Convergence of Meridians Approximation Calculator
Spherical transverse-Mercator meridian convergence approximation for |longitude offset|<=6 degrees; not ellipsoidal survey correction.
Description
Approximate meridian convergence from latitude and a small central-meridian longitude offset.
Meridian convergence describes an angular difference between grid north and true north under a projection convention. This calculator supplies a limited approximation from latitude and longitude offset from a central meridian.
When to use this tool
Approximate meridian convergence from latitude and a small central-meridian longitude offset. Use it when the input measurements and conventions below match the operation you need.
- Prepare latitudeDegrees, longitudeDifferenceDegrees, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter every field in the input table using the stated units and exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
For latitude from -80 to 84 degrees and longitude offset from -6 to 6 degrees, convergence is atan(tan(offset) times sin(latitude)), converted back to degrees.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeDegrees | Latitude degrees. Degrees. | Finite number; from -80 to 84 inclusive |
| longitudeDifferenceDegrees | Longitude difference degrees. Degrees. | Finite number; from -6 to 6 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.approximateConvergenceDegrees | Approximate convergence degrees; use the stated units and sign convention. |
{
"input": {
"latitudeDegrees": 30,
"longitudeDifferenceDegrees": 0
},
"output": {
"result": {
"approximateConvergenceDegrees": 0
}
}
}Limitations and assumptions
- This formula does not carry out a complete ellipsoidal projection or resolve a survey's sign convention. Supply an offset relative to the intended central meridian, not an absolute longitude.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
For a map-layout decision, inspect the rendered map at its intended size as well as its numerical dimensions. For classification or coordinate work, retain the chosen boundary and coordinate conventions with the result. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- utm central meridian zone
Central meridian in degrees for a numbered UTM zone.
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Aspect Direction Octant Classifier from Slope Components: return downhill aspect, bearing degrees.