Coordinate Inverse Calculator
📍 Point A (Start / Instrument)
🎯 Point B (End / Target)
Horizontal Distance
0.000 m
Whole Circle Bearing
0° 00' 00"
Delta N (Latitude)
0.000
Delta E (Departure)
0.000
What is the Inverse Calculation?
In Total Station surveying, every point is defined by a coordinate pair: Northing (Y) and Easting (X). The "Inverse" calculation is the process of taking two known coordinates and calculating the straight-line distance and direction (Bearing) between them.
(A diagram showing Point A and Point B on a Cartesian plane, with Delta N and Delta E forming a triangle)
Why is this used daily?
- Traverse Checking: Confirming the distance between two known stations before starting work.
- Setting Out: Calculating the angle to turn to find a specific peg.
- Missing Line Measurement: Finding the distance between two points that cannot be measured directly.
The Formulas
1. Calculate Differences (Partials)
$$ \Delta N = N_2 - N_1 $$ $$ \Delta E = E_2 - E_1 $$
$$ \Delta N = N_2 - N_1 $$ $$ \Delta E = E_2 - E_1 $$
2. Horizontal Distance (Length)
$$ \text{Distance} = \sqrt{(\Delta N)^2 + (\Delta E)^2} $$
$$ \text{Distance} = \sqrt{(\Delta N)^2 + (\Delta E)^2} $$
3. Bearing (Angle)
$$ \theta = \tan^{-1} \left( \frac{\Delta E}{\Delta N} \right) $$ Note: You must apply Quadrant Rules to convert \(\theta\) to Whole Circle Bearing (0-360°).
$$ \theta = \tan^{-1} \left( \frac{\Delta E}{\Delta N} \right) $$ Note: You must apply Quadrant Rules to convert \(\theta\) to Whole Circle Bearing (0-360°).
Solved Example
Given:
Stn A: N=1000, E=1000
Stn B: N=1020, E=1020
1. Partials:
\(\Delta N = 20, \Delta E = 20\)
2. Distance:
\(D = \sqrt{20^2 + 20^2} = \sqrt{800} = 28.284 \text{ m}\)
3. Bearing:
\(\tan^{-1}(20/20) = \tan^{-1}(1) = 45^\circ\)
Stn A: N=1000, E=1000
Stn B: N=1020, E=1020
1. Partials:
\(\Delta N = 20, \Delta E = 20\)
2. Distance:
\(D = \sqrt{20^2 + 20^2} = \sqrt{800} = 28.284 \text{ m}\)
3. Bearing:
\(\tan^{-1}(20/20) = \tan^{-1}(1) = 45^\circ\)