A pedometer is an instrument that counts the number of steps taken while walking or running, and deduces an approximate distance from it. On a smartphone, it relies on the accelerometer, which detects the acceleration peak produced at each step.
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How to measure it in class
FizziQ gives access to the raw signal of the accelerometer: you can therefore see the steps in the curve, count them by hand, then compare with the phone’s automatic pedometer.
Steps:
- Place the smartphone in a trouser pocket or attached to the belt, select absolute acceleration and start recording.
- Walk exactly 50 steps counted out loud, then stop the recording.
- Observe the curve: each step appears as a marked peak of the vertical acceleration, separated from the next by a regular interval.
- Count the peaks on the graph and compare with the number of steps actually taken: the difference measures the error of the detection method.
- Start again walking very slowly, then swinging the arm holding the phone without walking, and observe in each case the direction of the error.
- Measure with a tape measure the distance actually covered in 50 steps to deduce the average step length, and compare it with the one the application assumes.
Scientific activities on this topic
- Create a pedometer using a smartphone’s accelerometer
- Linear acceleration: principle
- Heart rate by accelerometer
Learn more
From the mechanical pendulum to the accelerometer
The first mechanical pedometers counted steps using a pendulum; electronic models appeared in the 1960s for studies on physical activity. Today, the function is built into smartphones, smartwatches and activity trackers, where it relies entirely on the accelerometer.
A pedometer does not count steps, it detects peaks
This is the central point. A modern pedometer has no sensor in contact with the ground: it only has the accelerometer signal, sampled at a few tens of hertz. During walking, the vertical component of the acceleration oscillates in a quasi-periodic way: at each footfall, the body is slowed down then relaunched, which produces a clear peak. The algorithm first filters the signal to remove the constant component due to gravity and the high-frequency noise, then it looks for local maxima. A peak is counted as a step only if it satisfies two conditions: exceeding an amplitude threshold, and being separated from the previous peak by a minimum duration, typically 250 to 300 ms. This time window prevents counting the same step twice, because a footfall often produces a secondary rebound just after the main peak.
Why it overcounts and why it undercounts
The two previous settings explain all the errors observed. The amplitude threshold is a compromise: too low, any jolt is counted; too high, light steps are ignored. This is why a pedometer overcounts when you gesticulate, when you clap, when you go down stairs stamping your feet or when you drive on a cobbled road, since all these situations produce peaks of amplitude comparable to that of a step. Conversely, it undercounts at very low speed: when walking slowly, strolling down a corridor or pushing a shopping cart, the vertical acceleration at each footfall becomes too weak to cross the threshold. The time window produces a symmetric error: at fast running, with a cadence exceeding three steps per second, two steps can fall in the same window and be counted as one.
Step length is estimated, not measured
This is the most important limitation to understand. The pedometer measures a discrete quantity, the number of steps, with fairly good reliability. But to display a distance, it must multiply this number by a step length that it does not measure: it deduces it from the user’s height, often by a relation of the type step length ≈ 0.41 × height, sometimes corrected by cadence. Yet the actual step length of the same person easily varies by 30% depending on whether they stroll, walk fast, climb a slope or run. The error on the displayed distance is therefore structurally much greater than the error on the number of steps. Remember this hierarchy: the number of steps is a measurement, the distance is an estimate, and the displayed calories are an estimate made from an estimate.
The link with the curriculum
The study of a pedometer belongs to signal processing and measurement. It involves the notions of periodic signal, frequency, detection threshold, as well as the vocabulary of uncertainty and accuracy of an instrument. It is also a good opportunity to address the gap between a measured physical quantity and a quantity reconstructed by an algorithm, a question now omnipresent in connected objects. The subject lends itself to simple programming in Python, from data exported by FizziQ.
Orders of magnitude
Normal walking cadence: 100 to 120 steps per minute, that is 1.7 to 2 Hz. Running cadence: 150 to 180 steps per minute. Step length when walking: 0.65 to 0.80 m for an adult. Number of steps to cover 1 km: about 1300 to 1500. Amplitude of the vertical acceleration peak when walking: 2 to 5 m/s² above the base level; when running: 10 to 30 m/s². Required sampling frequency: at least 50 Hz. Average daily step count of an adult in France: about 6000 to 7000. Typical error of a smartphone pedometer on the number of steps: 5 to 10%; on the distance: 15 to 30%.
Formula
The distance covered is obtained by multiplying the number of steps by the average step length:
d = N × L
where:
- d: distance covered (m)
- N: number of steps counted
- L: average step length, estimated and not measured (m)
The step length is most often estimated from the user’s height:
L ≈ 0.41 × h
where:
- h: height of the user (m)
The cadence, that is the frequency of the steps, is deduced from the count over a known duration:
f = N / Δt
where:
- f: cadence (steps per second, Hz)
- Δt: duration of the walk (s)
The average walking speed combines the two:
v = N × L / Δt = f × L
where:
- v: average speed (m/s)
The step detection condition of the algorithm is written:
a_vertical > a_threshold and t_peak - t_previous peak > Δt_min
where:
- a_threshold: amplitude threshold above which a peak is retained (m/s²)
- Δt_min: minimum duration imposed between two steps, typically 0.25 to 0.30 s
Application examples
- A student 1.70 m tall takes 1400 steps to cover one kilometer: their step length is 1000 / 1400 ≈ 0.71 m, very close to the estimate 0.41 × 1.70 = 0.70 m
- A walk of 1200 steps in 10 minutes corresponds to a cadence of 1200 / 600 = 2.0 steps per second, that is 120 steps per minute
- With a step length of 0.70 m and a cadence of 2.0 Hz, the speed is 1.4 m/s, that is about 5 km/h: the classic order of magnitude of walking
- A seated student who shakes their phone for one minute can make it count several dozen false steps, which directly illustrates the limit of the detection threshold
- A hiker climbing a steep slope shortens their steps by 20%: the pedometer counts the steps correctly but overestimates the distance by the same amount
- Epidemiological studies on physical activity use the number of steps rather than the distance, precisely because it is the most reliable quantity
FAQ
Q: Why does my phone count steps while I am sitting? A: Because it does not detect steps but acceleration peaks. Gesticulating, tapping your foot or handling the phone produces peaks of amplitude comparable to that of a walking footfall, which the algorithm cannot distinguish from a real step.
Q: Why does the pedometer count too few when I walk slowly? A: Because the vertical acceleration at each footfall is proportional to the vigor of the step. When walking very slowly, the peaks no longer cross the detection threshold and are ignored. This is the typical case of wandering around a shop or walking while pushing a stroller.
Q: Why is the displayed distance less reliable than the number of steps? A: Because the step length is not measured. It is deduced from your height by a statistical formula, whereas it varies strongly with pace and terrain. A 20% error on the step length carries over entirely to the distance, even if the step count is perfect.
Q: Does the smartphone count better in a pocket or in a bag? A: In a trouser pocket or on the belt, because the sensor then directly follows the movement of the pelvis. In a backpack or in the hand, the phone moves partly independently of the body, which attenuates or disturbs the peaks and degrades the count.
Q: Why is a minimum duration imposed between two steps? A: Because the impact of a foot on the ground does not produce a single peak but a main peak followed by damped oscillations. Without this window, each rebound would be counted as an additional step and the total would be roughly doubled.
Related concepts
Accelerometer - Frequency - Biomechanics - Human Physiology - Instantaneous vs Average Speed - Measurement Uncertainty