First, we will give a example for a transformation of reference frame for Continental Portugal. The input frame is ETRS89 and the output frame is Datum73. All coordinates will be given in the Universal Transverse Mercator coordinate system. That is, we have Easting, Northing and ellipsoidal height, all with metre as unit. In a new tab, open the main web application and:

Select as Input Frame
ETRS89/PT-TM06 (EPSG:3763)

Select as Output Frame
Datum73/Hayford-Gauss (EPSG:27493), also select ellisoidal height for the output.

Insert as Input Coordinates
-48246.833; 250393.5715; 701.784

Keep ellipsoidal heights both in the input and output. After selecting the Bursa-Wolf method, and clicking on the "transform" button, you should get:
-48242.355; 250396.600; 643.677

If you change the transformation method to 'Grid NTv2', you should get:
-48242.055; 250397.550; 701.784

.

The 'Grid NTv2' method does not alter heights but only performs a transformation in the horizontal plane. However, if you now select orthometric heights for the output, you should get:
-48242.055; 250397.550; 646.417

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Using the same input and output frame and only ellipsoidal heights, now enter the coordinate:
60120.415; -207760.586; 316.010

.

For the Bursa-Wolf method, you should get:
60117.045; -207762.685; 262.878

.

For the Grid NTv2 method, you should get:
60116.858; -207762.256; 316.010

.

For the Grid NTv2 method, but selecting orthometric height for the output, you should get:
60116.858; -207762.256; 261.098

.

Of course, the inverse transformation should again give us the original coordinates. Again, select ellipsoidal height for both the input and output frame.

Select as Input Frame
Datum73/Hayford-Gauss (EPSG:27493)

Select as Output Frame
ETRS89/PT-TM06 (EPSG:3763)

Insert as Input Coordinates
-48242.355; 250396.600; 643.678

Keep ellipsoidal heights both in the input and output. After selecting the Bursa-Wolf method, and clicking on the "transform" button, you should get:
-48246.833; 250393.571; 701.784

The transformation of coordinates from Datum73 to the Datum Lisbon frame is computed in two steps, first the coordinates are transformed to ETRS89 after which they are transformed to Datum Lisbon. Of course, the user does not notice anything about this.

Select as Input Frame
Datum73/Hayford-Gauss (EPSG:27493)

Select as Output Frame
DatumLisboa/Hayford-Gauss (EPSG:5018)

Insert as Input Coordinates
-48242.355; 250396.600; 643.678

Keep ellipsoidal heights both in the input and output. After selecting the Bursa-Wolf method, and clicking on the "transform" button, you should get:
-48245.900;250397.480;639.100

Next, do the following:

Select as Input Frame
EPSG:5018 (DatumLisboa/Hayford-Gauss)

Select as Output Frame

Insert as Input Coordinates
-48245.900;250397.480;639.100

Keep ellipsoidal heights both in the input and output. After selecting the Bursa-Wolf method, and clicking on the "transform" button, you should get:
-48246.840;250393.570;701.790
which is equal to our first example. This proves that all transformations can be performed in various steps and in any order. The reason for this is that the Bursa-Wolf transformation is a linear operation.

For the other regions, the procedure is the same. For example, select the Azores region.

Select as Input Frame
ITRF93/PTRA08-UTM 25N - Western Azores (EPSG:5014)

Select as Output Frame
Datum Observatório (Flores)/UTM 25N - Western Azores (EPSG:2188)

Insert as Input Coordinates
661832.145; 4395153.084; 551.047

The Azores are divided into a western part (UTM zone 25N) that constains everything west of -30 degrees longitude. Keep ellipsoidal heights both in the input and output. After selecting the Bursa-Wolf method, and clicking on the "transform" button, you should get:
662209.069;4395086.880;493.775

In you now select orthometric heights for the output, you should get:
662209.069; 4395086.880; 493.794

Select the Continental Portugal region.

Select as Input Frame
ETRS89 - Geodetic Coordinates (EPSG:4937)

Select as Output Frame
ETRS89 - Cartesian Coordinates (EPSG:4936)

Insert as Input Coordinates
40.12564; -8.23874; 55.342

Keep ellipsoidal heights both in the input and output. After selecting the Bursa-Wolf method, and clicking on the "transform" button, you should get:
4833368.341; -699835.242; 4088698.134

Note that here we are not transforming from one frame to another, just changing the coordinate system from geodetic coordinates to cartesian coordinates. Thus, the method does not matter.

let us now switch the input and output frame and enter the output as input:

Select as Input Frame
ETRS89 - Cartesian Coordinates (EPSG:4936)

Select as Output Frame
ETRS89 - Geodetic Coordinates (EPSG:4937)

Insert as Input Coordinates
4845133.828;-680939.153; 4078020.925

You should get:
40° 0' 0.00";-8° 0' 0.00";54.999
which is again the value we started with.