Description
Return circular travel length under an explicit winding choice.
Spherical geometry distinguishes central angle, surface arc and straight chord. They coincide only in a small-angle limit, and a sphere-radius sensitivity differs from a geodesic calculation on an ellipsoid.
Return circular travel length under an explicit winding choice.
When to use this tool
Use Circular Arc Distance Winding Choice when checking a stated spherical arc, chord or radius relationship.
How to use the tool and how it works
- Enter fromRadians, toRadians, radius, winding. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedAngle, length. Use the output convention below.
Return circular travel length under an explicit winding choice. Require radius >= 0 and whole winding in [-1000000,1000000]; signedAngle = toRadians-fromRadians+2*pi*winding and length = radius*abs(signedAngle).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| fromRadians | From Radians | Required. Finite number. |
| toRadians | To Radians | Required. Finite number. |
| radius | Radius | Required. Finite number. |
| winding | Supplied whole winding count; angles are retained without automatic shortest-path normalization. | Required. Safe integer; minimum -1000000; maximum 1000000. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedAngle | Signed Angle | Required. Finite number. |
| length | Length | Required. Finite number. |
{
"input": {
"fromRadians": 0,
"toRadians": 3.141592653589793,
"radius": 2,
"winding": 0
},
"output": {
"signedAngle": 3.141592653589793,
"length": 6.283185307179586
}
}Limitations and assumptions
- Angles are not automatically normalized; winding selects a path rather than the shortest route.
- 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
Use endpoint coordinates and an appropriate spherical or ellipsoidal geodesic model for real geographic distance.
References
Similar or alternative tools
- Geodesic Radius Relative Distance Scale
Rescale a spherical arc distance for a new radius at fixed central angle.
- Fixed Radius Angular Gap Halfwidth
Return a fixed-radius arc-length envelope.