HomeCalculatorsMathLinear Equation Calculator
Math calculator

Linear Equation Calculator

Solve ax + b = rhs for x. Identity and inconsistent cases when a = 0. Not the quadratic formula. Runs locally.

Instant result
Result

Enter values to calculate.

Inputs
Mode
Formula
Trust summary Engine tested · Specification checked · 10/10 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
Model
x in ax + b = rhs.
Scope
Degree 1 only
Verification
Engine tested · 10/10 tests · Production surface contract 4/4 · Specification checked · v1.0.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
3 golden · 2 boundary · 5 property · Production surface contract 4/4 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Solutionx = (rhs − b) / a
Identitya = 0 and b = rhs → every x
Inconsistenta = 0 and b ≠ rhs → no solution
iThis page is not ax² + bx + c = 0. Use /calc/math/quadratic for quadratics.

How to use

1

Enter a, b, and rhs

b may be 0. rhs is the right-hand side (REST also accepts c).

2

Read x or the status

success, infinite, or inconsistent.

Example calculations

Common configurations with formula and result.

ϟ

One solution

2x + 3 = 11

x = (11 − 3) / 2
4
ϟ

Identity

0x + 5 = 5

every x
infinite

Linear Equation calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A linear equation in one unknown has the form ax + b = rhs. If a ≠ 0 there is exactly one solution x = (rhs − b)/a.
What it calculates
x in ax + b = rhs.
Inputs
  • a
  • b?
  • rhs
Outputs
  • x
  • status
Formula
x = (rhs − b) / a
Assumptions
  • Degree 1 only
  • Not quadratic
Units
  • dimensionless
Boundary conditions
  • missing a or rhs → MISSING_REQUIRED_INPUT
  • unknown mode → INVALID_MODE
Example
a=2 b=3 rhs=11 → x=4
Validation cases

2 published on this page · 10/10 tests · Production surface contract 4/4 · View evidence

  • a=2 b=3 rhs=11 → x=4
  • a=0 b=5 rhs=5 → status=infinite
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.0.0

Other calculators in this family: Linear system, Quadratic, Triangle solver, Complex numbers .

}

Frequently asked questions

Key distinctions behind the calculation.

Is this the quadratic formula?

No. Quadratics are /calc/math/quadratic. This page is degree 1.

Where does this run?

Locally in the browser by default. REST and MCP call the same linear-equation engine.