Coordinate Geometry (COGO) Point Calculator

COGO means coordinate geometry. In surveying and civil layout, a COGO point calculation projects a new point from a known coordinate using a bearing or azimuth and a horizontal distance. It is the basic operation behind boundary calls, construction offsets, stakeout points, parcel line work, traverse legs, and simple GIS sketches.

This calculator handles the most common COGO task: start point plus direction plus distance equals destination point. Grid mode is designed for easting and northing coordinates from a local site grid, state plane grid, UTM grid, or construction coordinate system. Latitude/longitude mode is useful when the starting point is in WGS84 decimal degrees and you need an approximate destination point from a bearing and distance.

In planar coordinate geometry, azimuth is measured clockwise from north. A zero-degree azimuth moves straight north, 90 degrees moves east, 180 degrees moves south, and 270 degrees moves west. The distance vector is split into an east component and a north component using sine and cosine.

The formulas are simple but the convention matters. Because the angle is measured from the north axis, delta easting is distance times sine of the azimuth, and delta northing is distance times cosine of the azimuth. The destination easting is the starting easting plus delta easting. The destination northing is the starting northing plus delta northing.

That sign convention is why a bearing in the southeast quadrant has positive easting and negative northing, while a northwest bearing has negative easting and positive northing. The calculator reports the deltas so you can check whether the movement direction matches the intended field call.

Azimuth is a single angle from 0 to 360 degrees, measured clockwise from north. Quadrant bearing uses a north or south reference, an acute angle from 0 to 90 degrees, and an east or west direction. A line written as N 35 E has an azimuth of 35 degrees. A line written as S 35 E has an azimuth of 145 degrees.

Survey plats and deed calls often use quadrant bearing notation, while GIS tools and programming formulas usually use azimuth. This calculator accepts both formats and returns both in the result, including the back azimuth. The back azimuth is the opposite direction of the line, offset by 180 degrees.

Grid coordinates are flat projected coordinates. Easting and northing are usually in meters, feet, or survey feet. On a site grid or projected CRS, short COGO lines are direct trigonometry problems. That is the best mode for construction staking, parcel sketching, road layout, and traverse examples.

Latitude and longitude are angular coordinates on the earth. A true destination point on the globe is a geodesic problem, not just a flat sine and cosine projection. The geographic mode uses a standard spherical direct-geodesic formula with the mean earth radius. It is appropriate for mapping, teaching, planning, and short field estimates, but precise long-distance survey work should use an ellipsoidal geodesic method tied to the project datum.

COGO point projection is used whenever a new point is described by a known point, a direction, and a distance. Typical examples include projecting a property corner from a deed call, laying out an offset point from a baseline, checking a traverse leg, creating approximate GIS features from field notes, and teaching how coordinate deltas work.

It also pairs naturally with inverse calculations. If you already have two coordinates and need the distance and bearing between them, use the distance and bearing calculator. If you are checking a closed survey loop, use the traverse closure calculator to inspect misclosure and adjustment.

This tool calculates mathematical destination points from the values you enter. It does not replace a licensed survey, local coordinate system documentation, ground-to-grid scale factors, combined scale factors, datum transformations, magnetic declination corrections, or legal boundary interpretation.

For grid work, make sure your distance units match the coordinate system units. For geographic work over long distances, use a datum-aware geodesic tool or professional GIS software. The calculator warns when the geographic distance exceeds 100 km because spherical approximations can drift from ellipsoidal results as distance increases.