Coordinate Frame Convert Online

The online coordinate conversion tool supports coordinate conversion between different coordinate systems. It supports the input of coordinates in spatial rectangular coordinate systems and geodetic coordinate systems. It also supports the input of two-dimensional planar coordinates, three-dimensional spatial coordinates, and four-dimensional spatiotemporal coordinates. Supports coordinate conversion with two, three, four, five, and seven parameters. Supports kinematic versions for corresponding parameter conversions.

1. Input Type : Select the type of coordinates to be input. This tool supports the following coordinate types:
   1. XYZ : Input 3D Cartesian coordinates, separated by commas, with one coordinate per line. Multiple lines are supported. The spatial rectangular coordinate format is X, Y, Z with units of meters (m). If you want to input two-dimensional plane coordinates, simply input 0 for the Z value.
   2. XYZT : Input the Cartesian coordinates in four-dimensional spacetime, separated by commas, with one coordinate per line. Multiple lines are supported. The format of the Cartesian coordinates in spacetime is X, Y, Z, T. The units of XYZ are meters (m), and T represents a decimal years. If you want to input the coordinates in flat spacetime, simply set the Z value to 0.
   3. LBH : Input geodetic coordinates, separated by commas, with one coordinate per line. Multiple lines are supported. The geodetic coordinate format is L, B, H. L represents the geodetic longitude, B represents the geodetic latitude, and the unit is degree (°), H represents the geodetic height, with the unit being meters (m). If you want to input planar geodetic coordinates, you can simply input 0 for the H value.
   4. LBHT : Input the spatio-temporal geodetic coordinates, separated by commas, with one coordinate per line. Multiple lines are supported. The spatial-temporal geodetic coordinate format is L, B, H, T. L represents the geodetic longitude, B represents the geodetic latitude, and the unit is degree (°), H represents the geodetic height, with the unit being meters (m), and T denotes a decimal years. If you are to input the plane spacetime geodetic coordinates, simply set the H value to 0.
2. Input Coordinates : Input the coordinates to be converted, with one coordinate per line. Up to 10,000 coordinates are supported for input. The coordinate format and type are determined by the Input Type parameter.
3. If the coordinate type is geodetic coordinates or spatio-temporal geodetic coordinates, you need to select the ellipsoid used by the coordinates or customize the ellipsoid through parameters. If the input coordinate type is geodetic coordinates or spatio-temporal geodetic coordinates, the input coordinates should be converted to spatial rectangular coordinates before further coordinate transformation. If the output coordinate type is geodetic coordinates or spatio-temporal geodetic coordinates, the converted spatial rectangular coordinates will be transformed into geodetic coordinates before the result is returned. This tool supports the following ellipsoids:

   Name	Semi-major Axis(a)	Reverse Flattening(rf)
   MERIT	6378137.0 m	298.257
   SGS85	6378136.0 m	298.257
   GRS80	6378137.0 m	298.257222101
   IAU76	6378140.0 m	298.257
   GRS67	6378160.0	298.2471674270
   helmert	6378200 m	298.3
   WGS60	6378165.0 m	298.3
   WGS66	6378145.0 m	298.25
   WGS72	6378135.0 m	298.26
   WGS84	6378137.0 m	298.257223563
   Beijing54	6378245 m	298.3
   Xian80	6378140 m	298.2570
   CGCS2000	6378137 m	298.257222101
   Custom	Custom, with unit of meter and range of 6370000 - 6379999	Custom, with a range of 270 - 300

