This calculator performs vector operations using polar coordinates (magnitude and angle). It is designed for rotor balancing applications where imbalance is measured as a mass at a specific angular position. The calculator helps combine multiple imbalance readings, determine correction weight placement, and convert between coordinate systems.

Each vector is defined by two values: mass (in grams or arbitrary units) and angle (in degrees from 0 to 360). The reference angle 0° points upward (12 o'clock position), with angles increasing clockwise. This matches the convention used by most balancing instruments where the phase reference is typically marked at the top of the rotor.

• Addition (+) — Combines two vectors into a single resultant vector. Use this when you need to find the total imbalance from multiple sources, or to combine two correction weights into one.
• Subtraction (−) — Calculates the difference between two vectors (A minus B). Useful for determining residual imbalance after a correction.
• Opposite (±180°) — Adds 180° to the angle of vector A. This gives you the position where the correction weight should be placed.
• Scale (k×) — Multiplies the mass by coefficient k. Essential when recalculating correction mass for a different mounting radius: m2 = m1 × (r1 / r2).
• Cartesian (X, Y) — Converts polar coordinates to Cartesian: X = m × cos(angle), Y = m × sin(angle).

• Single-plane balancing: Measure imbalance, use Opposite function to find correction angle, install weight and verify.
• Combining weights: Replace two installed correction weights with a single equivalent weight using Addition.
• Radius conversion: Use Scale to recalculate mass when moving correction weight to a different radius.
• Split weights: When exact angle is not accessible, distribute correction mass to two adjacent blades.