Altitude is the vertical position of a point relative to a reference level, most often mean sea level (altitude 0). It is expressed in metres (m) and differs from mere height, measured from an arbitrary local reference.
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How to measure it in class
With the FizziQ app, the altitude of a point can be estimated in two complementary ways: by GPS, which provides an absolute altitude, and by the barometer, which excels at measuring altitude differences. Comparing them is instructive.
Steps:
- Open FizziQ and select the GPS altitude instrument. Read the displayed altitude at a given point and note that it fluctuates by several metres from one moment to the next.
- Compare this GPS altitude with a known value (topographic map, altitude sign) to appreciate the absolute accuracy, of the order of ten metres.
- Then select the “Barometer” instrument (if present: not all smartphones have one). Note the pressure P₁ at the foot of a building or a slope.
- Climb to the top, safely, and read the pressure P₂: the altitude difference is Δh ≈ (P₁ - P₂) × 8.3, in metres if the pressures are in hPa.
- Compare the two approaches: the barometer gives a precise relative height difference (resolution of the order of a metre), while GPS gives an absolute but coarser altitude.
Scientific activities on this topic
- Measuring the height of a building
- Elevator speed by barometer
- Climb rate during a flight
- Variation of g with altitude
Possible extensions with FizziQ: draw the altitude profile of a hike by recording pressure and GPS position simultaneously, or estimate the height of a cliff. See the smartphone sensors guide.
Learn more
How it works:
Two methods coexist on a smartphone. GPS computes the position in three dimensions by trilateration from the signals of several satellites; the absolute altitude follows, but with a large vertical uncertainty, because the satellite geometry is unfavourable to the vertical measurement (see the GPS altimeter entry). Barometric altimetry instead derives altitude variations from the pressure measured by the barometer, the pressure decreasing by about 0.12 hPa per metre near the ground. The first gives an absolute reference, the second an excellent relative measurement.
Relative resolution vs absolute accuracy: the barometer offers a fine resolution (of the order of a metre) on altitude differences, but a poor absolute accuracy without calibration. GPS provides an absolute altitude, but with an accuracy of the order of ten metres. Combining both sensors draws on each one’s quality.
Availability: barometric altimetry is only possible if the smartphone has a barometer, which is not the case on all models. GPS, on the other hand, equips virtually all current smartphones.
Orders of magnitude:
- Reference altitude (mean sea level): 0 m, where the pressure averages 1013 hPa.
- Vertical uncertainty of GPS: about ± 10 m in favourable conditions (up to ± 20 m with poor reception).
- Resolution of barometric altimetry: of the order of a metre for a height difference measured quickly.
- Pressure gradient near the ground: 0.12 hPa/m, about 8.3 m per hPa.
- One building floor (≈ 3 m) corresponds to a pressure variation of about 0.36 hPa.
Formula
In barometric altimetry, an altitude difference follows from the pressure difference, near the ground:
Δh ≈ (P₁ - P₂) × 8.3
Where:
- Δh: altitude difference (m)
- P₁, P₂: pressures at the two points (hPa)
- 8.3 m/hPa: inverse of the 0.12 hPa/m gradient
This rule holds for small height differences and assumes a stable weather pressure during the measurement. Over a wider range, the barometric formula for an isothermal atmosphere is used:
h = H × ln(P₀/P), with H ≈ 8,400 m at 15 °C
where H = RT/(Mg) is the scale height (about 8,000 m at 0 °C) and P₀ the reference pressure at altitude h = 0.
Application examples
- Hiking: track the cumulative elevation gain of a mountain walk from the barometer.
- Aviation: flight altitude is read on a barometric altimeter set to a reference pressure.
- Indoor navigation: detect which floor a user is on, where GPS does not reach.
- Cartography: attach an altitude to each point of a field survey.
- Sport: measure the height of a jump or a climb.
- Emergency services: the vertical location of a caller increasingly relies on the smartphone’s barometer.
FAQ
Q: Should I use GPS or the barometer to measure an altitude? A: It depends on the need. For an absolute altitude (height above the sea), GPS is indicated, to about ± 10 m. For a height difference or a floor change, the barometer is far more precise, down to about 1 m.
Q: Why does GPS altitude fluctuate so much? A: The vertical GPS measurement is intrinsically less precise than the horizontal one, because of the position of the satellites above the horizon. An uncertainty of around ten metres, fluctuating over time, is therefore normal.
Q: Can altitude be measured without a barometer? A: Yes, with GPS alone, present on almost all smartphones. Barometric altimetry, however, requires a pressure sensor, absent from many entry-level devices.
Q: What is the origin of altitude 0? A: It is mean sea level, a reference surface called the geoid. Maps and GPS refer to it, which allows comparing altitudes from one place to another.
Related concepts
Barometric altimetry - GPS altimeter - Barometer - GPS geolocation - Atmospheric pressure