Description
Return hypot(inner,outer)/sqrt(2).
Circle calculations distinguish radius, diameter, chord, sagitta, tangent, and oriented offsets. Branch choices determine signs and which arc or segment is meant; a scalar identity does not always establish an actual geometric construction.
Return hypot(inner,outer)/sqrt(2).
When to use this tool
Use Circular Annulus Area Bisecting Radius when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter inner, outer. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read radius. Use the output convention below.
Require nonnegative inner radius and greater outer radius. Return hypot(inner,outer)/sqrt(2).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inner | Inner | Required. Finite number; minimum 0. |
| outer | Outer | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number. |
{
"input": {
"inner": 0,
"outer": 4
},
"output": {
"radius": 2.82842712474619
}
}Limitations and assumptions
- This radius bisects annular area rather than radial thickness; both radii share one center and unit and actual circle geometry is not validated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Construct the circles, chord, or segment in coordinates when existence or orientation matters. Use the complete geometry and an appropriate tolerance for intersection or tangency decisions.
References
Similar or alternative tools
- Circular Segment Centroid Height Factor
Return 4r sin(halfAngle)³/[3(2 × halfAngle-sin(2 × halfAngle))].
- Circle Common Chord Midpoint Offset
Return (d²+r1²-r2²)/(2d) along the first-to-second center axis and sqrt(max(0, r1²-offset²)) for halfChord.