4. Transform Type : Select the type of coordinate transformation. This tool supports the following transform types:

   Type	Category	Property	Parameters	Description
   Two Parameter	2D Transform	Static Transform	x, y	Use x-axis translation and y-axis translation to transform coordinates
   Two Parameter Kinematic	2D Transform	Kinematic Transform	x, y, dx, dy, tepoch	Convert coordinates using x-axis translation, y-axis translation, x-axis translation speed (dx), y-axis translation speed (dy), and center epoch (tepoch)
   Three Parameter	2D Transform	Static Transform	x, y, z	Convert coordinates using x-axis translation, y-axis translation, and z-axis translation
   Three Parameter Kinematic	2D Transform	Kinematic Transform	x, y, z, dx, dy, dz, tepoch	Convert coordinates using x-axis translation, y-axis translation, z-axis translation, x-axis translation speed (dx), y-axis translation speed (dy), z-axis translation speed (dz), and center epoch (tepoch)
   Four Parameter 1	2D Transform	Static Transform	x, y, z, theta	Convert coordinates using x-axis translation, y-axis translation, z-axis translation, and plane rotation angle theta
   Four Parameter 1 Kinematic	2D Transform	Kinematic Transform	x, y, z, theta, dx, dy, dz, dtheta, tepoch	Convert coordinates using x-axis translation, y-axis translation, z-axis translation, plane rotation angle theta, x-axis translation speed (dx), y-axis translation speed (dy), z-axis translation speed (dz), plane rotation angular speed (dtheta), and center epoch (tepoch)
   Four Parameter 2	2D Transform	Static Transform	x, y, theta, s	Transform the coordinates using x-axis translation, y-axis translation, plane rotation angle theta, and scale factor s
   Four Parameter 2 Kinematic	2D Transform	Kinematic Transform	x, y, theta, s, dx, dy, ds, dtheta, tepoch	Transform the coordinates using x-axis translation, y-axis translation, plane rotation angle theta, scale factor s, x-axis translation speed (dx), y-axis translation speed (dy), plane rotation angular speed (dtheta), scale factor speed (ds), and epoch center (tepoch)
   Five Parameter	2D Transform	Static Transform	x, y, z, theta, s	Transform the coordinates using x-axis translation, y-axis translation, z-axis translation, plane rotation angle theta, and scale factor s
   Five Parameter Kinematic	2D Transform	Kinematic Transform	x, y, z, theta, s, dx, dy, dz, dtheta, ds, tepoch	Convert coordinates using x-axis translation, y-axis translation, z-axis translation, plane rotation angle theta, scale factor s, x-axis translation speed (dx), y-axis translation speed (dy), z-axis translation speed (dz), plane rotation angular speed (dtheta), scale factor speed (ds), and epoch center (tepoch)
   Seven Parameter	3D Transform	Static Transform	x, y, z, rx, ry, rz, s	Convert coordinates using x-axis translation, y-axis translation, z-axis translation, x-axis rotation angle (rx), y-axis rotation angle (ry), z-axis rotation angle (rz), and scale factor s
   Seven Parameter Kinematic	3D Transform	Kinematic Transform	x, y, z, rx, ry, rz, s, dx, dy, dz, drx, dry, drz, ds, tepoch	Convert coordinates using x-axis translation, y-axis translation, z-axis translation, x-axis rotation angle (rx), y-axis rotation angle (ry), z-axis rotation angle (rz), scale factor s, x-axis translation speed (dx), y-axis translation speed (dy), z-axis translation speed (dz), x-axis rotation angular velocity (drx), y-axis rotation angular velocity (dry), z-axis rotation angular velocity (drz), and scale factor speed ds

5. Detailed explanation of the definition of rotation angle direction:
   1. Coordinate conversion runs by default in the right-handed spatial Cartesian coordinate system.
   2. If the coordinate transformation has a rotation angle (such as theta or rx, ry, rz), the rotation angle has two directions defined, The rotation angle direction applied to the coordinate axis and the rotation angle direction applied to the coordinate point.
   3. Table of rotation angle directions for four and seven parameters:

      Transform Type	Convention	Parameters	Apply to Coordinate Frame	Apply to Position Vector	Note
      Four parameters	Default	theta	Anticlockwise is positive	Clockwise is positive	The four parameter related tools on this site are defined in this direction
      Seven parameters	coordinate_frame	rx, ry, rz	Clockwise is positive	Anticlockwise is positive	reference document EPSG 1032
      Seven parameters	position_vector	rx, ry, rz	Anticlockwise is positive	Clockwise is positive	reference document EPSG 1033

