Vectors are arrows with attitude — they carry both a size and a direction, which makes them the natural language of motion. Adding vectors is delightfully physical: walk 3 blocks east then 4 blocks north, and your total displacement is the arrow straight from start to finish, (3, 4), with length 5. The head-to-tail rule says it all — place the second arrow's tail at the first arrow's head, and the sum runs from the very first tail to the very last head. Sailors adding current to their heading, pilots correcting for wind, and quarterbacks leading a receiver all do vector addition, whether they name it or not.

Component-wise addition keeps the bookkeeping honest: add the x's, add the y's, done. (2, 5) + (3, −1) = (5, 4). Scalar multiplication stretches or shrinks: 2 × (3, 4) = (6, 8) doubles the length without changing direction, while −1 flips it end for end. This calculator performs vector operations on your two inputs: type the first vector's values in Variable A and the second in Variable B, then read the Result. The geometric check never lies — sketch the arrows head-to-tail and confirm the computed sum matches the drawn diagonal. If it doesn't, an x got added to a y somewhere.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Vector 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.