Azimuth Calculator

You have two GPS coordinates on a spreadsheet and need the compass heading from one to the other—not a rough map guess, but the actual initial bearing a pilot, surveyor, or antenna installer would use. Azimuth is that angle measured clockwise from true north at your starting point. Pair it with great-circle distance and you know both which way to point and how far apart the points sit on Earth's surface. I reach for this whenever I am sanity-checking a flight plan segment or verifying a radio link line-of-sight before climbing a tower.

Enter decimal latitude and longitude for initial point A and final point B, pick a distance unit, and click Calculate. The result panel shows forward azimuth in degrees plus a sixteen-point compass label, with great-circle distance underneath. Step-by-step work expands below the card when you need to document the transformation for a report or homework submission.

How to Use This Azimuth Calculator

• Enter the initial point (A). Type decimal latitude and longitude for your starting location. Use positive values for north and east, negative for south and west—for example 40.7128 and −74.0060 for New York City.
• Enter the final point (B). Add the destination coordinates the same way. London might be 51.5074, −0.1278.
• Pick distance units. Choose kilometers, miles, meters, or nautical miles for the great-circle distance shown alongside the bearing. Azimuth itself is always in degrees clockwise from true north.
• Click Calculate. The result panel shows forward azimuth in degrees plus a 16-point compass label (N, NE, E, …). Distance appears underneath as an as-the-crow-flies measurement. Step-by-step math expands below the card when you need to document the work.

Need only the separation between two pins? The Latitude Longitude Distance Calculator focuses on Haversine distance without bearing. To find the point on the opposite side of Earth, try the Antipode Calculator.

Azimuth Calculator Formulas and Practical Applications

Earth is treated as a sphere with mean radius R = 6371 km. Two separate calculations run on the same coordinate pair: Haversine distance for how far apart the points are, and forward azimuth for the initial heading from A toward B along the shortest surface path.

Haversine great-circle distance

Convert latitudes φ₁, φ₂ and longitudes λ₁, λ₂ to radians. Let Δφ = φ₂ − φ₁ and Δλ = λ₂ − λ₁:

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

c = 2 × atan2(√a, √(1 − a))

d = R × c

Example: New York to London spans roughly 5,570 km (3,460 mi) great-circle distance—far shorter than any airline's filed route, which bends for wind and airspace, but the baseline geodesy number you expect on a planning worksheet.

Forward azimuth (initial bearing)

At point A, the bearing toward B uses the standard spherical forward-azimuth formula:

y = sin(Δλ) × cos(φ₂)

x = cos(φ₁) sin(φ₂) − sin(φ₁) cos(φ₂) cos(Δλ)

θ = atan2(y, x) (converted to degrees, normalized to 0°–360°)

The result is the angle you'd read off a compass aligned to true north at the instant you depart A—not the constantly changing heading you'd follow for the entire voyage. On long ocean routes the rhumb line (constant compass heading) and great-circle path diverge noticeably; aviators and mariners pick whichever trade-off fits the mission.

In my experience on small-site RF surveys, azimuth from tower to customer premises equipment is the number that goes on the mount bracket. Distance tells you if you are within spec; azimuth tells you which way to swing the dish before you ever leave the ground.

Where azimuth math shows up in practice

• Aviation and marine planning. Initial true course from departure fix toward destination—before wind correction and airspace bends the filed route.
• Radio and antenna work. Line-of-sight links need both separation and bearing from site A to site B when aiming directional gear.
• GIS and field QA. Sanity-check whether two exported coordinates point roughly where the map thumbnail suggests before publishing a layer.
• Outdoor navigation sketches. Ballpark heading between trailheads or camps when you have GPS coords but no routing app—crow-flight distance plus bearing, not turn-by-turn roads.

Standard Units and Conversion Tables

Coordinates use decimal degrees (DD). If your source data is degrees-minutes-seconds, convert before entering—there is no DMS parser on this page.

Coordinate and bearing reference

• Latitude range: −90° (South Pole) to +90° (North Pole). Equator = 0°.
• Longitude range: −180° to +180°. Prime meridian (Greenwich) = 0°; west longitudes are negative in DD form.
• Azimuth output: 0° = due north, 90° = east, 180° = south, 270° = west. Values wrap at 360°.
• Compass rose: Sixteen-point labels (N, NNE, NE, …) round azimuth to the nearest 22.5° sector.

Distance unit conversions

• 1 km ≈ 0.621371 mi ≈ 1000 m ≈ 0.539957 nmi
• 1 nmi = 1.852 km (one arc-minute of latitude on charts)
• Earth radius: 6371 km (IAU mean); sufficient for planning; sub-meter survey work needs an ellipsoid model.

Frequently Asked Questions

What is forward azimuth?

Forward azimuth is the angle measured clockwise from true north at your starting point to the direction of the destination along the shortest great-circle path. It answers "which compass heading do I leave on?" from point A toward point B—not the reverse bearing from B back to A.

Does this calculator use magnetic north or true north?

Results reference true north (geographic north). Magnetic declination shifts compass needles away from true north, and the offset depends on where you stand and when. Look up current declination for your area and add or subtract it when translating azimuth to a handheld compass.

Why is great-circle distance shorter than driving distance?

Great-circle distance cuts across Earth's curvature—the straightest line on a sphere. Highways follow valleys, grids, and borders. A 300 km crow-flight hop might be 420 km by road. The Haversine result is the geodesic baseline, not a routing engine estimate.

What latitude and longitude format should I enter?

Decimal degrees only: positive latitude for north, negative for south; positive longitude for east, negative for west. Example: 40.7128, −74.0060 for New York City. Keep values within −90°–90° latitude and −180°–180° longitude.

Is azimuth the same at both endpoints of a route?

No. The forward azimuth from A to B generally differs from B to A by about 180° on a great circle (poles excepted). This tool reports the initial bearing at A facing B—the heading you'd take at departure, not the arrival heading seen when looking back from the destination.