A weather report says the wind is 20 mph from the northwest — that's a vector: a magnitude (20 mph) plus a direction (northwest). Vector analysis is the toolkit for taking such quantities apart and putting them back together: splitting a vector into x- and y-components, finding its length and heading angle, and recombining components into a resultant. Pilots do it on every crosswind landing (the wind splits into headwind and crosswind components), engineers do it for every force on a bridge, and game developers do it sixty times a second for every moving object.

The component formulas are the foundation: a vector with magnitude r at angle θ has x-component r·cos θ and y-component r·sin θ. A 20-mph wind from the northwest (135° from east) pushes about 14.1 mph west and 14.1 mph north. Going the other way, components recombine via the Pythagorean theorem and the arctangent. This calculator performs vector analysis on your two inputs: enter the pair of values (magnitude and angle, or x and y components) and read the computed analysis. The direction convention to memorize: angles are measured counterclockwise from the positive x-axis (east), so northwest is 135° — mixing up the reference direction is the classic error.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Vector Analysis Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.