Circle Calculator (Radius, Diameter, Area & Circumference)
The Circle Calculator instantly computes geometric parameters of a circle given any single dimension (radius, diameter, circumference, or area). It uses high-precision Archimedean constant approximations.
PARAMETERS(3)
LOAD VERIFIED SCENARIO
ACTIVE COMPUTATION
Circle Area
78.5398cm²
Radius: 5 cm
Circumference
31.4159cm
Diameter
10cm
Radius
5cm
STEP-BY-STEP MATHEMATICAL DERIVATION
1Derived radius r = 5 cm
2Diameter d = 2 × r = 10 cm
3Circumference C = 2 × π × r = 2 × π × 5 = 31.4159 cm
4Area A = π × r² = π × (5)² = 78.5398 cm²
MATHEMATICAL FORMULA & GOVERNING PRINCIPLES
A = π * r², C = 2 * π * r, d = 2 * r
Given radius r, the area A is pi times radius squared. The circumference C is two times pi times radius. Diameter d is twice the radius.
FREQUENTLY ASKED QUESTIONS (FAQ)
How do you calculate the area from diameter?
Divide the diameter by 2 to get the radius r = d / 2, then apply A = π * r² = (π * d²) / 4.
What value of π is used in Calcyra?
Calcyra evaluates π up to 28 decimal places using Decimal.js for zero rounding drift.
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