Vector subtraction is how you answer "how do I get from here to there?" If you're at point A = (2, 5) and your friend is at B = (7, 1), the displacement from you to them is B − A = (5, −4): five units east, four south. Component by component — subtract the x's, subtract the y's — and the result is the arrow pointing from the first point to the second. It's the same operation behind "final minus initial" in physics: displacement is final position minus initial position, change in velocity is final minus initial, and every "how much did it change?" question is a subtraction in vector clothing.

Order is the entire game: B − A points from A to B, while A − B points the opposite way. Mixing them up is the classic error — the components just flip sign, so (5, −4) becomes (−5, 4), a completely different direction. This calculator subtracts your two vectors: enter the first vector's values as the First Number input and the second as the Second Number input, then read the Difference. Verify geometrically: place the result's tail at A and its head should land exactly on B. The worked relationship "final minus initial" is worth memorizing — it's the single most-used vector subtraction in science.

With the pre-filled defaults — First Number 15, Second Number 8 — the Vector Subtraction Calculator returns Difference 7.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.