# Calculating with coordinates

These calculations are based on GeographicLib, resulting in a very high accuracy; even on long distances.
Calculations are performed along a great circle, the shortest distance over the earth's surface. This results in curved lines on the map, which can be clearly seen on long distances.

The lines and circles can sometimes have a strange appearance; this is the case when the borders of the visible map are exceeded (the earth is a slightly flattened sphere; sometimes the shortest path runs via the poles or the "rear").

You can put a moveable marker on the map with the button "User marker"; the coordinates are shown right above it.

The calculations will be executed automatically after you change a value in a input box.

You can select the units for the display of calculated coordinates (see below), of calculated distances ((kilo)meters, feet/miles or nautical miles) and of calculated bearings (degrees (°) or gradians (gon)). You can also select the unit when entering distances and bearings or angles.

This tool supports coordinates in several different notations:

 WGS84 coordinates: example decimal 52.09495,5.13393 degrees N 52.09495° E 5.13393° degrees and minutes N 52° 05.697' E 005° 08.036' degrees, minutes and seconds N 52° 5' 41.8" E 005° 8' 2.1" Universal Transverse Mercator: 31U 646177 5773747 Dutch Grid: 137644,456329

The tool recognizes the used notation automatically. The examples all relate to the same point.

Explanation option 14 & 15: Triangulation

Figure 1: The coordinates of points A and B are known; those of point P aren't. Measure the angles between the lines AP and AB (angle α) and between the lines BA and BP (angle β). Using triangulation you can determine the coordinates of point P.

Figure 2: Standing at the observer position P with unknown coordinates you can see three points with known coordinates: A, B and C. Measure the angles between the lines PA and PB (angle α) and between the lines PB and PC (angle β). Now you can determine the coordinates of point P with the theory behind the Snellius-Pothenot problem. Explanation option 17: Distance to horizon

Here you can enter your position and eye level. When you don't want to know the distance to the horizon on ground level, but instead the distance to where you can still see an object, enter the height of the object too.

The earth isn't a perfect sphere; it is flattened at the poles. Because of this the distance to the horizon in north/south direction is smaller than the distance in west/east direction.

The tool calculates the distance over ground to the horizon. The straight line distance is almost the same when using small heights; when using greater heights it will be larger (but still neglectable in proportion to the total distance).

Because light is refracted by the atmosphere, the observed horizon will be further away than the true horizon. This effect is highly dependent on the differences in temperature above the surface of the earth, and it's impossible to calculate the distance to the observed horizon exactly with this tool. The calculations use the factor 7/6 for the radius of the earth as a rule of thumb.
(see also the article Distance to the Horizon. Contrary to this article this tool does take into account the flattening of the earth)

The blue circle is the true horizon; the green one is the observed horizon.

1. Distance and center point between two points
2. Distance from a point to a line
3. Projecting a point
4. Intersection of the lines from two points with a defined bearing
5. Intersection of the lines between four points
6. Intersection of line with defined bearing and line between two points
7. Center of gravity, area and perimeter of a triangle
8. Orthocenter, circumscribed and inscribed circle of a triangle
9. Center of gravity, area and perimeter of a quadrilateral
10. Intersection points of two circles
11. Intersection point of three circles
12. Intersection points of a line and a circle
13. Circle through three points
14. Triangulation
15. Triangulation: Snellius-Pothenot problem
16. Area, perimeter and center of gravity of a polygon
17. Distance to horizon
Display calculated coordinates:

Display calculated distances:
(kilo)metres feet/miles nautical miles

Display calculated bearings:
degrees (°) decimal degrees (gon)

Map:

Regular version

hoi