How GPS Works
How GPS works — 31 satellites at 20,200 km altitude, atomic-clock trilateration, the four-unknown equation, relativistic corrections, and the ~5 m accuracy budget.
By Steve K.. Published . Last updated .
GPS works by trilateration of precisely-timed radio signals from a constellation of 31+ satellites at 20,200 km altitude. Each satellite broadcasts its position and the time the signal was sent; a receiver computes signal travel time to four or more satellites and solves for its own 3D position plus clock offset.
The Global Positioning System (GPS) is the most pervasive position-determination technology in history — embedded in every smartphone, vehicle, aircraft, ship and asset-tracker on Earth. Its operation is also one of the most demanding engineering achievements in modern infrastructure: 31 atomic-clock-bearing satellites in medium Earth orbit, broadcasting signals timed to nanosecond precision, corrected for both special and general relativity, all so a $5 GPS chip in a phone can solve a four-unknown system of equations and output a latitude/longitude pair accurate to ~5 m. This article runs the physics, the constellation geometry, the signal structure, the trilateration math, and the error budget that adds up to that 5 m accuracy. The companion supports /learn/gps-accuracy-explained, /learn/gps-vs-gnss, and /learn/differential-gps cover specific sub-topics in depth.
The constellation
The GPS constellation is designed so that at least four satellites are visible from any point on Earth's surface, 24/7, above a 5° elevation mask. The actual count is typically 8-12 visible at once under open sky.
| Constellation parameter | Value | Source |
|---|---|---|
| Operational satellites | 31 (24-satellite baseline + spares) | GPS.gov, ongoing |
| Orbital altitude | ~20,200 km (above WGS-84 ellipsoid) | IS-GPS-200 |
| Orbital radius from Earth centre | ~26,560 km | Derived |
| Orbital period | 11 h 58 min (~43,080 s) | Half a sidereal day |
| Orbital velocity | ~3.87 km/s | Derived: 2π × 26,560 km / 43,080 s |
| Number of orbital planes | 6 | IS-GPS-200 |
| Inclination of each plane | 55° | IS-GPS-200 |
| Right ascension spacing | 60° between planes | IS-GPS-200 |
| Min visible at 5° elevation | 4 | Design requirement |
| Typical visible (open sky) | 8-12 | Observed |
The 11-hour-58-minute orbital period is exactly half a sidereal day, which means each satellite traces out the same ground track every day. The orbital geometry, combined with WGS-84 datum precision (/learn/wgs84-explained), is what lets a phone solve for its position in seconds. This is a design choice that simplifies the operational control: the ground monitoring stations see the same set of satellites pass overhead at the same sidereal time each day. The 55° inclination is high enough to give visibility from polar latitudes; lower inclinations would leave the poles with poor satellite geometry.
The signal
Every GPS satellite continuously broadcasts on multiple frequencies. Each frequency carries a pseudo-random noise (PRN) code that identifies the satellite plus a navigation message that contains the satellite's position (ephemeris), clock corrections, and almanac data for the constellation.
| Frequency band | Centre frequency | Wavelength | Code rate | Use |
|---|---|---|---|---|
| L1 | 1575.42 MHz | ~19.0 cm | C/A: 1.023 MHz; P(Y): 10.23 MHz | Civilian (C/A), military (P(Y)) |
| L2 | 1227.6 MHz | ~24.4 cm | L2C: 1.023 MHz; P(Y): 10.23 MHz | Civilian modernized (L2C), military (P(Y)) |
| L5 | 1176.45 MHz | ~25.5 cm | 10.23 MHz | Safety-of-life (aviation, etc.) |
| L1C | 1575.42 MHz | ~19.0 cm | 1.023 MHz | Modernized civilian (interoperable with Galileo, BeiDou) |
All frequencies are integer multiples of a 10.23 MHz fundamental: L1 = 154 × 10.23, L2 = 120 × 10.23, L5 = 115 × 10.23. The fundamental itself is locked to the satellite's atomic clock. Two-frequency receivers (L1 + L2 or L1 + L5) cancel out the ionospheric delay, the single largest source of error after Selective Availability was switched off in 2000.
