Coordinates Finder Calculator
Easily calculate destination coordinates (latitude and longitude) given a starting point, distance, and bearing. Our Coordinates Finder Calculator uses spherical geometry for accurate results.
Calculate Destination Coordinates
Results
Starting Point: –
Distance & Bearing: –
Earth Radius Used: –
Common Bearings
| Direction | Bearing (Degrees) |
|---|---|
| North (N) | 0 or 360 |
| North-East (NE) | 45 |
| East (E) | 90 |
| South-East (SE) | 135 |
| South (S) | 180 |
| South-West (SW) | 225 |
| West (W) | 270 |
| North-West (NW) | 315 |
Visual Representation
What is a Coordinates Finder Calculator?
A Coordinates Finder Calculator is a tool used to determine the latitude and longitude of a destination point when you know the starting point's coordinates, the distance to travel, and the direction (bearing). It's essentially a navigation tool that helps predict where you'll end up if you travel a certain distance in a specific direction from a known location. This is particularly useful in aviation, sailing, surveying, and even for recreational activities like hiking or geocaching.
Anyone needing to find a location based on a starting point and travel vector can use a Coordinates Finder Calculator. This includes pilots, sailors, geographers, surveyors, and outdoor enthusiasts. Common misconceptions include thinking it provides turn-by-turn directions (it doesn't, it gives a single destination point) or that it works accurately for very large distances without considering the Earth's ellipsoidal shape (most simple calculators assume a sphere, which is an approximation). Our Coordinates Finder Calculator uses a spherical Earth model.
Coordinates Finder Formula and Mathematical Explanation
The calculation to find the destination coordinates involves spherical trigonometry, as we are dealing with positions on the surface of a sphere (or an approximation of it, like the Earth). Given a starting point (latitude φ1, longitude λ1), a distance d, and a bearing θ (clockwise from North), we can find the destination point (latitude φ2, longitude λ2).
The formulas are:
φ2 = asin( sin(φ1) * cos(d/R) + cos(φ1) * sin(d/R) * cos(θ) )
λ2 = λ1 + atan2( sin(θ) * sin(d/R) * cos(φ1), cos(d/R) - sin(φ1) * sin(φ2) )
Where:
- φ1, λ1 are the starting latitude and longitude in radians.
- φ2, λ2 are the destination latitude and longitude in radians.
- d is the distance travelled.
- R is the Earth's radius (e.g., 6371 km or 3959 miles).
- θ is the bearing in radians (clockwise from North).
asinis arcsin,acosis arccos,atan2is the 2-argument arctangent.
All angles (latitude, longitude, bearing) must be converted to radians for these calculations (degrees * π / 180), and the resulting latitudes and longitudes are converted back to degrees.
Variables Table:
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| φ1 (startLat) | Starting Latitude | Degrees | -90 to +90 |
| λ1 (startLon) | Starting Longitude | Degrees | -180 to +180 |
| d (distance) | Distance | km or miles | > 0 |
| θ (bearing) | Bearing (from North) | Degrees | 0 to 360 |
| R | Earth's Radius | km or miles | ~6371 km or ~3959 miles |
| φ2 (destLat) | Destination Latitude | Degrees | -90 to +90 |
| λ2 (destLon) | Destination Longitude | Degrees | -180 to +180 |
Our Coordinates Finder Calculator performs these conversions and calculations for you.
Practical Examples (Real-World Use Cases)
Let's look at a couple of examples using the Coordinates Finder Calculator:
Example 1: Sailing Trip
A boat starts at latitude 34.05° N, longitude 118.24° W (near Los Angeles). They sail 150 nautical miles (approx 277.8 km) on a bearing of 225° (South-West). We use our Coordinates Finder Calculator with:
- Start Lat: 34.05
- Start Lon: -118.24
- Distance: 277.8
- Unit: km
- Bearing: 225
The calculator would output a destination latitude of approximately 32.28° N and longitude of -120.01° W.
Example 2: Hiking Expedition
A hiker starts at a base camp with coordinates 45.5° N, 10.0° E. They plan to hike 15 km on a bearing of 90° (East). Using the Coordinates Finder Calculator:
- Start Lat: 45.5
- Start Lon: 10.0
- Distance: 15
- Unit: km
- Bearing: 90
The destination would be approximately 45.5° N, 10.21° E. Notice the latitude barely changes when traveling due East.
How to Use This Coordinates Finder Calculator
- Enter Starting Latitude: Input the latitude of your starting point in decimal degrees (e.g., 40.7128). Positive for North, negative for South.
- Enter Starting Longitude: Input the longitude of your starting point in decimal degrees (e.g., -74.0060). Positive for East, negative for West.
- Enter Distance: Specify the distance you will travel.
- Select Distance Unit: Choose between kilometers (km) and miles from the dropdown.
- Enter Bearing: Input the direction of travel in degrees clockwise from North (0° is North, 90° is East, 180° is South, 270° is West).
- Calculate: The calculator automatically updates the results as you input values. You can also click "Calculate".
- Read Results: The "Primary Result" shows the destination latitude and longitude. Intermediate values give more context.
- Reset: Click "Reset" to clear inputs and go back to default values.
- Copy Results: Click "Copy Results" to copy the main result and key details to your clipboard.
Use the results from the Coordinates Finder Calculator to plot your destination on a map or input it into a GPS device.
Key Factors That Affect Coordinates Finder Results
- Accuracy of Starting Coordinates: Small errors in the starting latitude or longitude will propagate to the destination coordinates. Ensure your start point is as accurate as possible.
- Accuracy of Distance Measurement: How accurately the travel distance is measured directly impacts the final location.
- Accuracy of Bearing Measurement: The precision of the bearing or direction of travel is crucial. A small error in bearing over a long distance leads to a significant deviation.
- Earth Model Used: Most simple calculators, including this Coordinates Finder Calculator, assume a perfectly spherical Earth. For very high precision over long distances, an ellipsoidal model (like WGS84) is more accurate, but the calculations are more complex.
- Unit Consistency: Ensure the distance unit selected matches the distance value entered, and that the Earth radius used corresponds to that unit. Our calculator handles this internally.
- Atmospheric/Oceanic Conditions: While not part of the calculation, real-world travel by air or sea is affected by winds and currents, which can cause deviation from the calculated bearing and distance over ground/water.