Whether you are extending a control network, picking up topographical features, or setting out a physical boundary from a single peg, Coordinate Radiation is the fundamental math of surveying. Also known as “Forward COGO” or “Radial Pick-up,” this process involves occupying a known coordinate and calculating the position of new points using a measured bearing and horizontal distance.
While total stations handle this internally, surveyors often need to calculate coordinate radiations back in the office. If you are drafting a plan from raw field notes, verifying a traverse leg, or pre-calculating set-out points before heading to site, you need a robust, field-ready calculator. We built the Coordinate Radiation Calculator at sitemath.net to do exactly that.
Coordinate Radiation
1. Instrument Setup Station
Enter the known coordinates of your instrument setup or starting point.
2. Radial Observations
Input your measured bearing and distance to calculate the new point coordinates.
Current Observations (0)
| ID | Bearing | Hz Dist | Delta Z | Action |
|---|---|---|---|---|
| No observations added yet | ||||
Sample Data
Let's test this with a standard 4-corner boundary pegging scenario. Make sure your unit selector is set to DMS (DDD.MMSS).
Step 1: Setup Station
Setup ID: PEG_1
Setup Easting (X): 5000.000
Setup Northing (Y): 10000.000
Setup Elev (Z): 50.000
Step 2: Radial Observations
Enter these four observations to calculate the corners of a square lot:
Observation 1 (North-East Corner): * Pt ID: NE_1
Bearing: 45.0000 (45 Degrees)
Hz Dist: 100.000
Delta Z: 1.500
Observation 2 (South-East Corner): * Pt ID: SE_1
Bearing: 135.3000 (135 Deg, 30 Min)
Hz Dist: 85.500
Delta Z: -0.500
Observation 3 (South-West Corner): * Pt ID: SW_1
Bearing: 225.0000
Hz Dist: 100.000
Delta Z: -1.250
Observation 4 (North-West Corner): * Pt ID: NW_1
Bearing: 315.0000
Hz Dist: 100.000
Delta Z: 0.000
Expected Results:
Hit "Calculate New Coordinates".
NE_1: Should hit exactly E: 5070.7107, N: 10070.7107, Z: 51.5000
SE_1: Should hit E: 5060.0384, N: 9939.0435, Z: 49.5000
SW_1: Should hit E: 4929.2893, N: 9929.2893, Z: 48.7500How Coordinate Radiation Works
The math behind coordinate radiation relies on simple trigonometry applied to a local grid.
Assuming True North is your Y-axis and East is your X-axis:
- $\text{Delta Easting} = \text{Distance} \cdot \sin(\text{Bearing})$
- $\text{Delta Northing} = \text{Distance} \cdot \cos(\text{Bearing})$
Our calculator automates this entire process. You simply lock in your Setup Station coordinates once, and then you can input as many radial observations as you want. The tool will process the list and generate a clean, exportable table of your new Easting, Northing, and Elevation coordinates.
Flexible Angular Input
Because surveyors worldwide use different formats, our tool includes a global unit selector. You can type your bearings in standard DMS (DDD.MMSS) format, Decimal Degrees, or Gons (Grads) and the calculator will instantly adapt the underlying math engine.
Frequently Asked Questions (FAQs)
What is the difference between Radiation and Traversing?
Radiation involves sitting at a single known station and taking multiple “spoke-like” measurements to create new, independent points. Traversing involves moving the instrument from point to point in a chain, where each new radiated point becomes the setup station for the next measurement.
How do I format angles using the DMS input?
Our calculator uses the standard surveyor shorthand of DDD.MMSS. If your bearing is 270 degrees, 15 minutes, and 45 seconds, you simply type 270.1545 into the input field. The math engine automatically parses the decimal string into true radians for the calculation.
Do I need to enter an elevation (Z)?
No. The Setup Elevation and Delta Z fields are completely optional. If you leave them blank, the calculator will simply perform a 2D radiation (Easting and Northing only). If you are doing a 3D survey and want to carry your heights forward, just input your starting Z and the height difference (Delta Z) to the new point.