Bearing And Distance Calculator

Work out bearing and distance instantly with clear inputs, formula shown and shareable results.

About Bearing And Distance Calculator

Surveyors measure bearings clockwise from north, so the bearing is atan2(ΔE, ΔN) reduced to 0°–360°. The distance is the plain Pythagorean hypotenuse of the easting and northing differences.

Formulas

Distance

d = √(ΔE² + ΔN²)

Bearing

θ = atan2(ΔE, ΔN), normalised to 0°–360°

Worked example

With the default values below, Bearing And Distance Calculator returns Straight-line distance of 500.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Start easting: 100
Start northing: 200
End easting: 400
End northing: 600

Results

Straight-line distance: 500.0000
Forward bearing from north: 36.8699 °
Back bearing: 216.8699 °
Change in easting: 300.0000

Step by step

1Values used
2Distance
3Bearing
4Straight-line distance= 500.0000
5Forward bearing from north= 36.8699 °
6Back bearing= 216.8699 °
7Change in easting= 300.0000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

From (100,200) to (400,600)?

ΔE = 300 and ΔN = 400, so the distance is 500 and the bearing atan2(300,400) ≈ 36.8699°.

Why atan2(ΔE, ΔN) and not atan2(ΔN, ΔE)?

Bearings are measured from north clockwise, which swaps the usual mathematical convention of measuring from the x-axis counter-clockwise.