Math calculator
Linear Equation Calculator
Solve ax + b = rhs for x. Identity and inconsistent cases when a = 0. Not the quadratic formula. Runs locally.
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
- 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- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @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.
iThis page is not ax² + bx + c = 0. Use /calc/math/quadratic for quadratics.
How to use
Enter a, b, and rhs
b may be 0. rhs is the right-hand side (REST also accepts c).
Read x or the status
success, infinite, or inconsistent.
Example calculations
Common configurations with formula and result.
ϟ
x = (11 − 3) / 2One solution
2x + 3 = 11
4
ϟ
every xIdentity
0x + 5 = 5
infinite
Linear Equation calculator specification
Version 1.0.0 · Engine tested
Calculation status
- Engine tested 10/10 tests · Production surface contract 4/4
- Named expert review Not performed
- Calculation version 1.0.0
- 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
Related tools
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.