Destination Point Calculator

How it is calculated

The tool moves along a great circle on a sphere of radius R = 6371 km. With the angular distance d = distance ÷ R, start latitude φ₁, longitude λ₁ and bearing θ (all converted to radians): φ₂ = asin(sin φ₁ cos d + cos φ₁ sin d cos θ) and λ₂ = λ₁ + atan2(sin θ sin d cos φ₁, cos d − sin φ₁ sin φ₂). Latitude and longitude are in decimal degrees (south and west negative), the bearing is in degrees clockwise from north (0 north, 90 east, 180 south), and the distance is in kilometres and cannot be negative. The longitude is wrapped into −180 to 180, and results show five decimals. Because the Earth is treated as a perfect sphere, errors of a few tenths of a percent against an ellipsoidal model are possible.

Common mistakes

• Entering the distance in miles or metres. The distance is read as kilometres.
• Entering west longitude or south latitude as positive. West and south must be negative, so London is −0.1278, not 0.1278.
• Thinking the bearing is a compass reading you can reverse. The bearing is the starting direction; on a great circle the heading changes along the way, so the return bearing is not simply 180° more.
• Expecting due east to keep the same latitude. Going east along a great circle bends toward the equator, as the small drop in latitude in the example shows.
• Entering degrees, minutes and seconds in one box. Convert to decimal degrees first.