What is compass bearing?

A compass bearing is the horizontal angle measured clockwise from true north (0°) to a direction. A bearing of 0° means due north, 90° is due east, 180° is due south, and 270° is due west. Bearings above 315° are northwest. The 16-point compass system subdivides these into finer directions such as NNE (22.5°), ENE (67.5°), and so on.

What is the difference between forward bearing and final bearing?

The forward bearing (also called the initial bearing) is the compass heading you face at point A to begin a great-circle path to point B. Because the Earth is curved, the heading continuously changes along that path. The final bearing is the compass heading at which you arrive at point B — it is equivalent to the reverse bearing from B back to A, plus 180°. For long-haul flights over thousands of kilometres the two values can differ by tens of degrees.

What is the Haversine formula, and why does this calculator use it?

The Haversine formula computes the great-circle distance between two points on a sphere from their latitudes and longitudes: a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2); d = 2R · arcsin(√a). It is numerically stable even for very short distances (unlike the simpler spherical law of cosines) and is accurate to within roughly 0.5% for any pair of surface points. The maximum error occurs near the poles where the Earth is slightly flattened; for most navigation purposes the formula is fully sufficient.

What does "true north" mean, and how does it differ from magnetic north?

True north points toward the geographic North Pole — the axis of the Earth's rotation. Magnetic north, by contrast, is where a compass needle points, which is currently about 500 km from the geographic pole and shifts several kilometres every year. This calculator outputs bearings relative to true north. To use the result with a magnetic compass, subtract (or add) the local magnetic declination for your location, which can be looked up from resources such as NOAA's magnetic declination calculator.

How do I enter coordinates in DMS format?

The input fields accept both decimal degrees (e.g. 48.8566) and degrees-minutes-seconds strings (e.g. "48° 51' 24" N" or "48 51 24 N"). Negative decimal values represent south latitudes and west longitudes; if you enter a direction letter (N/S/E/W) the sign is applied automatically.

How accurate is the destination-point calculation?

The destination-point formula uses spherical trigonometry: φ₂ = arcsin(sin φ₁ · cos(d/R) + cos φ₁ · sin(d/R) · cos θ) and λ₂ = λ₁ + atan2(sin θ · sin(d/R) · cos φ₁, cos(d/R) − sin φ₁ · sin φ₂). It assumes a perfectly spherical Earth with radius 6 371.009 km. Real-world accuracy is within about 0.3% for any distance; for precision maritime or aviation navigation an ellipsoidal model (Vincenty or Karney) would give sub-metre results.

Compass Bearing Calculator

A compass bearing calculator that gives you the exact true bearing between any two GPS coordinates, together with the great-circle distance and a live compass rose — or works the problem backwards, finding your destination when you know your starting point, heading, and distance to travel.

What this tool calculates

The calculator has two modes:

Bearing and Distance — Enter the decimal-degree (or DMS) coordinates of two places on Earth. The tool instantly returns:

Forward bearing — the compass heading (0–360°) you face at point A to begin the shortest path to point B, plus its 16-point compass label (N, NNE, NE, ENE …)
Final bearing — the heading at which you arrive at B (differs from the forward bearing for long routes because the Earth is curved)
Great-circle distance in kilometres, statute miles, and nautical miles
Midpoint — the halfway coordinates on the great-circle arc
A live compass rose that rotates the needle to the forward bearing

Find Destination — Enter a starting point, a bearing, and a travel distance (km, mi, or NM). The tool computes where you end up, returning decimal degrees and DMS.

How the formulas work

Haversine great-circle distance

The straight-line distance across a flat map is useless for navigation; we need the shortest path along the curved surface of the Earth. That is the great-circle (or orthodromic) distance, calculated by the Haversine formula:

a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2)

d = 2R · arcsin(√a)

where φ is latitude in radians, λ is longitude in radians, R = 6 371.009 km (IUGG mean radius), and Δ denotes the difference between the two points. The intermediate value a is the square of half the chord length; d is the arc distance.

Forward (initial) bearing

θ = atan2( sin Δλ · cos φ₂ , cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ )

The result of atan2 is in the range (−180°, 180°]; we normalise it to (0°, 360°) by adding 360° and taking modulo 360.

Final bearing

The final bearing equals the reverse initial bearing (from B to A) plus 180°, normalised to (0°, 360°). On a short route of a few hundred kilometres the two bearings are nearly the same; on a trans-Pacific crossing they can differ by 30° or more.

Destination point

Given origin (φ₁, λ₁), bearing θ, and angular distance δ = d/R:

φ₂ = arcsin( sin φ₁ · cos δ + cos φ₁ · sin δ · cos θ )

λ₂ = λ₁ + atan2( sin θ · sin δ · cos φ₁ , cos δ − sin φ₁ · sin φ₂ )

This is the inverse of the Haversine distance calculation and is used in the “Find Destination” tab.

Worked example — London to New York

London: 51.5074° N, 0.1278° W
New York: 40.7128° N, 74.0060° W

Plugging into the Haversine formula:

Δφ = −10.7946° = −0.18840 rad
Δλ = −73.8782° = −1.28942 rad
a ≈ 0.17924
c = 2 · arcsin(√0.17924) ≈ 0.87431 rad
d = 6 371.009 × 0.87431 ≈ 5 570 km

Forward bearing (all angles converted to radians before applying trig):

y = sin(−1.28942 rad) · cos(0.71063 rad) ≈ −0.72818
x = cos(0.89884 rad) · sin(0.71063 rad) − sin(0.89884 rad) · cos(0.71063 rad) · cos(−1.28942 rad) ≈ 0.24124
θ = atan2(−0.72818, 0.24124) ≈ −71.7° → normalised to 288.3° (WNW)

This means an aircraft departing London heads west-northwest at takeoff, arcs northward over Iceland, then descends into New York — a classic polar great-circle route.

Route	Distance	Forward bearing
London → New York	5 570 km	288° WNW
Tokyo → Sydney	7 826 km	170° S
Cape Town → Cairo	7 239 km	12° NNE
Yerevan → Tbilisi	170 km	9° N

Reading the compass rose

The compass rose shows the forward bearing as a blue needle. North is always at the top. The 16 compass points are marked around the ring with major tick marks at the cardinal directions (N, E, S, W) and minor ticks at every 22.5°. The bearing in degrees is displayed inside the dial for quick reference.

All bearings are true north, not magnetic. To use the result with a physical compass, apply your local magnetic declination (available from NOAA for free).
Haversine is accurate to within ~0.5% for any pair of surface points. The small error arises because the Earth is slightly oblate (flattened at the poles). For sub-metre precision use the Vincenty formula or Karney’s algorithm.
Nautical miles (NM) are the natural unit for maritime and aviation navigation: 1 NM equals exactly 1 minute of arc of latitude, making chart work straightforward.
The midpoint on a great-circle arc is not the same as the midpoint on a rhumb line (a path of constant bearing). For routes that cross significant longitude ranges, the great-circle midpoint can be hundreds of kilometres north of the straight-looking map midpoint.