Coordinate Deviation

About This Tool

This tool compares two sets of coordinates — a reference set and a measured set — and computes per-point deviations alongside aggregate accuracy statistics. It is used in geodesy, surveying, and GPS quality control to quantify how closely field measurements agree with known control points.

Key Concepts

Reference Coordinates

The "truth" — coordinates from a reliable source such as a geodetic control network, cadastral survey, or high-accuracy GNSS measurement. Each point in this set is treated as the accepted correct position.

Measured Coordinates

The observations to be evaluated — typically GPS/GNSS fixes, digitised points, or coordinates derived from a less accurate method. Points are matched to the reference set by their order in the list.

Delta Lat / Delta Lng (m)

The signed difference between measured and reference position along the north–south and east–west axes respectively, converted from degrees to metres using the standard approximation: 1° latitude ≈ 111,319.9 m; 1° longitude ≈ 111,319.9 m × cos(latitude).

Distance (m)

The horizontal straight-line distance between each reference–measured pair, computed as the Euclidean distance of the planar delta components: √(ΔLat² + ΔLng²). Valid for small separations (under a few kilometres) where flat-earth approximation holds.

RMSE — Root Mean Square Error

The square root of the mean of squared distances across all point pairs: √(Σd²/n). RMSE is the standard single-number summary of positional accuracy; it weights large errors more heavily than the mean distance.

CE95 — Circular Error 95th Percentile

The radius of a circle centred on the reference point within which 95% of measured positions are expected to fall. Derived from RMSE as CE95 ≈ 2.448 × RMSE (assuming a 2D normal error distribution). CE95 is the standard accuracy metric in mapping standards such as ASPRS and NMAS.