Directions Calculator — Free Online Bearing and Compass Tool

How to Use the Directions Calculator

1. Enter the origin point coordinates: Input the latitude and longitude of your starting location in the Origin Point section. The default is set to New York City (40.7128, -74.006). Northern latitudes are positive, southern are negative. Eastern longitudes are positive, western are negative. To find coordinates for any location, search the city name on a mapping service or use the GPS on your mobile device. For the most accurate bearing, use coordinates as precise as possible (at least four decimal places).
2. Enter the destination point coordinates: Input the latitude and longitude of your destination in the Destination Point section. The default is Los Angeles (34.0522, -118.2437). You can calculate bearings between any two points on Earth, from neighboring addresses to antipodal locations on opposite sides of the globe. The calculator handles all edge cases including cross-equator, cross-prime-meridian, and near-polar routes.
3. Review the bearing and direction results: The results panel displays the initial bearing (the compass heading at the starting point toward the destination), the compass direction (one of 16 cardinal/intercardinal directions), the final bearing (the heading upon arrival), the reverse bearing (the heading from destination back to origin), and the great-circle distance in both kilometers and miles.
4. Check the midpoint coordinates: The midpoint shows the geographic coordinates of the point exactly halfway along the great-circle path. This is useful for identifying intermediate navigation waypoints, finding the geographic center of a journey, or locating potential refueling or rest stops at the route's halfway mark.

All results update instantly as you change any coordinate value. The bearings are referenced to true north (geographic north), not magnetic north. If you need magnetic bearings for compass navigation, apply your local magnetic declination to the displayed values.

Bearing Calculation Formula

Variables Explained

• lat1, lat2: The latitudes of the origin and destination points, converted from degrees to radians for trigonometric computation. One radian equals approximately 57.296 degrees.
• Δlng: The difference in longitude between the destination and origin, in radians. This determines the east-west component of the bearing calculation.
• θ: The initial bearing angle in radians, computed using the atan2 function which correctly handles all four quadrants. The atan2 function returns values from -π to +π.
• atan2(y, x): The two-argument arctangent function that computes the angle from the positive x-axis to the point (x, y). Unlike atan(y/x), it correctly identifies the quadrant, avoiding ambiguity when both sine and cosine components are needed.
• Bearing: The final bearing in degrees, normalized to the range 0 to 360 by adding 360 and taking the modulo. This gives a compass heading where 0 degrees is true north, increasing clockwise.
• Reverse Bearing: The bearing from the destination back to the origin, calculated by adding 180 degrees to the initial bearing. This is a simplification; for the most accurate return heading at the destination point, a separate calculation using swapped coordinates is required.

Step-by-Step Example

Calculate the bearing from New York (40.7128° N, 74.0060° W) to Los Angeles (34.0522° N, 118.2437° W):

1. Convert to radians: lat1 = 0.7106, lat2 = 0.5942, Δlng = -0.7713
2. Calculate y: sin(-0.7713) × cos(0.5942) = -0.6989 × 0.8300 = -0.5801
3. Calculate x: cos(0.7106) × sin(0.5942) - sin(0.7106) × cos(0.5942) × cos(-0.7713) = 0.4467 - 0.4235 = 0.0232
4. Calculate θ: atan2(-0.5801, 0.0232) = -1.5309 radians
5. Convert to degrees: -1.5309 × 180/π = -87.71°
6. Normalize: (-87.71 + 360) mod 360 = 272.29° (W)

The initial bearing from New York to Los Angeles is approximately 272.29 degrees, which is nearly due west (W). This matches our intuition since Los Angeles is almost directly west of New York on the map. The reverse bearing would be about 92.29 degrees (nearly due east).

Practical Examples

Example 1: Captain James Planning a Sailing Route

Captain James is planning a sailing route from Miami (25.7617, -80.1918) to Bermuda (32.3078, -64.7505). He enters these coordinates and the calculator shows an initial bearing of 32.18 degrees (NNE) with a distance of 1,683 km (1,045 miles or 909 nautical miles). The midpoint is approximately at (29.09, -72.62), which falls in the open Atlantic. James notes the reverse bearing of 212.18 degrees (SSW) for the return trip. He adjusts the initial bearing by the local magnetic declination of approximately -6 degrees (west) to get a magnetic compass heading of about 38 degrees for departure. The midpoint coordinates help him identify the halfway mark for weather routing decisions.

Example 2: Elena Setting Up a Radio Antenna

Elena is a ham radio operator in Chicago (41.8781, -87.6298) who wants to aim a directional antenna toward Tokyo (35.6762, 139.6503) for a planned long-distance contact. She enters the coordinates and finds the initial bearing is 325.74 degrees (NNW). This surprises her at first, but she realizes the great-circle path from Chicago to Tokyo goes northwest over the North Pole region rather than west across the Pacific. The distance is 10,132 km. Elena adjusts the bearing by the local magnetic declination of approximately -3 degrees to get a magnetic heading of about 329 degrees and orients her antenna accordingly for the 40-meter band contact.

