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3D Acceleration Magnitude — result sheet
Find the total acceleration magnitude and g-equivalent from perpendicular x, y, and z acceleration components.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: |a| = √(aₓ² + aᵧ² + a_z²); g-equivalent = |a|/g₀.
Acceleration is a vector, so its signed components cannot be added as ordinary scalars. The Euclidean norm combines the three perpendicular components into one non-negative magnitude. The optional reference gravity turns that magnitude into a dimensionless comparison, which is useful for describing loads but is not a safety or injury threshold.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- x-component of acceleration — m/s²; minimum -1000000000000; maximum 1000000000000
- y-component of acceleration — m/s²; minimum -1000000000000; maximum 1000000000000
- z-component of acceleration — m/s²; minimum -1000000000000; maximum 1000000000000
- Reference gravity — m/s²; minimum 1.0E-6; maximum 1000
Worked example
| Input | Value |
|---|---|
| x-component of acceleration | 3 |
| y-component of acceleration | 4 |
| z-component of acceleration | 12 |
| Reference gravity | 9.80665 |
Magnitude = 13 m/s², or about 1.325 g.
Assumptions and limits
- The three entered components use the same coordinate frame and units and are mutually perpendicular Cartesian components.
- The g-equivalent uses the entered reference gravity only as a comparison scale.
- The calculation does not separate gravitational, vehicle, rotational, vibration, or occupant-specific acceleration effects.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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