CalcaTools

Vector Subtraction Calculator

Calculates vector subtraction using A − B = (aₓ − bₓ, aᵧ − bᵧ), live in your browser.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Inside the Vector Subtraction Calculator

The engine behind this calculator evaluates A − B = (aₓ − bₓ, aᵧ − bᵧ); |R| = √(x²+y²); θ = atan2(y, x) directly in your browser — nothing is sent to a server, and results update as you type.

For context, the sections beneath the calculator include typical values, a worked example you can recompute by hand, and an FAQ covering the practical details of vector subtraction calculator.

Quick reference

ABA − B|A − B|
(5, 3)(2, 1)(3, 2)3.606
(1, 0)(0, 1)(1, −1)1.414
(4, 4)(4, 4)(0, 0)0

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

ResultMeaning
A − BThe vector from point B to point A
MagnitudeDistance between the two tips
DirectionAngle of that displacement from +x

Formula & methodology

Formula: A − B = (aₓ − bₓ, aᵧ − bᵧ); |R| = √(x²+y²); θ = atan2(y, x)

  1. Enter the x and y components of vectors A and B.
  2. Subtract component-wise: R = (aₓ − bₓ, aᵧ − bᵧ).
  3. Magnitude |R| = √(x² + y²); direction θ = atan2(y, x), measured from the +x axis.

Example: (5, 3) − (2, 1) = (3, 2); |R| = √13 ≈ 3.6056 at 33.69°.

Frequently asked questions

How do you subtract vectors?
Subtract matching components: (5,3) − (2,1) = (3,2). Geometrically that is adding the reversed B to A, tip-to-tail.
What does A − B represent?
The displacement from B’s tip to A’s tip — relative position. Velocity of A relative to B in physics is v_A − v_B, computed the same way.
Is vector subtraction commutative?
No: B − A points the opposite way — same magnitude, direction rotated 180°.
How do I get magnitude and direction?
Magnitude = √(x² + y²); direction = atan2(y, x). The calculator reports both for the result vector.
Does this handle 3-D vectors?
It is built for 2-D. For 3-D, subtract z the same way and use √(x²+y²+z²) for magnitude.