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Two-Force Resultant Calculator — result sheet
Add two planar force vectors by magnitude and angle, returning Cartesian components, resultant magnitude, and direction.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Fx = ΣF cosθ; Fy = ΣF sinθ; resultant magnitude R = √(Fx²+Fy²); direction θ = atan2(Fy,Fx).
Forces are vectors, so their directions must be resolved before addition. The direction is reported counterclockwise from the positive x-axis.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Force 1 magnitude — N; minimum 0; maximum 1000000000
- Force 1 angle from +x — degrees; minimum -1000000000; maximum 1000000000
- Force 2 magnitude — N; minimum 0; maximum 1000000000
- Force 2 angle from +x — degrees; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Force 1 magnitude | 10 |
| Force 1 angle from +x | 30 |
| Force 2 magnitude | 8 |
| Force 2 angle from +x | 120 |
Resultant ≈ 12.806 N at 68.66°; components are Fx ≈ 4.660 N and Fy ≈ 11.928 N.
Assumptions and limits
- Both vectors lie in one plane and use the same force unit.
- Angles are measured counterclockwise from the positive x-axis.
- The result is a static vector sum; acceleration, constraints, friction, and moments are not inferred.
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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