 3-metre accuracy | 3 ÷ (3×10⁸) = 0.00000001 s = 10 nanoseconds (1/100,000,000 s) |
| Satellite altitude | about 20,000 km |
| Time for signal to arrive | 20,000,000 ÷ (3×10⁸) ≒ 0.067 s |
Why you need 4 is a one-liner in mathematical terms too. There are four unknowns (position x, y, z and clock error t), so you need four equations. Each satellite gives you one.
Let satellite i be at position (xᵢ, yᵢ, zᵢ) and let τᵢ be the measured time difference. Then:
√((x−xᵢ)² + (y−yᵢ)² + (z−zᵢ)²) = c(τᵢ − t)
Four of these give you x, y, z, t. In practice, more satellites than that are used, and the most likely solution is chosen accounting for errors.
HS+Two relativistic effects
There are two reasons the clock's rate changes.
- Moving fast slows a clock down (special relativity). A satellite moves at about 3.9 km/s, and this effect is about −7 microseconds a day
- Weaker gravity speeds a clock up (general relativity). At 20,000 km up, gravity is weaker than on the ground, giving about +45 microseconds a day
| Total drift | −7 + 45 = +38 microseconds/day |
| Converted to distance | 38 × 300 = about 11,400 m (about 11 km) |
* These figures are representative estimates and vary with orbital detail.
What's striking is that the two effects run in opposite directions but don't cancel out. Had they happened to balance exactly, this technology could conceivably have been built without ever needing relativity.
UnivWhat determines accuracy
Positioning error is organised as (ranging error) × (amplification from satellite geometry). This amplification factor is called DOP (Dilution of Precision).
If satellites are bunched on one side of the sky, the equations carry "similar information," making the solution unstable. Mathematically, the coefficient matrix becomes ill-conditioned. The more spread out they are, the better the solution.
Several established methods reduce error further.
- Using two frequencies: since ionospheric delay differs by frequency, comparing two signals cancels out the delay. This is increasingly built into recent phones
- Differencing against a reference station: measuring at the same time as a receiver at a known location and subtracting the common error. This enables centimetre-level positioning, used in automated farm equipment and surveying
- Using the carrier wave's phase: counting the radio wave itself gives far finer ranging. But it requires resolving the ambiguity of "how many whole wave cycles" are involved
ResearchOpen problems today
- Predicting ionospheric disturbance is still not possible. When solar activity is high, the ionosphere fluctuates sharply, and positioning accuracy can drop significantly. "Space weather" forecasting — accurately estimating the effect of solar flares in advance — remains an active research area, and matters for aviation and surveying.
- There's no decisive fix yet for urban reflections either. In places surrounded by buildings, a direct signal mixes with a reflected one. Methods being tried include judging sky visibility with a camera, or accounting for buildings using map data, but no method works reliably across every kind of cityscape yet.
- Defending against jamming and spoofed signals is an ongoing challenge. Because satellite signals are extremely weak, it's technically possible to jam them with a stronger signal, or broadcast fake signals to trick a receiver into believing a false position. Countermeasures are advancing, but as reliance grows, so does the impact of an attack, so research continues into backup positioning methods that don't depend on satellites.
- Even more accurate clocks may reshape positioning next. Clocks even more precise than atomic clocks (ones using light) are becoming practical. If put to use, positioning accuracy would improve further — but at the same time, "time runs differently at different gravitational strengths" becomes impossible to ignore, sparking debate over redefining time itself. An era where a height difference of a few centimetres can be measured through clock rate is approaching.
Links to the textbook (by level)
| Level | Subject/unit | Where in this article |
|---|---|---|
| MS | Science - radio waves and the speed of light / Maths - construction and intersection points | The idea of fixing a position by overlapping circles |
| HS | Physics Basics - waves and speed / Maths - spatial coordinates and simultaneous equations | Calculating the required precision, the 4-unknown equations |
| HS+ | Physics - relativity (treated as advanced in many textbooks) | The two effects, and 38 microseconds a day |
| Univ | Positioning engineering, numerical computation, general relativity | DOP, least squares, dual frequency, carrier phase |
| Research | Space weather, positioning engineering, metrology (unresolved) | Ionospheric prediction, urban reflections, jamming countermeasures, optical clocks |
- Misra, P. & Enge, P., Global Positioning System: Signals, Measurements, and Performance (a standard textbook on positioning).
- Ashby, N., Relativity in the Global Positioning System, Living Reviews in Relativity 6, 1, 2003 (details of the relativistic corrections).
- Cabinet Office (内閣府) explainer on the Quasi-Zenith Satellite System "Michibiki" (みちびき).
- National Institute of Information and Communications Technology (情報通信研究機構, NICT) information on space weather forecasting and ionospheric disturbances.
- Geospatial Information Authority of Japan (国土地理院) materials on GNSS reference stations and positioning technology.
* Figures for altitude, speed, and correction size vary somewhat by satellite and orbit. This article gives commonly cited representative values.
※ This article is a general-audience science explainer. The figures given are approximate, meant to aid understanding, and can vary with conditions. When operating a device outdoors, avoid using it while walking, and stay alert to your surroundings.