How fast does a plane need to go to take off?

An aircraft leaves the ground when the wing generates enough lift to overcome its weight. That lift grows with the square of the speed, with the wing's surface area, with air density, and with the angle at which the wing meets the airflow. That's why the necessary speed isn't a fixed property of the air but a consequence of how much the aircraft weighs and how much wing it has to hold itself up.

That relationship between weight and wing area, wing loading, is what orders the whole scale. A light training aircraft, with a large wing relative to its low weight, takes off at about 90-110 km/h (50-60 kn). A single-aisle airliner needs between 240 and 290 km/h (130-155 kn). Large wide-body aircraft at maximum weight exceed 300 km/h. A fighter jet with a small, heavily loaded wing can need even more.

No transport aircraft takes off with a clean wing. Flaps and slats increase curvature and, in some cases, effective wing area, allowing the same lift to be produced at considerably lower speed. The trade-off is more drag, so the configuration chosen is always a compromise between shortening the takeoff run and preserving good initial climb performance.

Heat and altitude reduce air density, and with it the available lift and the engines' thrust. That's why the same aircraft needs more runway and a higher ground speed at a mountain airport in midsummer than at a sea-level airport on a cold morning. Headwind works the opposite way: if it's blowing at thirty kilometers an hour, the wing is already receiving that airflow while the aircraft is still stationary on the ground.