VoriTools

Angle Unit Converter

Type an angle into any of the eight rows and the other seven follow as you edit; there is no Convert button. The rows cover turns, degrees, arcminutes, arcseconds, radians, milliradians, gradians and right angles.

Runs locally in your browser

How to convert between turns, degrees, arcminutes, arcseconds, radians, milliradians, gradians and right angles

Type an angle into any of the eight rows and the other seven follow as you edit; there is no Convert button, and the row you are typing in is never reformatted under your cursor. The rows cover turns, degrees, arcminutes, arcseconds, radians, milliradians, gradians and right angles.

The conversion runs in this browser: no value is sent to a server, the page keeps working offline, and nothing you type is stored.

  1. Click one of the eight fields and type an angle, or paste one from a drawing note, a CAD export or a log.
  2. Read the other seven rows. They describe the same angle, so 90 in Degrees also fills 100 in Gradians, 0.25 in Turns and 1 in Right angles.
  3. Type into a different row to convert from that unit instead: the eight rows are one linked set, not eight independent sums.
  4. Negative angles are kept. -45 in Degrees reads back as -0.125 turn and -50 gon, because rotations, bearings and phase offsets are signed.
  5. Clear a field to empty the set, or press Reset all to empty every row; the line under the fields names the reason when a value cannot be read.

Unit definitions, precision and limits

The eight units and their exact definitions

A turn is 2π rad, and every other row is defined from it: one degree is π/180 rad, an arcminute is a sixtieth of a degree, an arcsecond a three-thousand-six-hundredth, a milliradian is exactly 0.001 rad, a gradian is π/200 rad so 400 gon make a full turn, and a right angle is π/2 rad. One turn is therefore 360° = 21600′ = 1296000″ = 400 gon = 4 right angles.

The rows are linked, so a single angle fills all eight: 90 degrees, 100 gon, 0.25 turn, one right angle, 5400 arcminutes, 324000 arcseconds, 1.5707963267949 rad and 1570.7963267949 mrad are the same angle written eight ways.

Precision and rounding

Turns, degrees, arcminutes, arcseconds, gradians and right angles relate by exact rational ratios, so those rows land on exact decimals: 1 gon is 0.9°, and 1° is 60′ or 3,600″. The radian and milliradian rows contain π = 3.141592653589793…, which has no finite decimal form, so those two rows can only be shown rounded.

Results carry up to 15 significant digits, the limit of a browser double, and switch to exponent notation below 0.000001 and at 10^15: one arcsecond is 7.71604938271605e-7 turn, and two π is written 6.28318530717959 rad. Whole numbers up to 9007199254740991 stay exact; past that the browser rounds the input itself and the page says so.

What the converter does not do

Each row takes a single number. Expressions such as 90+30, fractions such as 1/2 and sexagesimal angles such as 40°30′15″ are not parsed, and a comma is reported rather than read as a decimal point — the page names what happened instead of guessing. Exponent notation (1e2, 1.5e-3) is accepted.

No unit is substituted silently: the value is converted from the unit of the row you are editing, and the other seven rows show what that means. Nothing leaves the page while you work.

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