Angle Converter: Degrees, Radians, Gradians and Turns

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.

Updated 2026-09-30Reviewed by CalcX Editorial Team5 sources4 min read

What the angle converter does

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.

How to use it

Pick the unit you have on the left card and the one you want on the right; both dropdowns list the same seven units.
Type on either side and the other converts as you type; the middle button swaps the units and carries the value across.
The focused field also takes expressions: 180/2 shows a quiet = 90 hint and converts the running value; Enter or = settles it, as on the scientific calculator.
An unfinished 360 + shows = ? and keeps the last settled value.
The All Units list repeats the angle in every unit; click a row to move it to the focused side. The keypad button opens a standard calculator.

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′.

Display and range limits

Twelve significant digits, capped at ten decimals.: Between 10⁻¹⁰ and 10¹⁵ results print with comma grouping and at most 10 decimal places; outside that band they switch to exponential form with six decimals. 1° shows 0.0174532925 rad, not the full 0.0174532925199433, and 1″ shows 0.0000048481 rad for the same reason.
Large and small angles.: 10,000,000,000 tr reads 1.296000e+16 ″; 10⁻¹¹° reads 1.000000e-11 °.
Minus signs convert normally.: An entry of -90 reads -1.5707963268 rad and -100 grad.
What it does not do.: It converts units only: there is no sin, cos or tan, no angular velocity such as rad/s or rev/min, and no combined degrees-minutes-seconds entry like 12° 30′ in one field. Trigonometry and the DEG/RAD/GRAD angle mode live on the scientific calculator; triangle work from a bearing and a distance continues in the Math Tools geometry solver.

The gradian, the mil and the mode

Gradian ≠ degree. A circle has 400 grad, not 360, so 100 grad is a right angle and one grad is only 0.9°. The numbers do not transfer: reading a 250 grad instrument bearing as 250° overstates the direction by 25°. Surveying, mining and geology are the fields that still read gon.
Milliradian ≠ mil. This list's mrad is exactly 1/1000 rad, which is 206.264806247″; artillery and compass "mil" scales round the turn into 6,400, 6,000 or 6,300 parts instead. The converter has no mil row.
The converter has no angle mode. Every row names its own unit, so 100 grad stays 90° whatever a function key is set to; the DEG/RAD/GRAD switch belongs to trigonometry, not to unit conversion.

Where it fits

Surveying and navigation instruments. In European surveying, theodolites and total stations often work in gon: a 250 grad bearing is 225°, a right angle is 100 grad, and 400 grad closes the circle. The list converts those readings without touching the instrument settings.
Astronomy and optics. The full Moon spans about 31′, which reads 0.5166666667° and 1,860″; scope and telescope figures come out as arcseconds too — 1 mrad is 206.264806247″, and one common 0.1 mrad click is 20.6264806247″.
Study and graphs. A unit-circle exercise that writes π/2 rad can be checked against the degree row, 90°, and the same function is plotted, with radians on the x-axis, on the graphing calculator.

References

BIPM, The International System of Units (SI Brochure), 9th edition — the radian as the SI unit of plane angle, and the degree among the units accepted for use with the SI. bipm.org （访问日期：2026-09-30）
NIST Special Publication 811, Appendix B.8 — the exact gon-to-degree factor 0.9, and the degree, minute, second, revolution and mil (angle) entries. nist.gov （访问日期：2026-09-30）
Wikipedia, Gradian — 1 gon = 1/400 turn = π/200 rad = 0.9°, 100 gon in a right angle, and its use in surveying. en.wikipedia.org （访问日期：2026-09-30）
Wikipedia, Milliradian — 1 mrad = 0.001 rad, and the 6,400 NATO, 6,000 Warsaw Pact and 6,300 Swedish mil variants. en.wikipedia.org （访问日期：2026-09-30）
Wikipedia, Minute and second of arc — 1′ = 1/60°, 1″ = 1/3600° = 1/1,296,000 turn, in astronomy, navigation and firearms. en.wikipedia.org （访问日期：2026-09-30）