6. When filling in the parameters for coordinate conversion, it is essential to ensure that the parameters are entered correctly and that the units of the parameters are in accordance with the required units. Detailed parameter description for coordinate transformation:
   1. x : Translation of the x-axis given in meters.
   2. y : Translation of the y-axis given in meters.
   3. z : Translation of the z-axis given in meters.
   4. theta : Rotation angle in the 2D Helmert given in arc seconds. The rotation angle direction is clockwise. If counterclockwise rotation is required, the theta value needs to be negated.
   5. s : Scale factor. In 2D coordinate transformation, s has no unit. In 3D coordinate transformation, s is measured in ppm.
   6. rx : X-axis rotation in the 3D Helmert given arc seconds.
   7. ry : Y-axis rotation in the 3D Helmert given arc seconds.
   8. rz : Z-axis rotation in the 3D Helmert given arc seconds.
   9. dx : Translation rate of the x-axis given in m/year.
   10. dy : Translation rate of the y-axis given in m/year.
   11. dz : Translation rate of the z-axis given in m/year.
   12. dtheta : In 2D coordinate transformation, the angular speed of plane rotation is measured in arc seconds per year. The direction of the rotational angular speed is clockwise. If counterclockwise rotation is required, the value of dtheta needs to be negated.
   13. ds : Scale factor speed: In 2D coordinate transformation, the unit of ds is /year. In 3D coordinate transformation, the unit of ds is ppm/year.
   14. drx : Rotation rate of the x-axis given in arc seconds/year.
   15. dry : Rotation rate of the y-axis given in arc seconds/year.
   16. drz : Rotation rate of the z-axis given in arc seconds/year.
   17. tepoch : Central epoch of transformation given in decimalyear. Only used spatiotemporal transformations.
   18. convention : Indicates the convention to express the rotational terms when a 3D transform is involved. As soon as a rotational parameter is specified (one of rx, ry, rz, drx, dry, drz), convention is required. The two conventions are equally popular and a frequent source of confusion. The coordinate frame convention is also described as an clockwise rotation of the coordinate frame. It corresponds to EPSG method code 1032 (in the geocentric domain) or 9607 (in the geographic domain) The position vector convention is also described as an anticlockwise (counter-clockwise) rotation of the coordinate frame. It corresponds to as EPSG method code 1033 (in the geocentric domain) or 9606 (in the geographic domain). The result obtained with parameters specified in a given convention can be obtained in the other convention by negating the rotational parameters (rx, ry, rz, drx, dry, drz)
   19. exact : Choose whether to compute the rotation matrix precisely or approximately. This is a parameter used for 3D coordinate transformation. When high-precision coordinate transformation is required, or when any rotation angle exceeds 0.1 arc seconds, the rotation matrix should be precisely calculated.
   20. The conversion convention for the Bursa-Wolf seven-parameter calculation model needs to be set as position_vector. Then, decide whether to precisely calculate the rotation matrix based on your needs.
7. Coordinate Transform Formula:
   1. Parameter calculation for kinematic conversion: , is the kinematically adjusted version of P, is the rate of change of a given transformation parameter P, t is the observation time of the coordinate, is the central epoch of the transformation.
   2. 2D Static Transform Formula:
      , are the converted XY coordinates, , are x-axis translation, y-axis translation. s is the scaling factor, and θ is the clockwise plane rotation angle. , is the input XY coordinates. 2D static coordinate transformation does not involve rotation about the z-axis. If there are parameters related to translation along the z-axis, additional transformation of the z-axis coordinates will be performed.
   3. 2D Kinematic Transform Formula:
      2D kinematic coordinate transformation does not involve z-axis rotation. If there are parameters related to z-axis translation, then the z-axis coordinates will be additionally transformed.
   4. 3D Coordinate Transform Formula:
      1. The general formula for 3D coordinate transformation is: ， is the output coordinate, T is a vector consisting of the three translation parameters, s is the scaling factor, is a rotation matrix, is the input coordinate.
      2. In position_vector convention, Rx=radians(rx), Ry=radians(ry), Rz=radians(rz) . In coordinate_frame convention, Rx=-radians(rx), Ry=-radians(ry), Rz=-radians(rz) . The rotation matrix for each coordinate axis is:
         The formula for the rotation matrix R is
         The expanded formula is
         When the rotation angle is small (such as less than 0.1 arc seconds), the rotation matrix R can be approximated as
      3. Approximate calculation formula for 3D static transformation:
      4. Approximate calculation formula for 3D dynamic transformation:
8. Open File : Supports opening text files encoded in UTF-8.
9. Download Format : Select the download file format for the conversion results. This tool supports txt, csv, and json download formats.
10. This tool has a certain frequency limit, please use this tool reasonably. Anonymous : 30/IP*Hour, Normal user : 30/Hour, VIP : 720/Hour.
    Anonymous and normal users can only input one coordinate at a time, and batch conversion is not supported. VIP and advanced VIP users support batch conversion.