Last updated: July 31, 2026
General Form of a Circle Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
D = -2h, E = -2k, F = h² + k² - r²
Where:
- h=Center h
- k=Center k
- r=Radius r
Worked Examples
Shifted circle
Center (3,-2), radius 5.
- 1D=-2(3)=-6
- 2E=-2(-2)=4
- 3F=3²+(-2)²-5²= -12
Origin-centered circle
Center (0,0), radius 7.
- 1D=0 and E=0
- 2F=0+0-49=-49
- 3Write compact equation
Decimal parameters
Center (1.5,2.5), radius 4.
- 1D=-3 and E=-5
- 2F=1.5²+2.5²-16=-7.5
- 3Assemble equation
Introduction
This converter maps geometric circle parameters to polynomial coefficients used in algebraic and analytic geometry.
Formula and Method
General Form of a Circle Calculator applies D = -2h, E = -2k, F = h² + k² - r² and returns deterministic outputs from validated inputs.
Validate each required input
Apply the stated formula
Round numeric outputs where needed
Return safe defaults when validation fails
Input Fields
Use these keys exactly as defined in calculation.ts.
- 1
h: Center h
- 2
k: Center k
- 3
r: Radius r
Output Fields
These values map directly to calculation.ts return keys.
- 1
D: Linear coefficient of x term
- 2
E: Linear coefficient of y term
- 3
F: Constant term in general form
- 4
equation: Formatted general-form equation string
Validation Rules
h and k must be finite and radius r must be a positive finite value.
Finite numeric values are required
Domain restrictions are enforced before solving
Invalid input returns default-safe outputs
Check examples to confirm expected behavior
How to Use This Calculator
Enter inputs, run the calculation, and read the primary output first.
Enter all required values
Click calculate
Review primary output first
Use supporting outputs for interpretation
Practical Uses
This calculator is useful for study, verification, and fast applied math checks.
Conic-equation conversion
Geometry homework
Graphing software input
Algebraic manipulation checks
FAQs
What does the General Form of a Circle Calculator compute?
It computes D Coefficient and supporting outputs from your inputs.
Which inputs are required?
Required inputs are: Center h, Center k, Radius r.
How are invalid inputs handled?
When validation fails, the calculator returns safe default values and does not attempt invalid math.
Are results rounded?
Yes. Numeric outputs are rounded inside calculation.ts (typically to 6 decimal places).
Can I use negative or decimal values?
Finite values are accepted with radius strictly greater than zero.
How should I verify my answer?
Use the worked examples and compare each output key with your manual steps.