Smartphone accelerometer: how it works and experiments

An accelerometer is a sensor that measures the acceleration experienced by an object along one or more axes, by detecting the force exerted on a small internal proof mass. In a smartphone, it drives automatic screen rotation and motion detection. In science, the phone’s accelerometer allows quantitative studies of falls, oscillations, vibrations and rotations, in meters per second squared (m/s²).

Discover FizziQ

How to measure it in class

FizziQ displays the components of the acceleration along the smartphone’s three axes, without the contribution of gravity (linear acceleration) or with it, as well as the absolute acceleration, which reads about 9.81 m/s² at rest and drops to zero in free fall.

Steps:

Open FizziQ and select the acceleration sensor. Observe the three components (x, y, z) and the magnitude of the acceleration. Identify which component changes when you tilt the smartphone in each direction.
Place the smartphone flat, then on its edge, then on its back. Note the values of the three components at each position and verify that the magnitude always stays close to 9.81 m/s².
Gently shake the smartphone and observe the acceleration peaks. Then shake it harder and compare the amplitudes. Estimate the maximum measurable acceleration before the sensor saturates.
Create a mini-pendulum by attaching the smartphone to a string and letting it swing. Observe the periodic variations in acceleration and deduce the oscillation period.

Scientific activities on this topic

The accelerometer is a very precise measuring instrument whose understanding is almost immediate for students. Care should be taken to distinguish between linear acceleration (due solely to the device’s movement, without gravity) and absolute acceleration (which includes gravitational acceleration).

Below we have gathered various activities that allow exploring physical principles related to the use of a smartphone’s accelerometer.

Learn more

Accelerometers are commonly used in portable electronic devices, such as cell phones and laptops, to detect the device’s position and change the screen orientation accordingly. They are also used in navigation devices, toys and drones to detect movements and direction changes.

The first mechanical accelerometers date from the late 19th and early 20th century. They were used to measure acceleration and vibration in industrial and military applications, and relied on a spring attached to a moving mass: under the effect of acceleration, the mass moves and the elongation of the spring makes it possible to work back to the value of the acceleration.

During the 1960s and 1970s, electromechanical accelerometers began to be used, which relied on electrical sensors to measure acceleration instead of mechanical mechanisms. These electromechanical accelerometers were used in guidance systems for missiles and spacecraft, as well as in acceleration measurement instruments in civil engineering and soil mechanics.

Today, most accelerometers are miniaturized electronic sensors, which use micro-machining technologies to measure acceleration. MEMS accelerometers built into smartphones became widespread from the 2000s onward, which made these measurements accessible to the general public. These sensors are widely used in portable electronic devices, navigation devices and industrial motion sensors.

Acceleration, which the accelerometer measures, describes the change in velocity of an object. It can be calculated either from the object’s velocity, or by using Newton’s second law, which relates the force exerted on an object to its acceleration. Modern accelerometers use the latter method, often by means of mechanical devices such as springs and capacitors to indirectly measure the force and therefore the acceleration.

In the process of measuring acceleration with an accelerometer, an ingenious system using both a spring and a capacitor is implemented. When the smartphone moves, a small mass attached to the spring initially stays in place by inertia, causing a change in the length of the spring, denoted x. This change in length generates a restoring force proportional to the elongation of the spring (F = kx, where k is the spring stiffness and x the displacement). According to Newton’s second law, this force results in an acceleration of the mass (F = ma, where a is the acceleration and m the mass), thus making it possible to calculate the acceleration (a = kx/m). To measure the displacement x, accelerometers exploit the properties of capacitors, whose storage capacitance is inversely proportional to the distance between the plates. By connecting one plate of the capacitor to the moving frame and the other to the mass attached to the spring, this distance can be estimated by calculating the capacitance of the capacitor, which makes it possible to deduce the acceleration. This method, combining a spring and a capacitor, is commonly used in accelerometer technology to provide precise acceleration measurements.

MEMS (Micro Electro Mechanical Systems) technology has made it possible to miniaturize these sensors for integration into smartphones. These devices not only measure the acceleration due to gravity (absolute acceleration) but also make it possible, after correction, to determine the linear acceleration, that is, the acceleration without the effect of gravity. Precision and calibration are essential to ensure the reliability of the measurements, although for many everyday applications extreme precision is not necessary. The measurement rate depends on the device: most smartphones deliver from a few dozen to a few hundred readings per second, with a noise floor at rest of a few hundredths of m/s². These characteristics are largely sufficient to study a fall, a pendulum or vibrations in class.

Formula

The operating principle is based on Newton’s second law applied to the proof mass:

F = m × a

Meaning: F: force exerted on the proof mass (N) m: mass of the sensing element (kg) a: measured acceleration (m/s²)

The displacement x of the proof mass is proportional to the acceleration: x = (m × a) / k k: stiffness of the restoring spring (N/m)

Application examples

The automatic rotation of the smartphone screen when you turn it, detected by the accelerometer
The step counter of a fitness tracker, which detects the jolts of walking
The deployment of a car’s airbag during a violent impact detected by an accelerometer
The optical stabilization of a camera, which compensates for hand tremors
Controlling a video game character by tilting the controller or the smartphone

FAQ

Q: How does a smartphone accelerometer work? A: It contains a micro-mass suspended by silicon springs. When the smartphone accelerates, the mass moves and changes the electrical capacitance between electrodes. This variation is converted into a digital value.

Q: Does the accelerometer measure velocity? A: No, it measures acceleration, that is, the change in velocity per unit of time. Velocity can be derived by integration, but errors accumulate rapidly.

Q: Why does the accelerometer show 9.81 m/s² when the smartphone is stationary? A: Because it measures the reaction force of the surface it rests on. This force, which opposes the weight, is interpreted as an upward acceleration of value g.

Q: What is the measurement range of a smartphone accelerometer? A: Most smartphone accelerometers measure up to ±16 g (approximately ±157 m/s²) or ±8 g depending on the model. Beyond that, the sensor saturates and the measurement is no longer reliable.

Q: Can the accelerometer be used to detect earthquakes? A: Yes. Several applications use the accelerometers of millions of smartphones to create a citizen seismic network. The sensitivity is limited, but sufficient to detect nearby earthquakes of magnitude 4 or greater.

Linear Acceleration - Absolute Acceleration - Gyroscope

Accelerometer