Description
Convert signed arc length and a supplied radius to central angle and turns.
Geographic coordinates use explicit angular, axis and vertical-datum conventions. Unwrapped longitude difference differs from the shortest circular separation, and a north-based bearing differs from a rightward-zero screen rotation. Ellipsoidal and orthometric heights require a compatible geoid-undulation model.
Convert signed arc length and a supplied radius to central angle and turns.
When to use this tool
Use Geographic Radius Angular Fraction when checking the stated geographic label, angular or height-reference convention.
How to use the tool and how it works
- Enter arcLength, suppliedRadius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read centralAngleRadians, turns. Use the output convention below.
Require suppliedRadius>0. Return signed arcLength/radius as centralAngleRadians and divide that angle by 2π for turns.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| arcLength | Signed supplied circular arc length, in the same length unit as suppliedRadius. | Required. Finite number. |
| suppliedRadius | Supplied Radius | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| centralAngleRadians | Central Angle Radians | Required. Finite number. |
| turns | Turns | Required. Finite number. |
{
"input": {
"arcLength": 10,
"suppliedRadius": 5
},
"output": {
"centralAngleRadians": 2,
"turns": 0.3183098861837907
}
}Limitations and assumptions
- Arc length and radius need matching units; this is ideal circular/spherical arc arithmetic rather than an ellipsoidal geodesic or inferred Earth radius.
- 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 authoritative coordinate/datum definitions and appropriate geodesic, projection and geoid models for actual locations, distances and height conversion.
References
Similar or alternative tools
- Geographic Bearing Screen Rotation Crosswalk
Convert a north-referenced bearing to a clockwise or counterclockwise screen rotation.
- Longitude Difference Unwrapped Sign
Calculate a signed longitude difference without wrapping around the date line.