Geodesy

Moving coordinates between datums, frames, and epochs.

• Helmert transformation (7 or 14 parameters)

  Applies a 7-parameter Helmert transformation, or a 14-parameter time-dependent one with rates, to ECEF coordinates, in the position-vector or coordinate-frame convention you name, forward or exactly reversed.

• Transform between ITRF and WGS 84 realizations

  Transforms a position between International Terrestrial Reference Frame realizations (ITRF2020 back to ITRF88) and the WGS 84 realizations aligned with them, at the coordinates' epoch, with the IERS parameters.

• Legacy datum to or from WGS 84

  Converts a latitude and longitude between a legacy datum (ED50, NAD27, OSGB36, Tokyo, AGD66, Pulkovo 1942, SAD69, or Arc 1960) and WGS 84 with the published EPSG transformation, and states its accuracy, which is meters, not centimeters.

• Transform between NAD 83 and ITRF or WGS 84

  Transforms a position between NAD 83 (2011, PA11, or MA11) and ITRF2020, ITRF2014, ITRF2008, ITRF2005, ITRF2000, or WGS 84 at one epoch, with the NGS HTDP parameters, and shows the meter-level difference between them.

• Old US datums to NAD 83 (NADCON5)

  Converts a latitude and longitude from a region's old datum to NAD 83 with the NGS NADCON5 grids, or back: NAD 27 in the conterminous US and Alaska, Old Hawaiian, Puerto Rico 1940, St. Paul 1952, American Samoa 1962, and Guam 1963.

• Move a position between epochs (ITRF2020 plate motion)

  Propagates an ITRF2020 position from one epoch to another with the rigid-plate velocity of its tectonic plate, or with a site velocity you give, and flags zones where plates deform and rigid motion does not apply.

Ellipsoid parameters, radii, and auxiliary latitudes.

• Auxiliary latitudes

  Converts between geodetic latitude and the geocentric, parametric (reduced), rectifying, conformal, authalic, and isometric latitudes, in either direction.

• Ellipsoid parameters

  The defining and derived parameters of a reference ellipsoid: semi-minor axis, flattening, eccentricities, third flattening, and the mean, authalic, and volumetric radii.

• Radii of curvature and degree lengths

  At a latitude: the meridional and prime-vertical radii of curvature, their Gaussian mean, the radius in any azimuth, the length of one degree of latitude and longitude, and the meridian arc from the equator or between two latitudes.

Earth-centered and local coordinates.

• ECEF to latitude, longitude, and height

  Converts Earth-centered, Earth-fixed X, Y, Z to geodetic latitude, longitude, and ellipsoidal height, in closed form at any height.

• Local ENU, NED, or AER to point

  Finds the latitude, longitude, height, and ECEF position of a point given in a local tangent plane at an origin: east-north-up, north-east-down, or azimuth-elevation-range.

• Latitude, longitude, and height to ECEF

  Converts geodetic latitude, longitude, and ellipsoidal height to Earth-centered, Earth-fixed X, Y, Z.

• Point to local ENU, NED, and AER

  Expresses a target point in a local tangent plane at an origin: east-north-up, north-east-down, and azimuth-elevation-range, with the rotation matrix on request.

The geoid height that separates GPS heights from heights above sea level.

• Geoid height (EGM96)

  The geoid height N (geoid undulation) above the WGS 84 ellipsoid at any point from the EGM96 global geoid, the number that turns GPS ellipsoidal heights into heights above mean sea level.

Military, aviation, and radio grid references.

• Latitude and longitude to GARS

  Encodes a latitude and longitude as a Global Area Reference System cell: 30′ cell, 15′ quadrant, or 5′ keypad, with its bounds.

• GARS to latitude and longitude

  Decodes a Global Area Reference System code (5 to 7 characters) to the center and bounds of its cell, quadrant, or keypad.

• Latitude and longitude to GEOREF

  Encodes a latitude and longitude in the World Geographic Reference System (GEOREF) from a 15° tile down to thousandths of a minute, with the cell's bounds.

• GEOREF to latitude and longitude

  Decodes a World Geographic Reference System (GEOREF) code to the center and bounds of its cell.

