Point-Circle Position Calculator
Determine whether a point lies inside, on, or outside a circle.
Inputs
Position
Inside the circle
Distance to Center
5.0000units
Step by step
Distance from point to center
d = √((3−0)² + (4−0)²)
= 5.0000
Compare with radius
d = 5.0000, r = 6
= Inside the circle
How it works
Compare the distance from the point to the circle's center with the radius. If d < r → inside, d = r → on, d > r → outside.
Formula
Distance to Center
d = √((x−h)² + (y−k)²)
- x,y
- The point
- h,k
- Circle center
- r
- Radius
Frequently Asked Questions
What does 'on the circle' mean exactly?
The point satisfies the circle equation exactly — it lies on the circumference.
Can I use this for a sphere?
The same principle applies in 3D with d = √((x−h)²+(y−k)²+(z−l)²).