Example 3: Survey Team Establishing Control Points

A survey team needs to establish a baseline bearing between two control points for a highway project. Point A is at (38.9072, -77.0369) and Point B is at (38.9156, -77.0281). The calculator shows an initial bearing of 43.45 degrees (NE) with a distance of 1.22 km. Since this is a short distance, the initial and final bearings are nearly identical (43.46 degrees). The team uses the bearing to orient their total station instrument. They also use the Coordinates Calculator to convert the decimal degree coordinates to DMS format for their survey records, getting 38° 54' 25.92" N and 77° 2' 12.84" W for Point A.

Example 4: Aisha's Cross-Country Hiking Orientation

Aisha is planning a multi-day wilderness hike from a trailhead (44.4280, -110.5885) to a backcountry camp (44.5511, -110.4067). She enters both coordinates and gets an initial bearing of 36.28 degrees (NE) with a distance of 19.6 km. She uses this bearing to set her compass for the general direction of travel on the first day. The midpoint coordinates (44.4896, -110.4977) help her identify a landmark roughly halfway along the route to verify her progress. She also calculates bearings to two additional intermediate waypoints, creating a series of compass legs for her navigation plan. Before heading out, she applies the local magnetic declination of approximately 11.5 degrees east, adjusting her compass bearing to about 25 degrees magnetic.

Compass Directions Reference Table

Table shows the 8 primary compass directions. The calculator uses all 16 compass points (including NNE, ENE, ESE, SSE, SSW, WSW, WNW, NNW) for finer directional resolution.

Tips and Complete Guide

Understanding Great-Circle Routes

The bearing calculated by this tool follows the great-circle path, which is the shortest route between two points on Earth's surface. On a flat (Mercator projection) map, great-circle routes appear as curves, while straight lines on the map represent rhumb lines (constant compass heading). For long-distance travel, the great-circle route saves significant distance compared to a rhumb line. For example, the great-circle distance from London to Tokyo is about 9,566 km, while the rhumb line distance is approximately 11,200 km. Airlines and shipping companies use great-circle routing to minimize fuel consumption and travel time. Use the Distance Between Cities Calculator to see the great-circle distance between any two locations.

Applying Magnetic Declination

This calculator provides bearings relative to true north (geographic north). If you are using a magnetic compass for navigation, you need to adjust the bearing by the local magnetic declination. Magnetic declination varies by location: it is approximately -14 degrees in Seattle (compass points east of true north), -1 degree in Chicago, +11 degrees in London, and varies significantly in polar regions. To convert true bearing to magnetic bearing, subtract east declination or add west declination: Magnetic Bearing = True Bearing - East Declination. The World Magnetic Model, maintained by NOAA and the British Geological Survey, provides current declination values for any location. Declination changes slowly over time (about 0.1 degree per year in most locations).

Navigation Tips for Outdoor Activities

When using calculated bearings for hiking, orienteering, or backcountry navigation, always cross-reference with a topographic map and visible landmarks. Set your compass to the adjusted magnetic bearing and identify a visible feature along that bearing to walk toward. Periodically recheck your bearing, especially after detours around obstacles. For multi-leg routes, calculate the bearing for each segment separately using intermediate waypoints. In featureless terrain like open desert, grassland, or fog-covered mountains, GPS devices with the calculator's coordinates provide more reliable navigation than compass bearings alone. Always carry a physical compass as a backup since electronic devices can fail in the field.

Common Mistakes to Avoid

• Ignoring magnetic declination: Using a true north bearing directly on a magnetic compass results in navigating off-course by the declination angle. In areas with large declination values (10+ degrees), this can lead you several kilometers off target over a 10 km journey.
• Assuming bearing stays constant on long journeys: The initial bearing is only valid at the starting point. As you travel along a great-circle path, the heading continuously changes. For a 5,000 km journey, the heading at the midpoint may differ by 20 to 40 degrees from the initial bearing. Use waypoints and recalculate the bearing at each stage.
• Confusing bearing with heading: Bearing is the direction from one fixed point to another. Heading is the direction you are actually facing or moving, which may differ from the bearing due to wind, current, or course corrections. In aviation and maritime navigation, the difference between bearing and heading is called the wind correction angle or crab angle.
• Swapping origin and destination coordinates: The bearing from A to B is different from the bearing from B to A (they differ by approximately 180 degrees but not exactly, due to Earth's curvature). Always enter the origin first and destination second to get the correct forward bearing.
• Using the calculator for turn-by-turn directions: This calculator provides the compass bearing and straight-line direction between two points. It does not provide road routing, turn-by-turn navigation, or account for terrain obstacles. For driving or walking directions along roads, use a dedicated navigation application.

Frequently Asked Questions