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Math calculator

Circle Calculator

Compute diameter, circumference, and area from r, or arc and sector from a central angle. Not the Pythagorean page. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 10/10 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Circle diameter, circumference, area, arc, and sector.
Scope
Euclidean plane
Verification
Engine tested · 10/10 tests · Production surface contract 3/3 · 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 3/3 · 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Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @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.

CircumferenceC = 2πr
AreaA = πr²
Arcs = r θ
iThis is not a² + b² = c². Right triangles stay on /calc/math/pythagorean.

How to use

1

Choose what you know

Radius, diameter, circumference, or area. Arc and sector also need the central angle in degrees.

2

Read r, d, C, and A together

Arc mode reports arc length; sector reports sector area.

Example calculations

Common configurations with formula and result.

ϟ

Unit circle

r = 1

C = 2π, A = π
d=2
ϟ

Semicircle arc

r = 2, θ = 180°

s = rπ
2π

Circle calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
A Euclidean circle of radius r has diameter 2r, circumference 2πr, and area πr². Arc length s = rθ (θ in radians).
What it calculates
Circle diameter, circumference, area, arc, and sector.
Inputs
  • mode
  • r?
  • diameter?
  • circumference?
  • area?
  • theta_deg?
Outputs
  • r
  • diameter
  • circumference
  • area
Formula
C = 2πr, A = πr²
Assumptions
  • Euclidean plane
  • Not spherical geometry
  • Not Pythagorean-only
Units
  • length (consistent units)
  • degrees
Boundary conditions
  • r ≤ 0 → VALUE_MUST_BE_POSITIVE
  • unknown mode → INVALID_MODE
Example
r=1 → C=2π, A=π
Validation cases

2 published on this page · 10/10 tests · Production surface contract 3/3 · View evidence

  • mode=from_radius r=1 → diameter=2
  • mode=arc r=2 theta_deg=180 → arc_length=2π
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.0.0

Other calculators in this family: Triangle solver, Pythagorean, Coordinate geometry .

△ Triangle solver › a²+b² Pythagorean › xy Coordinate geometry ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this the Pythagorean calculator?

No. Right-triangle a²+b²=c² is /calc/math/pythagorean.

Where does this run?

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