Camera Gimbal Payload Center of Gravity & Torque Sizer is a lightweight engineering evaluation tool that calculates mechanical sizing factors from load, operating coefficient, and safety variables.

### Implemented Mathematical Formulas This component provides a three-variable parameter evaluation: 1. **Design Result:** $$\text{Result} = \frac{\text{Primary Load} \times \text{Operating Coefficient}}{\text{Safety Factor}}$ 2. **Root Factor (Geometric Mean):** $$\text{Root Factor} = \sqrt{\text{Primary Load} \times \text{Operating Coefficient}}$ 3. **Efficiency Rating:** $$\text{Efficiency (\%)} = \frac{\text{Primary Load}}{\text{Primary Load} + \text{Operating Coefficient}} \times 100$

### Note on 3-Axis Gimbal Sizing This tool provides an index calculation based on the three input numbers. For physical 3-axis camera gimbal balancing (calculating pitch, roll, and yaw motor holding torques $\tau = I\alpha + m g r \sin\theta$ in 3D Euclidean space), camera operators must balance the physical sled along all axes or consult motor torque payload ratings from manufacturers like DJI or Freefly.

### Worked Numeric Example Using the default calculator inputs: - **Primary Dimension / Load ($L$):** 100 - **Operating Coefficient ($C$):** 20 - **Safety / Rate Factor ($S$):** 5 - **Design Output:** $(100 \times 20) / 5 = 2,000 / 5 = 400.00$. - **Root Factor:** $\sqrt{100 \times 20} = \sqrt{2000} \approx 44.72$. - **Efficiency Rating:** $[100 / (100 + 20)] \times 100 = (100 / 120) \times 100 = 83.3\%$.

### In-Browser Processing Note All formulas evaluate immediately in your browser runtime. No mechanical payload dimensions or camera specifications are transmitted over the internet.