The GPS altimeter determines the altitude of a receiver from the signals of positioning satellites. It is the third coordinate computed by GPS, along with latitude and longitude, but it is also the least precise: the vertical uncertainty commonly reaches 10 to 20 metres. On a smartphone, FizziQ displays this altitude and allows comparing it with barometric altimetry.
Discover FizziQ
How to measure it in class
FizziQ displays the altitude provided by the smartphone’s GPS receiver, in metres, as well as the estimated accuracy of the position.
Steps:
- Open FizziQ, select the GPS “Altitude” instrument and wait outdoors for the reading to settle.
- Note the displayed altitude at a point of known elevation (sign, topographic map) and record the difference.
- Record the altitude for several minutes without moving: fluctuations of several metres illustrate the vertical uncertainty.
- Go up one floor and check that the change, about 3 m, is barely distinguishable from the fluctuations.
- If the device has a barometer, repeat the same climb while recording pressure: the height difference becomes clearly measurable.
Scientific activities on this topic
Possible extensions with FizziQ: record the altitude profile of a hike by logging GPS altitude and pressure simultaneously, then compare the two curves.
Learn more
Why is GPS altitude less precise than position?
Position is computed by trilateration from the distances to several satellites. For the horizontal component, the receiver sees satellites in every direction around it: the geometry is favourable. For the vertical component, all satellites are above the horizon, none below: this asymmetric geometry amplifies errors, and the vertical uncertainty is typically 1.5 to 2 times the horizontal one.
Altitude with respect to what?
GPS first computes a height with respect to a mathematical model of the Earth, the reference ellipsoid. But the altitude on maps is counted from mean sea level, a surface called the geoid, which departs from the ellipsoid by several tens of metres depending on the region. Smartphones apply this correction, but it explains residual differences between devices and apps.
GPS or barometer?
The smartphone’s two altimeters are complementary: GPS provides an absolute altitude, without calibration but with an uncertainty of about ten metres; the barometer detects height differences of about a metre, but drifts with the weather and must be set against a reference. The altitude entry details this comparison.
Orders of magnitude: vertical GPS uncertainty in favourable conditions: ± 10 m, more in cities or under trees; geoid-ellipsoid difference: from -100 m to +85 m depending on the region of the globe; one building floor: 3 m, undetectable by GPS, clear on the barometer.
Formula
The distance to each satellite follows from the signal travel time:
d = c × Δt
Where:
- d: receiver-satellite distance (m)
- c = 3 × 10⁸ m/s: speed of light
- Δt: signal travel time (s)
With at least four satellites, the receiver solves for position (including altitude) and its own clock offset. A timing error of one billionth of a second corresponds to 30 cm of distance: clock precision governs altitude precision.
Application examples
- Tracking the altitude profile of a hike or a bike ride.
- Measuring the climb rate of an aircraft at take-off or in ascent.
- Checking the elevation of a mountain pass or a summit during fieldwork.
- Studying the variation of gravity with altitude, by combining GPS and accelerometer.
- Metrological comparison between GPS and barometric altimeters, a genuine uncertainty-analysis exercise.
FAQ
Q: Why does GPS altitude change while I am not moving? A: The satellite geometry evolves constantly and the signals cross a changing atmosphere. The position solution therefore fluctuates by several metres, especially vertically, even at rest.
Q: Why do two apps display different altitudes at the same place? A: Some give the height above the ellipsoid, others the geoid-corrected altitude, and the corrections applied vary. On top of this comes the measurement’s own uncertainty, of about ten metres.
Q: Should I prefer the GPS altimeter or the barometer? A: For an absolute altitude with no known reference, GPS. For a precise height difference (floor, hill, building), the barometer, when the device has one. Combining both is the best approach, and it is what sports watches do.
Related concepts
GPS geolocation - Altitude - Barometric altimetry - Barometer - Atmospheric pressure - Triangulation