Trilateration: how four satellites become one position
The receiver doesn't actually measure distance directly — it measures the time the signal took to travel from satellite to receiver, multiplied by the speed of light. But the receiver's own clock is a cheap quartz oscillator, off from the satellites' atomic time by some unknown offset δt. The unknown clock offset is the fourth unknown (after x, y, z) that demands a fourth satellite.
| Unknown | Source | Why a satellite is needed |
|---|---|---|
| x (position) | Receiver's east coordinate | Need 1 satellite (intersect 1 sphere) |
| y (position) | Receiver's north coordinate | Need 2 satellites (intersect 2 spheres = a circle) |
| z (position) | Receiver's altitude / vertical | Need 3 satellites (intersect 3 spheres = 2 points; ground constraint disambiguates) |
| δt (clock offset) | Receiver's quartz clock offset from GPS time | Need 4 satellites (4 unknowns, 4 equations) |
The system of equations the receiver solves for each of n ≥ 4 visible satellites:
(x − xᵢ)² + (y − yᵢ)² + (z − zᵢ)² = (c × (tᵢ − tᵣ − δt))²
where (xᵢ, yᵢ, zᵢ) is satellite i's known position in ECEF coordinates, tᵢ is the broadcast timestamp, tᵣ is the receiver's measured-receipt time, c is the speed of light, and the unknowns are the receiver's position (x, y, z) plus its clock offset δt. With 4+ equations and 4 unknowns the system is over-determined and gets solved by least-squares iteration.
The same four-satellite minimum applies to every GNSS — GPS, Galileo, GLONASS, BeiDou, QZSS, NavIC — because they all solve the same x, y, z, δt problem.
The clocks: why atomic precision is non-negotiable
GPS works because the signal travel time is measured to nanoseconds. A 1 ns clock error becomes a 30 cm position error (light travels 30 cm in 1 ns). A 1 μs error becomes 300 m. The atomic clocks in the GPS satellites have an absolute accuracy on the order of 10−13 — one part in 1013, which corresponds to drift of about 1 ns over 3 hours.
| Clock type | Stability (Allan deviation) | Drift over 1 day | Location | Cost |
|---|---|---|---|---|
| Cesium (Cs) beam | ~10⁻¹³ to 10⁻¹⁴ | ~1-10 ns/day | Master Control Segment (ground) | $50K-$500K |
| Rubidium (Rb) vapor | ~10⁻¹² to 10⁻¹³ | ~10-100 ns/day | Satellites (primary clock) | $1K-$50K |
| Hydrogen maser | ~10⁻¹⁵ | ~0.1 ns/day | Some ground stations, ITRF observatories | $200K+ |
| Quartz oscillator | ~10⁻⁶ to 10⁻⁹ | ~10-100 μs/day | Consumer GPS receiver | <$1 |
| Chip-scale atomic clock (CSAC) | ~10⁻¹¹ | ~1 μs/day | Military, surveying receivers | $1K-$5K |
The receiver's cheap quartz oscillator drifts thousands of nanoseconds per second, but the receiver doesn't care — the δt unknown in the four-satellite equation absorbs the drift exactly. The receiver effectively measures its own clock error continuously from the satellite observations and recomputes its position each second with the corrected clock.
Relativity: why GPS clocks need correction
Einstein's relativity is not an academic detail in GPS; it is an operational engineering correction without which the system would accumulate position errors of about 11 km per day.
| Effect | Direction | Magnitude (μs/day) | Cause |
|---|---|---|---|
| Special relativity (time dilation due to satellite velocity ~3.87 km/s) | Satellite clock SLOWER than ground | ~7.2 μs/day | v²/(2c²) × 86,400 s |
| General relativity (lower gravitational potential at altitude) | Satellite clock FASTER than ground | ~45.9 μs/day | ΔΦ/c² × 86,400 s |
| Net effect (general dominates) | Satellite clock FASTER | ~38.7 μs/day | Sum of the two |
| Position error per μs | ~300 m | — | c × 1 μs |
| Uncorrected daily position error | ~11.6 km/day | — | 38.7 μs × c |
The satellite clocks are deliberately offset in frequency before launch by the predicted net relativistic rate, so on-orbit they tick in lockstep with ground clocks. The full accuracy budget that results — ~4.9 m typical, sub-cm with RTK — is on /learn/gps-accuracy-explained. This is one of the very few engineering systems where Einstein's 1915 general relativity is the mainline design correction, not a footnote.
