Point-Circle Position Calculator
Determine whether a point lies inside, on, or outside a circle.
About Point-Circle Position Calculator
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
Worked example
With the default values below, Point-Circle Position Calculator returns Position of Inside the circle. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Point x
- 3
- Point y
- 4
- Center x
- 0
- Center y
- 0
- Radiusminimum 0
- 6
Results
- Position
- Inside the circle
- Distance to Center
- 5.0000 units
Step by step
- 1Distance from point to center= 5.0000
- 2Compare with radius= Inside the circle
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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).