HomeCalculatorsMathGeometryVector Subtract Calculator
Math calculator

Vector Subtract Calculator

Componentwise vector difference u − v. Same engine as Vector. uz/vz default to 0. Not /subtraction. Not /vector-add. Not a matrix. Not CAS. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 11/11 tests · Production surface contract 3/3 · v1.6.0
Input interpretation
Enter values to calculate.
Result
—
Model
Componentwise vector difference u − v.
Scope
Euclidean R²/R³
Verification
Engine tested · 11/11 tests · Production surface contract 3/3 · Specification checked · v1.6.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
3 golden · 2 boundary · 6 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.6.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (3 capabilities; 161 remain CURRENT) @ 2026-09-20T23:37:12.315Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Differenceu − v
Components(ux−vx, uy−vy, uz−vz)
iSame engine as /vector. Default (1, 2, 3) − (4, 5, 6) → (−3, −3, −3). Not a second engine.

How to use

1

Enter u and v

uz and vz are optional and default to 0. (1, 2, 3) − (4, 5, 6) = (−3, −3, −3).

2

Read the difference

Each component is subtracted independently. Addition stays on /calc/math/vector-add.

Example calculations

Common configurations with formula and result.

ϟ

1-2-3 − 4-5-6

u = (1, 2, 3), v = (4, 5, 6)

(1−4, 2−5, 3−6)
(−3, −3, −3)
ϟ

2-D

u = (3, 4, 0), v = (1, 0, 0)

(3−1, 4−0, 0)
(2, 4, 0)

Vector Subtract calculator specification

Version 1.6.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
u − v = (ux−vx, uy−vy, uz−vz). This page is mode=sub on math.vector. uz and vz default to 0. Scalar subtraction stays on /calc/math/subtraction. Addition is /calc/math/vector-add. Not a second engine. Not CAS.
What it calculates
Componentwise vector difference u − v.
Inputs
  • ux
  • uy
  • uz?
  • vx
  • vy
  • vz?
Outputs
  • rx
  • ry
  • rz
Formula
u − v
Assumptions
  • Euclidean R²/R³
  • uz/vz default to 0
  • Not /subtraction
  • Not /vector-add
  • Not a matrix
  • Not CAS
Units
  • length (consistent units)
Boundary conditions
  • missing ux, uy, vx, or vy → MISSING_REQUIRED_INPUT
  • unknown mode → INVALID_MODE
Example
u=(1,2,3) v=(4,5,6) → (−3, −3, −3)
Validation cases

2 published on this page · 11/11 tests · Production surface contract 3/3 · View evidence

  • ux=1 uy=2 uz=3 vx=4 vy=5 vz=6 → rx=-3 ry=-3 rz=-3
  • ux=3 uy=4 vx=1 vy=0 → rx=2 ry=4 rz=0
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.6.0

Other calculators in this family: Angle Between Lines Calculator, Annulus Calculator, Arc Calculator, Circle Calculator, Cone Calculator, Conic Section Calculator, Coordinate Geometry Calculator, Cross Product Calculator . Explore all Geometry.

→ Angle Between Lines Calculator Acute angle between two plane lines, each given by two points. Parallel is 0°. Perpendicular is 90°. Degenerate points are invalid. Same engine as Coordinate Geometry. Not a second engine. Not CAS. Runs locally. › → Annulus Calculator Annulus A = π(R² − r²) and P = 2π(R + r) with outer R > inner r. Same engine as Plane Geometry. Not /circle. Not a square. Not CAS. Runs locally. › → Arc Calculator Circle arc s = r θ from radius and central angle. Same engine as Circle. Not /sector. Not /spherical-sector. Not CAS. Runs locally. › → Circle Calculator Compute diameter, circumference, and area from r, or arc and sector from a central angle. Discovery /sector, /arc. Not the Pythagorean page. Not /spherical-sector. Not CAS. Runs locally. › → Cone Calculator Right circular cone V = (1/3)πr²h and slant l = √(r²+h²). Same engine as Solid Geometry. Not ISO 5167-5. Not CAS. Runs locally. › → Conic Section Calculator Axis-aligned ellipse, parabola, and hyperbola in standard form. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page. Not coordinate geometry. Not CAS. Runs locally. › → Coordinate Geometry Calculator Distance, midpoint, and slope of two points in the plane. Line through two points is /line-equation. Point-to-line distance is /point-line-distance. Intersection is /line-intersection. Angle is /angle-between-lines. Not the Pythagorean-only page. Runs locally. › → Cross Product Calculator Vector product u × v in R³. 2-D uses uz = vz = 0. Same engine as Vector. Not a matrix. Not CAS. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a second vector engine?

No. It is mode=sub on math.vector, the same engine as /calc/math/vector.

Is this the arithmetic subtraction page?

No. Scalar subtraction stays on /calc/math/subtraction. This page subtracts two Euclidean vectors.

Where does this run?

Locally in the browser by default. REST and MCP call the same vector engine.