An inclinometer is an instrument that measures the tilt angle of an object relative to the vertical or the horizontal. It combines the plumb line and the spirit level in a single tool. On a smartphone, it is derived from the accelerometer, which detects the direction of gravity.
Discover FizziQ
How to measure it in class
With FizziQ, the accelerometer at rest directly reads the tilt of the device.
Steps:
- Open FizziQ and display the tilt measurement: the app offers a front-back inclinometer (pitch) and a side inclinometer (roll), from -90° to +90°.
- Lay the phone flat: check that the angle from the horizontal is close to 0°.
- Stand the phone upright: the angle should approach 90°.
- Tilt the device on a slope of known angle (raised book, ramp) and compare the measured angle with the geometric one.
- Use the inclinometer for sighting to estimate the height of a tree or a building by trigonometry (angle + distance).
Scientific activities on this topic
- Inclined plane: weight components
- Height of a tree with the theodolite
- Height of the Sun and seasons
- Magnetic inclination and latitude
Possible extensions with FizziQ: measuring the slope of an inclined plane in mechanics, determining the height of an object by trigonometric sighting, or checking that a bench is horizontal. See the smartphone sensors guide.
Learn more
At rest, the accelerometer measures no motion: it only detects gravity, whose vector points downwards with a magnitude of about 1 g. By comparing how this vector is distributed over the device’s three axes, the phone’s orientation in space is deduced. A smartphone lying flat measures all of gravity on the vertical axis; tilted, it spreads part of it onto the other axes, and this distribution gives the angle. The measurement is only reliable at rest: as soon as the device accelerates (jolt, vibration), the accelerometer adds gravity and motion together, and the angle becomes wrong. A smartphone is not a metrology instrument, but it gives very decent angles under stable conditions.
Orders of magnitude: the acceleration of gravity is g ≈ 9.81 m/s². The noise of a consumer accelerometer is of the order of a few thousandths of g, which corresponds to a tilt resolution of a few tenths of a degree near the horizontal. In practice, the realistic accuracy of a stable slope measurement is about 0.5 to 1°.
Formula
For a tilt around a single axis, the angle from the horizontal follows from the components of the measured gravity:
θ = arctan(a∥ / a⊥)
Where:
- a∥: component of gravity in the tilt plane (m/s²)
- a⊥: component of gravity along the reference axis (m/s²)
- θ: tilt angle (degrees)
This relation is only valid at rest, when the accelerometer measures gravity alone.
Application examples
- Measuring the slope of an inclined plane in mechanics lab work.
- Checking that a shelf or a bench is horizontal (digital spirit level).
- Estimating the height of a tree or a building by sighting and trigonometry.
- Measuring the angle of a roof or an access ramp.
- Checking the tilt of a solar panel.
- Studying the tipping of an object up to its stability limit.
FAQ
Q: Why does the inclinometer go wild when I move the phone? A: The accelerometer then measures the sum of gravity and the motion’s acceleration. The angle is only reliable when the device is still.
Q: Do I need to hold the phone in a specific way? A: The tilt depends on the position of the axes. It helps to note which edge the device rests on and to keep the same configuration throughout a series of measurements.
Q: Can any smartphone be used as an inclinometer? A: Yes, all of them have an accelerometer, the sensor required for automatic screen rotation. The inclinometer is therefore available on virtually every device.
Related concepts
Accelerometer - Gravitational acceleration - Orientation - Theodolite - Triangulation