How does GPS actually work?

How on earth (pun intended 😜 ) does GPS find your location? I came across a reel (Instagram finally being useful for something other than brainrot haha) that completely blew my mind!

The answer, as it turns out, is through time! Because without nanosecond-level precision, “where am I?” becomes an unanswerable question.

GPS satellites carry ultra-precise Cesium or Rubidium atomic clocks. Each one continuously broadcasts a time-stamped signal. Your phone compares the arrival times from at least four satellites to triangulate your position to the meter: three to calculate latitude, longitude, and altitude, and a fourth to correct your phone’s imperfect internal clock.

Here's the basic math for it:

• Light travels ~30 cm in a nanosecond.

• Distance = (received time – sent time) × speed of light.

• A 1 microsecond error = ~300 m location error.

• Ground stations constantly monitor & re-synchronize the satellite clocks to prevent drift.

How 3 satellites triangulate position (and why a 4th fixes your clock)

• Each satellite has known coordinates in space: (x1, y1, z1), (x2, y2, z2), (x3, y3, z3).

• Your phone is at an unknown position (x, y, z).

• The distance from you to satellite i is the straight-line distance between these points.

For each satellite, the distance equation is:

(x – xi)² + (y – yi)² + (z – zi)² = ri²

where ri is the measured distance from your phone to that satellite (calculated from signal travel time × speed of light).

Solving with 3 satellites (perfect clock):

• Subtract the equation for satellite 1 from satellite 2. This cancels out the squared x², y², z² terms and leaves a linear equation in x, y, z.

• Do the same: subtract satellite 1 from satellite 3.

• Now you have two linear equations in x, y, z. Solve these for x and y.

• Substitute x and y back into any one sphere equation to solve for z.

• You get up to two possible solutions; one is physically impossible (e.g., deep inside Earth), so the other is your position.

Why the 4th satellite is needed:

In reality your phone’s clock is not synchronized to GPS time. This adds an unknown bias b. That bias shifts all measured ranges equally by c × b (speed of light × bias). Now you have 4 unknowns: x, y, z, and b. To solve 4 unknowns, you need 4 equations i.e. signals from 4 satellites.

There is, however, a tradeoff to be considered here. Atomic clocks are heavy, costly, and power-hungry. But the payoff is enormous: planes land safely, stock trades stay reliable, cars are able to navigate properly—all thanks to this global orchestra of clocks in space, beating in nanosecond precision.

So the next time your map app reroutes you in real time, consider the hidden infrastructure: a global orchestra of atomic clocks in space, synchronized down to nanoseconds, quietly answering a simple question—“Where am I?”

What other everyday technologies do you think are powered by invisible layers of extreme precision most of us take for granted?