To be precise – The Maximum “DEMONSTRATED” crosswind that the 172 can take off , or land, is 15 knots.
Contrary to what some pilots may think, an aircraft’s maximum demonstrated crosswind component is only an operating limitation if the aircraft’s manufacturer says so. **It’s not a limitation imposed by FAA regulations.
One of those requirements is a demonstration of crosswind controllability, and more specifically, how the aerodynamics of the airplane allows pilots “with no exceptional skill or alertness” to safely take off and land in crosswind conditions.
The test pilot must be able to control the airplane in 90-degree crosswinds not less than a velocity equal to 0.2 Vso**, or the stalling speed of the aircraft in a landing configuration. That’s a windspeed equal to at least 20% of the power-off landing configuration stalling speed. Keep in mind, manufacturers can test aircraft at crosswind velocities higher than 0.2 Vso (and they often do), but that’s the minimum speed.
In addition to the 0.2 Vso limitation, “The airplane must be satisfactorily controllable in power-off landings at normal landing speed, without using brakes or engine power to maintain a straight path until the speed has decreased to at least 50 percent of the speed at touchdown.” (FAA)
Finally, every airplane certificated after May 3rd, 1962 is required to have a “demonstrated crosswind velocity” placard inside the airplane.