Coordinate Inverse Calculator
📍 Point A (Start / Instrument Station)
🎯 Point B (End / Target Station)
Horizontal Distance
0.000 m
Whole Circle Bearing
0° 00' 00"
Delta N (Latitude)
0.000
Delta E (Departure)
0.000
What is the Coordinate Inverse Calculation?
In modern topographical surveying, every physical location is defined by a Cartesian coordinate pair: Northing (Y-axis) and Easting (X-axis). The "Inverse" calculation is the mathematical process of taking two known coordinates and computing the straight-line horizontal distance and the directional bearing between them.
Why is this calculation used daily?
- Traverse Checking: Before starting a day of surveying, engineers must check the distance between two known control points (benchmarks) to ensure their Total Station is calibrated correctly.
- Setting Out / Staking: If an engineer needs to physically place a peg for a building column, they input the coordinates. The instrument performs an inverse calculation to tell the surveyor exactly what angle to turn and how far to walk.
- Missing Line Measurement (MLM): Finding the precise distance between two inaccessible points (like the tops of two separate buildings) by shooting their coordinates from a third location.
The Surveying Formulas
The calculation relies on basic trigonometry and the Pythagorean theorem. First, we find the differences between the coordinates, known in surveying as Latitude (ΔN) and Departure (ΔE).
1. Calculate Differences (Partials)
ΔN = N2 - N1
ΔE = E2 - E1
2. Horizontal Distance (Length)
Distance = √(ΔN² + ΔE²)
3. Bearing (Angle)
θ = tan-1 ( ΔE / ΔN )
*Note: Depending on whether ΔN and ΔE are positive or negative, Quadrant Rules must be applied to convert the raw angle into a 360° Whole Circle Bearing (WCB).
Solved Example
Given Field Data:
Station A (Instrument): N = 1000.00, E = 1000.00
Station B (Target): N = 1020.00, E = 1020.00
Step 1: Find Partials:
ΔN = 1020 - 1000 = +20.00
ΔE = 1020 - 1000 = +20.00
Step 2: Calculate Distance:
D = √(20² + 20²)
D = √(800) = 28.284 m
Step 3: Calculate Bearing:
θ = tan-1(20 / 20) = tan-1(1) = 45° 00' 00"
Station A (Instrument): N = 1000.00, E = 1000.00
Station B (Target): N = 1020.00, E = 1020.00
Step 1: Find Partials:
ΔN = 1020 - 1000 = +20.00
ΔE = 1020 - 1000 = +20.00
Step 2: Calculate Distance:
D = √(20² + 20²)
D = √(800) = 28.284 m
Step 3: Calculate Bearing:
θ = tan-1(20 / 20) = tan-1(1) = 45° 00' 00"