Description
chord = 2*radius*cos(latitude)*abs(sin(longitudeDifference/2)).
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.
chord = 2*radius*cos(latitude)*abs(sin(longitudeDifference/2)).
When to use this tool
Use Spherical Surface Same Latitude Chord when checking a stated spherical arc, chord or radius relationship.
How to use the tool and how it works
- Enter radius, latitude, longitudeDifference. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read chord. Use the output convention below.
Require positive radius and latitude in [-pi/2,pi/2]. chord = 2*radius*cos(latitude)*abs(sin(longitudeDifference/2)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius | Required. Finite number; strictly above 0. |
| latitude | Latitude | Required. Finite number. |
| longitudeDifference | Longitude Difference | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| chord | Chord | Required. Finite number. |
{
"input": {
"radius": 5,
"latitude": 0,
"longitudeDifference": 3.141592653589793
},
"output": {
"chord": 10
}
}Limitations and assumptions
- Angles are radians. This is the straight three-dimensional chord between same-latitude points, not parallel-circle arc length or shortest spherical surface distance.
- 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
- Distance: Spherical Arc Chord Ratio
Return arcToChordRatio = angle/(2*sin(angle/2)), using the continuous limit one at zero.
- Weighted Geodesic Radius Derivative
radiusDerivative = centralAngleRadians*weight, the radius derivative of weighted spherical arc length with the angle fixed.