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Datum Shift Magnitude Calculator

The 3D length of an offset vector with frame-correct horizontal and vertical labels — a magnitude, never a datum transformation.

100% FreeRuns in your browserIntermediate
How to use this calculator

Inputs

The 3D length of an offset vector, with frame-correct horizontal/vertical labels — a magnitude, never a datum transformation.

The frame decides what the components mean: only local axes have a horizontal and a bearing.

Vector
More options
Check
Metadata (recorded, never applied)

Enter the values and press Calculate.

Or load an example to see a worked result.

Signed components
Illustrative
Signed componentsHorizontal bars for each signed component of the vector, drawn from a common zero line.0ΔEΔNΔUNot to scale in 3D — a flattened component view
Each component is a signed bar from zero; the magnitude is the length of the whole vector, not the sum of the bars.
Calculate first: a stale result cannot be exported.

Batch from CSV

One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Choose the frame: local E/N/U or geocentric X/Y/Z (ECEF).
  2. Enter the three signed components, two positions of the same point, or a CSV of vectors.
  3. For ECEF, optionally add latitude and longitude to rotate into local E/N/U.
  4. Press Calculate. Datum, epoch and method labels are recorded but never applied.

How it works

Magnitude = √(dx² + dy² + dz²), computed with hypot so very large or very small components do not overflow.

Only local axes have a horizontal (√(ΔE² + ΔN²)), a vertical (ΔU) and a bearing. In ECEF, √(ΔX² + ΔY²) is an XY component norm — a chord through the Earth — and is labelled that way. The ENU rotation preserves the length exactly.

A batch reports mean components, RMS magnitude, the largest magnitude, and both the magnitude of the mean vector and the mean of the magnitudes, which are different quantities.

Worked example

ΔE 0.06, ΔN −1.5, ΔU 1.2 m. Magnitude = √(0.06² + 1.5² + 1.2²) = √3.6936 = 1.921874 m; local horizontal = √(0.06² + 1.5²) = 1.501199 m; vertical = 1.2 m. In ECEF at latitude 0°, longitude 0°, the vector (1, 2, 3) rotates to E 2, N 3, U 1 with the same length 3.741657 m.

Frequently asked questions

Does this convert between datums?

No. It measures the length of a vector you already have. A real conversion needs the transformation parameters or grid for your datums and epochs.

Why is the ECEF XY figure not a horizontal distance?

Geocentric X and Y point through the centre of the Earth, so their combined length is not measured along the ground. Rotate into local E/N/U for a horizontal.

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Cite this tool

Zerdly. (2026). Datum Shift Magnitude Calculator. Retrieved from https://www.zerdly.com/tools/datum-shift-magnitude-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.