The error budget: from atomic clock to ~5 m accuracy
The journey from a satellite atomic clock's 10−13 precision to a consumer GPS's 5 m accuracy is one of accumulated errors. The dominant ones, in order:
| Error source | Typical magnitude (m) | Mitigation |
|---|---|---|
| Ionospheric delay (signal slows in plasma) | ~5-10 m (single-frequency); ~0.1 m (dual-frequency) | Dual-frequency receiver (L1+L2 or L1+L5); SBAS corrections |
| Tropospheric delay (signal slows in dry/wet air) | ~0.5-2 m | Tropospheric model (Saastamoinen, etc.); SBAS |
| Satellite ephemeris error | ~1-2 m | Real-time orbit corrections from MCS; precise post-processed ephemerides |
| Satellite clock error | ~1-2 m | Real-time clock corrections from MCS |
| Multipath (signal bounces off buildings/terrain) | ~0.5-1 m open sky; up to 100 m urban canyon | Antenna design (choke ring); receiver algorithms |
| Receiver noise | ~0.1-1 m | Better antenna and front-end electronics |
| Geometry (DOP, dilution of precision) | Multiplier 1× to 10× on the above | More visible satellites reduce DOP |
| Selective Availability (intentional degradation) | ~50-100 m, 1990-2000 | Switched off by Clinton, 2000 |
The 95% global accuracy specification of ≤ 9.0 m (GPS.gov SPS PS 2020) is calculated by combining these error sources at typical magnitudes. Open-sky observed performance is usually better (~4.9 m, 95%) because the worst sources (multipath in particular) are minimal under open sky. Augmentation systems (SBAS like WAAS, EGNOS) bring single-receiver accuracy under 1 m; differential GPS (RTK) reaches centimetre level by phase-tracking the L1 carrier.
How a consumer receiver actually computes a fix
| Step | Receiver action | Time |
|---|---|---|
| 1. Acquire | Search for PRN codes of up to 32 GPS satellites in the L1 signal | 1-30 s cold start |
| 2. Track | Lock onto 4+ acquired satellites | continuous |
| 3. Decode navigation message | Read each satellite's position, clock corrections, almanac | 30 s (full message) |
| 4. Measure pseudorange | Multiply signal travel time by c for each satellite | each second |
| 5. Solve | Least-squares fit (x, y, z, δt) to the pseudoranges | <1 ms |
| 6. Smooth | Apply Kalman filter to position history | each second |
| 7. Output | Latitude, longitude (and altitude, speed, time) | 1-10 Hz typical |
A cold-start (no prior almanac) takes 30 seconds to acquire the navigation message. A warm start (almanac in memory, clock roughly known) takes a few seconds. A hot start (almanac valid, position roughly known) takes under a second. Modern phones use Assisted GPS (AGPS) to download the almanac via cellular data and skip the 30-second wait.
When GPS is the right (and wrong) choice
| Right choice for | Wrong choice for |
|---|---|
| Outdoor open-sky navigation (cars, ships, aircraft, hikers) | Indoor positioning (no signal penetration through buildings) |
| Vehicle tracking and asset management | Sub-metre precision without augmentation |
| Geocaching, sports, fitness | Underground or underwater positioning |
| Timing infrastructure (cell towers, power grids, banks) | Polar latitudes above ~80° (low satellite visibility) |
| Surveying with RTK augmentation | Anti-jamming-sensitive applications without backup |
| Continental cartography | Inertial-only navigation environments (submarines, spacecraft) |
Most consumer use cases — phones, cars, sports trackers — combine GPS with other sensors (inertial, magnetic, Wi-Fi, cellular) to handle GPS-poor environments. The fully integrated stack is called GNSS+IMU+SLAM and is the standard for autonomous vehicles.
Common misconceptions
Related pillars
The other seven pillar concepts on Coordinately:
- What is latitude and longitude? — the coordinates GPS produces
- Coordinate formats explained — how to write a GPS fix
- What is a map projection? — flattening the GPS-derived coordinate for display
- What is a geodetic datum? — WGS-84, the frame every GPS broadcasts in
- Time zones explained — converting GPS time to civil time
- History of latitude and longitude — the longitude problem GPS finally solved
- Great-circle distance — distance between two GPS fixes
Related
- WGS 84 Explained— The datum every GPS satellite broadcasts in
- Precision vs Accuracy in Coordinates— GPS produces high precision but limited accuracy
- What Is Latitude and Longitude?— The coordinate format every GPS receiver outputs
- My Location tool— Reads your browser GPS position
- Methodology— How content is sourced and verified
Frequently asked questions
How does GPS work in one sentence?
A network of satellites broadcasts the time and their own position; a ground receiver listens to four or more satellites, computes how long each signal took to travel to it, and uses those distances to trilaterate its own 3D position and clock offset. The arithmetic is geometry, the precision comes from atomic clocks on the satellites, and the entire system is run by the US Department of Defense as a free public utility.
