What the angle converter does
The angle converter changes a value between seven units of plane angle: degree (°), radian (rad), gradian (grad), arcminute (′), arcsecond (″), turn (tr) and milliradian (mrad). Typing on either card updates the other card and the All Units list.
Every factor is an exact definition: 1 turn = 2π rad = 360° = 400 grad, 1° = π/180 rad, 1 grad = 0.9°, one arcminute = 1/60°, one arcsecond = 1/3600° and 1 rad = 1,000 mrad. The same direction travels between houses — a right angle is 90°, π/2 rad, 100 grad or 0.25 turn — so the unit label matters as much as the number.
Worked examples
Every readout below comes from this converter.
Half a turn. Enter 180 on the degree card and the list reads 3.1415926536 rad, 200 grad, 0.5 tr, 10,800′, 648,000″ and 3,141.59265359 mrad.
One radian. 1 rad reads 57.2957795131°, 63.6619772368 grad and 206,264.806247″; entering 57.2957795131° returns 1 rad.
The gradian trap. 100 grad reads 90° — a right angle — and 250 grad reads 225°. One grad is 0.9°, and 30° comes back as 33.3333333333 grad.
A second of arc. 1″ reads 0.0002777778° and 0.0000048481 rad; a 0.1 mrad scope click is 20.6264806247″, and 1 mrad is 3.4377467708′.