# How to calculate straight line distance from spherical distance

I have longtitude and lattitude coordinates of one point and spherical distance between this and another point on Earth in kilometers (the shortest distance over the earth’s surface). I need to calculate what is the distance between these points in straight line. Can anybody help?

• Do you have those two points or just the distance-value? – Matte Oct 20 '16 at 14:45
• I have one of them and the distance. – BartholomeusR Oct 20 '16 at 15:25

## 1 Answer

Thanks to trigonometric functions we know that

where is your spherical distance, is the earth radius in km, and stands for "euclidian".

Since the earth is only approximately spherical, you should consider Matte's comment. Indeed,

Distances from points on the surface to the center range from 6,353 km to 6,384 km (3,947–3,968 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 km (3,959 mi).
• Depending on the needed accuracy and position of the points the radius is for example 6378 on equator of the wgs84 spheroid. It depends on what formula was used to calculate the original distance (haversine vs vincenty). As a rough estimation it is commonly said that it may have an error up to 0,5% if you use earth as a sphere. – Matte Oct 20 '16 at 16:11