Calculate acceleration X, acceleration Y, or angle from two known values for accelerometer readings in m/s², ft/s², g, degrees, or radians.
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Accelerometer Angle Formula
The accelerometer angle is found from the ratio of the Y-axis acceleration to the X-axis acceleration. The calculator uses the two values you enter to solve for the missing value.
\theta = atan2(a_y, a_x)
a_y = a_x * tan(\theta)
a_x = a_y / tan(\theta)
- θ = angle of the acceleration vector, in degrees or radians
- a_x = acceleration along the X axis
- a_y = acceleration along the Y axis
- tan(θ) = tangent of the angle
- atan2(a_y, a_x) = inverse tangent function that preserves the correct quadrant of the angle
If you enter acceleration X and acceleration Y, the calculator finds the angle using atan2(a_y, a_x). This is better than a simple inverse tangent because it can return the correct direction when one or both acceleration values are negative.
If you enter acceleration X and the angle, the calculator finds acceleration Y using a_y = a_x * tan(θ).
If you enter acceleration Y and the angle, the calculator finds acceleration X using a_x = a_y / tan(θ). The angle cannot be zero in this mode because division by tan(0) is division by zero.
Acceleration and Angle Unit Reference
The calculator converts acceleration values to meters per second squared and angle values to radians before applying the formulas.
| Unit | Type | Conversion to base unit |
|---|---|---|
| m/s² | Acceleration | 1 m/s² = 1 m/s² |
| ft/s² | Acceleration | 1 ft/s² = 0.3048 m/s² |
| g | Acceleration | 1 g = 9.80665 m/s² |
| degrees | Angle | degrees × π / 180 = radians |
| radians | Angle | 1 radian = 1 radian |
Common Accelerometer Angle Results
| Acceleration X | Acceleration Y | Angle | Meaning |
|---|---|---|---|
| Positive | 0 | 0° | Vector points along the positive X axis |
| Positive | Positive | 0° to 90° | Vector is in the first quadrant |
| 0 | Positive | 90° | Vector points along the positive Y axis |
| Negative | Positive | 90° to 180° | Vector is in the second quadrant |
| Positive | Negative | Negative angle | Vector is below the positive X axis |
Example Problems
Example 1: Find the angle
Suppose acceleration X is 4 m/s² and acceleration Y is 3 m/s².
\theta = atan2(3, 4)
\theta = 0.6435 \text{ radians} = 36.8699^\circThe angle is about 36.87°.
Example 2: Find acceleration Y
Suppose acceleration X is 6 m/s² and the angle is 30°.
a_y = 6 * tan(30^\circ)
a_y = 6 * 0.57735 = 3.4641 \text{ m/s}^2The acceleration Y value is about 3.4641 m/s².
FAQ
Why does the angle calculation use atan2 instead of atan?
atan2 uses both acceleration values separately, so it can identify the correct quadrant of the angle. A simple atan(a_y / a_x) can lose direction information, especially when acceleration X is negative or zero.
Can acceleration X or acceleration Y be negative?
Yes. Negative acceleration values indicate direction along the negative side of that axis. The angle result changes based on the signs of both X and Y. For example, a negative X value with a positive Y value places the vector in the second quadrant.
Why do the formulas convert angles to radians?
Trigonometric functions such as tangent and inverse tangent are normally evaluated in radians. If you enter degrees, the calculator converts them to radians before calculating, then converts the final angle back to your selected unit if needed.