Asked by: Tony Carter, by E-mail
It’s tricky. If the aircraft is directly overhead, you can hold your thumb outstretched and compare it to the apparent size of the plane. Your thumb subtends an angle of roughly 1° (in other words, covers 1° of your field of view). A Boeing 747 has a wingspan of 64m so it’ll be exactly covered by your thumb at around 3700m, and half the size of your thumb at roughly 7400m, and so on.
But this is very inaccurate, relies on you identifying the plane and knowing its wingspan, and doesn’t work if the plane is at an oblique angle to you. Rain clouds form below 2000m and cirrus clouds between 5000 and 12,000m so you can use this to provide an upper limit if you see a plane flying under clouds. Also, contrails normally only form behind the plane at altitudes above 7900m. Commercial jetliners normally cruise at about 11,000m.