Trilateration Location Math

Right now, at least 4 satellites are zooming above your head about 12,550 miles up, traveling roughly 8,700 miles per hour. In less than a second, your phone uses signals from those satellites to figure out exactly where you are standing - usually within about 16 feet. The math trick that makes this possible is called trilateration, and you can actually do a simple version of it yourself with just a piece of string.

What trilateration means and how it is different from triangulation. How knowing your distance from three known points can pinpoint your exact location. How to try trilateration yourself using circles on a map. Why GPS receivers actually need a signal from a fourth satellite.

Imagine you know you are exactly 3 miles from your friend Maya's house. That could put you anywhere on a big circle drawn around Maya's house - not very helpful yet! Now add a second friend, Jamal, and say you are also exactly 4 miles from his house. Draw that circle too, and the two circles only cross at two possible points - you have narrowed it down a lot. Add a third friend, Priya, who says you are 2 miles from her house. Draw a third circle, and it crosses the other two circles at exactly one single point. That one point is your exact location. This is trilateration - using distances from three known points to find one exact spot.

GPS satellites work the same way, just with radio signals instead of string. Each satellite constantly broadcasts the exact time the signal was sent. Your phone receives the signal and calculates how long it took to arrive - since radio waves travel at the speed of light (about 186,000 miles per second), your phone can turn that tiny travel time into an exact distance to that satellite. With distances to three satellites, your phone could calculate its location - but clocks are never perfectly precise, so GPS receivers use a signal from a fourth satellite to correct tiny timing errors and pinpoint your location accurately.