There is a residual computation error at level of about 10 ppm, reasons unknown. The residual error is practically meaningless when computing Maidenhead distances, which usually are computed with spheroid equations and thus can have about 0.1 - 0.2 % error due to wrong geodetics...

Source format: KKJ P/I, KKJ Lat/Long, WGS84 Lat/Long, Maidenhead, Explanations.

Various commentaries / explanations:

A very short intro to KKJ coordinates into here...

The P coordinate is meters north from the equator, at 60° north about 6.7 million, and at 70° north about 7.8 million.

The I coordinate is also given in meters east the projection zone centre meridian plus 500 000 to make sure there are no negative numbers. Further complication is that the ``millions'' (1-4) are telling which of the 4 zones the coordinate is valid.

This program has been made to handle the Uniform Coordinates (zone 3) for the whole Finland. Accuracy further away from the meridian of 27° east is compromised, don't use for positions more precise than 2m...

On Latitude (P-coordinate) 0.0001 arc-minutes corresponds to 0.185 meters. 0.01 arc-seconds corresponds to 0.30 meters. Longitudal correspondence of angle to linear measure varies by factor of ``cos(Latitude)''

Explanations for KKJ-P/I to Lat/Long (KKJ and WGS84) conversions:

The method used for this tool is to iteratively search for a Lat/Long pair within a source rectangle so that it matches as closely to the user input as possible. The source rectangle is: Latitude: 58.0° to 71.0°, and Longitude: 19° to 35°. Search is done iterating 32 times giving theorethically 1440000/(2^32) = 0.00034 meter resolution. Inaccuracy of Lat/Long-to-KKJ-P/I projection limits the result's reliability. (The algorithm is somewhat modified as source and destination coordinates are not in linear correspondence with each other. Strict halving may lead into locking at a wrong Lat/Long coordinate.)

At the midline meridian the conversion is quite accurate, but at 2 degrees from the meridian it deviates several centimeters, and at 10+ degrees it is meters off.

Explanations for conversion from geographic KKJ coordinates (Finnish Hayford) to KKJ-P/I and WGS84 Lat/Long.

This conversion to WGS84 does use a 2nd degree polynomial transfer functions per M.Ollikainen 1994 (Internal memo of Finnish Geodetical Institute.) Largest errors are about 0.50 meters, but when using this for near-by positions ( < 30 km away ), error is usually same size and direction at both sites, or at least the error difference is negligible.

Explanations for Converting from Maidenhead Grid to WGS84 coordinates and KKJ grid:

This tool consists of following source components:

• mhbearing.php: The main code itself
• kkj-funcs.php: Common stuff, coordinate transformations, HTML things, etc.
• maidenheadfuncs.php: Maidenhead grid coordinate processing
• geodinver.php: Mathematics for the "geodetic inverse" problem. (Finding distance and Azimuth between two points on an ellipsoid.)
• selitykset.php: Explanations seen above...

Matti Aarnio <matti.aarnio@zmailer.org>; OH2MQK