Description
Calculate a signed two-point geoid-undulation gradient in m/km and dimensionless slope.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Calculate a signed two-point geoid-undulation gradient in m/km and dimensionless slope.
When to use this tool
Use this tool when you need to calculate a signed two-point geoid-undulation gradient in m/km and dimensionless slope.
How to use the tool and how it works
- Enter firstUndulationMeters, secondUndulationMeters, distanceKm using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.signedMetersPerKm, result.dimensionlessSlope, using the stated boundary, ordering, sign and absence conventions.
Subtract first undulation from second and divide by positive distanceKm for m/km. Divide by an additional 1000 for dimensionless slope.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstUndulationMeters | First geoid undulation in meters, magnitude≤1000. | Finite numeric value satisfying the stated comparisons. |
| secondUndulationMeters | Second geoid undulation in meters, magnitude≤1000. | Finite numeric value satisfying the stated comparisons. |
| distanceKm | Positive separation/route length in kilometers, with the operation-specific bound stated above. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.signedMetersPerKm | Second-minus-first geoid undulation per kilometer. |
| result.dimensionlessSlope | Second-minus-first undulation divided by separation in meters. |
{
"input": {
"firstUndulationMeters": 10,
"secondUndulationMeters": 12,
"distanceKm": 2
},
"output": {
"result": {
"signedMetersPerKm": 1,
"dimensionlessSlope": 0.001
}
}
}Limitations and assumptions
- Undulations are within ±1000 m and distance in (0,10,000] km. This is a signed two-point slope of supplied geoid values, without geoid interpolation, uncertainty or a vertical-deflection model.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
Similar or alternative tools
- Orthometric Height H from h minus N Calculator
Convert ellipsoidal height to orthometric height using a supplied compatible geoid undulation.
- Ellipsoidal Height h from H plus N Calculator
Convert orthometric height to ellipsoidal height using a supplied compatible geoid undulation.