• Latitude and longitude to Maidenhead locator

  Encodes a latitude and longitude as a Maidenhead (QTH) locator of 2 to 10 characters, as used in amateur radio, with the cell's bounds.

• Maidenhead locator to latitude and longitude

  Decodes a Maidenhead (QTH) locator of 2 to 10 characters, in any letter case, to the center and bounds of its cell.

• Latitude and longitude to MGRS

  Encodes a WGS 84 latitude and longitude as an MGRS grid reference at any precision, truncating (never rounding) as the standard requires.

• MGRS to latitude and longitude

  Decodes an MGRS or USNG grid reference to the south-west corner and center of the square it names, with the square's size.

• Latitude and longitude to USNG

  Encodes a latitude and longitude as a U.S. National Grid reference, written with spaces (17T NE 86309 77770), truncating to the precision chosen.

• USNG to latitude and longitude

  Decodes a U.S. National Grid reference, including a truncated local one like NE 863 777 when you give the grid zone, to the center and south-west corner of the square it names.

Ellipsoidal and orthometric heights.

• Ellipsoidal and orthometric height

  Converts a GPS ellipsoidal height to height above mean sea level (orthometric) or back, with h = H + N and the EGM96 geoid height N.

Magnetic declination and true and magnetic bearings.

• Magnetic declination

  Magnetic declination (variation), inclination, and field strength at any place and date from the World Magnetic Model 2025 or IGRF-14, with the model's uncertainty and compass warning zones.

• Grid variation (grivation)

  The angle from grid north (UTM or UPS) to magnetic north, for navigating by a grid near the poles or on military maps: declination minus grid convergence, with the sign convention stated.

• True and magnetic bearings

  Converts a true bearing to magnetic or back, with a chart variation like 12°W, the magnetic model at a place and date, or both side by side.

Reading, formatting, and comparing coordinates and bearings.

• Add and subtract DMS angles

  Adds and subtracts angles in degrees, minutes, and seconds (or decimal degrees), carrying seconds and minutes exactly, with the result normalized to 0-360° or ±180° if you like.

• Difference between two bearings

  The smallest signed turn from one bearing to another, across north when needed.

• Read any coordinate

  Reads a coordinate in almost any notation (decimal, DMS, DDM, packed aviation, labeled, MGRS, or UTM) and reports what it assumed.

• Format a coordinate

  Writes a latitude and longitude as decimal degrees, DMS, or DDM with the precision you choose, and tells you what that precision means on the ground.

Corrections for lines drawn on a map projection.

• Arc-to-chord correction (t − T)

  The small angle between a line's straight grid bearing and its curved projected geodesic, at each end, in UTM or a State Plane zone, with the grid and ellipsoid distances.

State plane coordinates (SPCS83).

• Latitude and longitude to state plane (SPCS83)

  Converts NAD83 latitude and longitude to State Plane Coordinate System of 1983 easting and northing in any of the 124 zones, in meters, international feet, or US survey feet, with convergence and scale factor.

• State plane (SPCS83) to latitude and longitude

  Converts SPCS83 easting and northing in any of the 124 zones back to NAD83 latitude and longitude, with convergence and scale factor.

• State plane zone lookup

  Finds SPCS83 zones by state or zone name, or the zones whose area of use covers a point, with each zone's NGS code, EPSG code, projection, and feet unit.

Universal Polar Stereographic, for the polar caps UTM does not cover.

• Latitude and longitude to UPS

  Converts polar coordinates (84° N and beyond, or 80° S and beyond) to Universal Polar Stereographic easting and northing.

• UPS to latitude and longitude

  Converts a Universal Polar Stereographic easting and northing back to latitude and longitude.

Universal Transverse Mercator.

• Latitude and longitude to UTM

  Converts a latitude and longitude to UTM zone, easting, and northing, with the Norway and Svalbard zone exceptions, an optional forced zone, and the grid convergence and scale factor.

• UTM to latitude and longitude

  Converts a UTM zone, hemisphere, easting, and northing back to latitude and longitude, with the grid convergence and scale factor.

• UTM zone and band lookup

  The UTM zone and MGRS latitude band for a point, including the Norway and Svalbard exceptions, and the zone's central meridian.