How many GPS satellites are there?
As of 2026, the GPS constellation is officially 31 operational satellites in medium Earth orbit at about 20,200 km altitude. The constellation is designed to ensure at least 24 satellites are always available with global coverage; the extras (currently ~7) provide redundancy and improved geometry. Each satellite orbits Earth twice per sidereal day (about every 11 hours 58 minutes), with the constellation distributed across six orbital planes inclined 55° to the equator. Per GPS.gov, the operational baseline guarantees ≥95% global coverage at any moment.
Why does GPS need at least four satellites?
Because trilateration needs four unknowns to be solved simultaneously: three spatial coordinates (X, Y, Z) and one time correction. Each satellite measurement gives one equation; four satellites give four equations to solve for the four unknowns. The time correction is needed because consumer GPS receivers don't have atomic clocks; the satellite signals provide the clock reference, but the receiver's internal clock has an unknown offset that has to be solved for as part of the position fix. With three satellites and an exact receiver clock, three equations and three unknowns would suffice; with four satellites and an unknown clock, the math closes.
How accurate is GPS?
Per GPS.gov, civilian GPS achieves approximately 4.9 m horizontal accuracy at the 95th percentile under open sky. With WAAS / SBAS augmentation (built into most consumer devices including smartphones and many handhelds), accuracy improves to 1–2 m. Real-time-kinematic (RTK) survey-grade GNSS can achieve 1–2 cm with a base station and dual-frequency receivers. Urban canyons, dense canopy, and indoor environments are much worse — often 10–50 m. The Coordinately /tools/elevation reports its expected accuracy band alongside each result.
What's the difference between GPS and GNSS?
GPS is one specific system — the US Department of Defense's NAVSTAR Global Positioning System. GNSS (Global Navigation Satellite System) is the generic term for all such systems, including GPS, GLONASS (Russia), Galileo (EU), BeiDou (China), QZSS (Japan, regional), and IRNSS / NavIC (India, regional). Modern receivers — including most smartphones — track signals from multiple GNSS constellations simultaneously, improving accuracy and reliability. The term 'GPS' is often used colloquially to mean any GNSS positioning; technically, only the US system is GPS.
Does GPS work without a SIM card or internet?
Yes. GPS is receive-only and uses satellite signals directly; it does not require any cellular or internet connection. Dedicated GPS handhelds (Garmin, Suunto) operate with no SIM. Assisted GPS (AGPS) on smartphones uses cellular data to speed up the first fix by downloading the satellite almanac in seconds rather than waiting 30 seconds for the satellites to broadcast it, but the position fix itself is computed from satellite signals.
Why is GPS time different from UTC?
GPS time started at midnight UTC on 1980-01-06 and has run without leap-second corrections since. UTC has accumulated 18 leap seconds in that period, so GPS time is now exactly 18 seconds ahead of UTC (as of 2024-2026). The GPS navigation message carries the current offset; receivers convert GPS time to UTC before display. Software that confuses the two has shipped 18-second bugs in flight planning and financial systems.
Why does Einstein's relativity matter for GPS?
Without relativistic correction, GPS would accumulate position errors of about 11 km per day. Special relativity makes the orbiting satellite clocks run ~7.2 μs/day slower (due to satellite velocity ~3.87 km/s); general relativity makes them run ~45.9 μs/day faster (due to weaker gravitational potential at altitude). The net ~38.7 μs/day correction is engineered in before launch — the satellite clocks are frequency-offset so that on-orbit they tick in lockstep with ground clocks.
Sources
- GPS.gov — GPS.gov — Systems overview · https://www.gps.gov/systems/gps/ · Accessed .
- GPS.gov — GPS.gov — Performance and accuracy · https://www.gps.gov/systems/gps/performance/accuracy/ · Accessed .
- FAA — FAA — Wide Area Augmentation System (WAAS) · https://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/waas · Accessed .
- NASA — NASA — GPS and global navigation references · https://www.nasa.gov/ · Accessed .
- NIST — NIST — Time and frequency standards (atomic clocks) · https://www.nist.gov/pml/time-and-frequency-division · Accessed .
Cite this article
APA format:
Steve K. (2026). How GPS Works. Coordinately. https://coordinately.org/learn/how-gps-works
BibTeX:
@misc{coordinately_howgpsworks_2026,
author = {K., Steve},
title = {How GPS Works},
year = {2026},
publisher = {Coordinately},
url = {https://coordinately.org/learn/how-gps-works},
note = {Accessed: 2026-06-05}
}