Last updated: July 31, 2026
Equation of a Circle Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
standard: (x-h)^2 + (y-k)^2 = r^2; general: x^2 + y^2 + d*x + e*y + f = 0 where d=-2h, e=-2k, f=h^2+k^2-r^2
Where:
- h=h
- k=k
- r=r
Worked Examples
Center (2,-1), radius 5
Translate and expand circle equation.
- 1standard: (x-2)^2 + (y+1)^2 = 25
- 2d=-4, e=2, f=-20
Origin-centered circle
h=0, k=0.
- 1standard: x² + y² = 9
- 2general constant f = -9
Decimal center
h=-1.5, k=2.25, r=4.5.
- 1Compute d,e,f from formulas
- 2Build both forms
Introduction
Generate both standard and general equations of a circle from center coordinates and radius.
Formula and Method
Equation of a Circle Calculator uses: standard: (x-h)^2 + (y-k)^2 = r^2; general: x^2 + y^2 + d*x + e*y + f = 0 where d=-2h, e=-2k, f=h^2+k^2-r^2
Enter all required inputs
Apply the underlying math formula(s)
Compute supporting terms where needed
Round numeric outputs for stable display
Input Fields
Provide values for: h, k, r.
- 1
h: h
- 2
k: k
- 3
r: r
Output Fields
The calculator returns: standardForm, d, e, f, generalForm.
- 1
standardForm: Circle equation in standard form
- 2
d: General-form coefficient d (x term)
- 3
e: General-form coefficient e (y term)
- 4
f: General-form constant f
- 5
generalForm: Circle equation in general form
Validation Rules
Input validation is applied before calculation to prevent invalid math states.
h, k, r must be finite numbers.
r must be positive.
String equations are built from rounded values.
d, e, and f are returned explicitly for algebra workflows.
How to Use This Calculator
Fill in the inputs, run the calculator, and review primary output first.
Enter the required values
Click calculate
Check the primary output
Use example scenarios for verification
Practical Uses
This calculator supports learning, quick checks, and day-to-day technical problem solving.
Homework and exam preparation
Engineering and science sanity checks
Classroom demonstrations
Fast recalculation with different inputs
FAQs
What does the Equation of a Circle Calculator compute?
Generate both standard and general equations of a circle from center coordinates and radius.
Which inputs are required?
Required inputs: h, k, r.
How should I format numbers?
Use finite numeric values; decimals and negative numbers are allowed unless restricted by validation rules.
How are results rounded?
Numeric outputs are rounded to about 6 decimal places for readability.
Why might I see an error?
h, k, r must be finite numbers.
Can I use this for learning and verification?
Yes. Use the examples and formula section to verify manual calculations quickly.