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Math calculator

Square Calculator

Square A = s², P = 4s, d = s√2. Same engine as Plane Geometry. Not /rectangle. Not /square-root. Not CAS. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 25/25 tests · Production surface contract 3/3 · v1.5.0
Input interpretation
Enter values to calculate.
Result
—
Model
Square area, perimeter, and diagonal from side s.
Scope
Euclidean plane
Verification
Engine tested · 25/25 tests · Production surface contract 3/3 · Specification checked · v1.5.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
9 golden · 5 boundary · 11 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.5.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

AreaA = s²
Diagonald = s√2
iSame engine as /plane-geometry. Default s=2 gives A=4. Not a second engine. Not the square-root page.

How to use

1

Enter s

Side must be positive. Default s=2.

2

Read A, P, and d

s=2 has area 4, perimeter 8, and diagonal 2√2.

Example calculations

Common configurations with formula and result.

ϟ

Side 2

s = 2

A = 4
A=4, P=8, d=2√2
ϟ

Unit square

s = 1

A = 1
A=1, d=√2

Square calculator specification

Version 1.5.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A square of side s>0 has area s², perimeter 4s, and diagonal s√2. This page is mode=square on math.geometry.plane. a=b is a valid square on /rectangle, but this URL locks square. Not /square-root. Not CAS.
What it calculates
Square area, perimeter, and diagonal from side s.
Inputs
  • s
Outputs
  • area
  • perimeter
  • diagonal
  • square
Formula
A = s², P = 4s, d = s√2
Assumptions
  • Euclidean plane
  • Not /rectangle
  • Not /square-root
  • Not CAS
Units
  • length (consistent units)
  • area (length²)
Boundary conditions
  • s ≤ 0 → VALUE_MUST_BE_POSITIVE
  • unknown mode → INVALID_MODE
Example
s=2 → A=4, P=8, d=2√2
Validation cases

2 published on this page · 25/25 tests · Production surface contract 3/3 · View evidence

  • s=2 → A=4 P=8 d=2√2 square=true
  • s=1 → A=1 d=√2
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.5.0

Other calculators in this family: Angle Between Lines Calculator, Annulus Calculator, Circle Calculator, Cone Calculator, Conic Section Calculator, Coordinate Geometry Calculator, Cross Product Calculator, Cylinder 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. › → Circle Calculator Compute diameter, circumference, and area from r, or arc and sector from a central angle. Not the Pythagorean page. 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. › → Cylinder Calculator Right circular cylinder V = πr²h and A = 2πr(r+h). Same engine as Solid Geometry. Not CAS. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a second plane engine?

No. It is mode=square on math.geometry.plane, the same engine as /calc/math/plane-geometry.

Is this the rectangle page?

No. a=b is a valid square on /calc/math/rectangle. This URL locks mode=square and only needs s.

Is this the square-root calculator?

No. √x stays on /calc/math/square-root.

Where does this run?

Locally in the browser by default. REST and MCP call the same plane-geometry engine.