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Last updated: July 31, 2026

Circle Equation from Diameter Endpoints

Dharmendra Singh - Creator

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Balram Rajput
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Formula

h=(x1+x2)/2; k=(y1+y2)/2; radius=distance((x1,y1),(x2,y2))/2; equation: (x-h)^2 + (y-k)^2 = radius^2

Where:

  • x1=x1
  • y1=y1
  • x2=x2
  • y2=y2
Circle from Diameter EndpointsA circle whose diameter connects two given points, with the center located at the midpoint of that diameter.(x₁, y₁)(x₂, y₂)CenterFormulasCenter = midpointr = distance / 2(x-h)² + (y-k)² = r²
The diameter's midpoint gives the circle's center, and half the diameter's length gives its radius.

Worked Examples

Diameter endpoints (1,2) and (7,6)

Compute midpoint and half-distance.

  1. 1h=(1+7)/2=4, k=(2+6)/2=4
  2. 2distance=√52 so radius=√52/2
Final Answer: h=4, k=4, radius≈3.605551, equation=(x - 4)² + (y - 4)² = 13

Horizontal diameter

Endpoints (-3,1) and (5,1).

  1. 1Midpoint is (1,1)
  2. 2Radius is half of 8
Final Answer: h=1, k=1, radius=4, equation=(x - 1)² + (y - 1)² = 16

Decimal endpoints

Endpoints (0.5,-1.5) and (3.5,2.5).

  1. 1Compute midpoint and radius numerically
Final Answer: h=2, k=0.5 with equation string returned

Introduction

Build a circle equation directly from two diameter endpoints by computing midpoint and radius automatically.

Formula and Method

Circle Equation from Diameter Endpoints uses: h=(x1+x2)/2; k=(y1+y2)/2; radius=distance((x1,y1),(x2,y2))/2; equation: (x-h)^2 + (y-k)^2 = radius^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: x1, y1, x2, y2.

  1. 1

    x1: x1

  2. 2

    y1: y1

  3. 3

    x2: x2

  4. 4

    y2: y2

Output Fields

The calculator returns: h, k, radius, equation.

  1. 1

    h: x-coordinate of the circle center

  2. 2

    k: y-coordinate of the circle center

  3. 3

    radius: Circle radius from diameter endpoints

  4. 4

    equation: Standard-form equation of the circle

Validation Rules

Input validation is applied before calculation to prevent invalid math states.

  • All endpoint coordinates must be finite.

  • Endpoints must be distinct points.

  • Center is the midpoint of the two points.

  • Numeric outputs are rounded to 6 decimals.

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 Circle Equation from Diameter Endpoints compute?

Build a circle equation directly from two diameter endpoints by computing midpoint and radius automatically.

Which inputs are required?

Required inputs: x1, y1, x2, y2.

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?

All endpoint coordinates must be finite.

Can I use this for learning and verification?

Yes. Use the examples and formula section to verify manual calculations quickly.

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