Angle Converter

Type an angle, pick the unit it's in, and this converts it into degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians all at once. There's no single "to" box to fight with. Your value shows up in every unit at the same time in the table below, updating as you type, and it all runs in your browser so nothing you enter ever leaves your machine.

Showing every unit at once is also a safeguard. Angle units are full of look-alikes that will quietly hand you a plausible but wrong number, and seeing all seven together is how you catch it before it bites. The worst offender by a distance is the "mil," which basic converters cram into a single box as if it's one thing when it's really four. That's covered further down, and it's the reason this tool names every unit exactly and sticks to the true milliradian instead of a vague "mil" box.

1. Type your angle into the Value box. Decimals, negatives, and enormous or microscopic numbers all work. Very large or very small values switch to scientific notation so they stay readable instead of becoming a wall of zeros.
2. Set the "From" unit to whatever your number actually is, degrees, say, or radians. That's the only dropdown you need, because the tool shows every other unit for you.
3. Read the table. Your angle appears in all seven units directly below, and the row for your source unit is highlighted so you don't lose your place. It recalculates the moment you change the value or the unit.
4. Copy any result with the copy link on its row, one click puts that number on your clipboard. No selecting and dragging a long decimal by hand.
5. Copy a shareable link to hand someone the exact conversion. The link reopens the tool with your value and unit already filled in, which beats typing "convert 47 gradians for me" into a chat.

The factors here come straight from the definitions, so nothing is a rounded guess. A full circle is exactly 360 degrees, exactly 2π radians, exactly 400 gradians, and exactly one turn. Rounding only ever happens in how the answer is shown, and it keeps enough digits for engineering or schoolwork.

Nine times out of ten the job is degrees to radians or the reverse, and the formula is worth carrying in your head: radians = degrees × π ÷ 180, and degrees = radians × 180 ÷ π. A half circle is π radians, a right angle is π/2, and one radian works out to roughly 57.3 degrees. If you've got a clean number and a calculator open, you barely need a tool for this one.

Radians look messier than 300° does, but they run math and physics for a real reason. A radian comes from the circle's own geometry, it's the angle whose arc along the edge is exactly as long as the radius. Because it's defined by the circle itself, the formulas stay clean. Arc length is just radius times angle, and the derivative of sin is cos, but both of those hold only when the angle is in radians. Switch to degrees and a stray factor of π/180 tags along through every step of the calculus.

Trig functions are where people actually lose an afternoon. A sine or cosine doesn't know what you meant, it just crunches the number you hand it in whatever mode it happens to be in. Ask a calculator for sin(90) expecting 1, but leave it set to radians, and you get about 0.894, with no warning, just a wrong answer that looks perfectly fine. A programming language gives you even less slack. In JavaScript, Python, or C, the sine and cosine functions accept radians only, full stop. So if your data is in degrees, and plenty of real-world data is, from compass bearings to CAD files, you have to convert first or the result is nonsense. It's one of the most common bugs in beginner graphics and games code, and checking your numbers against a converter is the quickest way to catch it.

Other converters skip this, and it's the reason to read the unit labels here with a bit of care.

A milliradian (mrad) is clean and unambiguous. It's one-thousandth of a radian, which puts about 6,283 of them in a full circle. That's the SI value, and it's what rifle scopes and optics marked "MRAD" mean. Shooters like it because at 100 meters a single milliradian covers almost exactly 10 centimeters, so the scope math stays simple. That is the unit this tool uses, labeled plainly as milliradians and nothing else.

The trouble is the military "mil," which is a rounded unit, and not even one rounded unit. NATO artillery rounds the circle to 6,400 mils because 6,400 divides neatly for gunnery tables. The old Soviet system used 6,000. Sweden used 6,300. All of them are called "mil," all of them roughly approximate a milliradian, and not one equals another or the real SI figure. So when a converter offers a single "mil" box, it's quietly picking one of those for you and not saying which. Convert a NATO firing solution as though 6,283 and 6,400 were the same number and you're off by around two percent, which is more than enough to miss with.

This tool refuses to guess for you. It offers only the true milliradian and labels it exactly that, so you always know which number you're getting. If your source says "mil" and expects 6,400 to the circle, that's the artillery mil, and you'll need to know which national system it came from before you trust any figure. For scope clicks and optics, the milliradian is what you're after, and it's what you'll get here.

The other units are far less treacherous, but each has a job. Gradians (also spelled gon, and unhelpfully abbreviated grad, which collides with the abbreviation for radian) cut the circle into 400 instead of 360, so a right angle lands on a round 100. Surveyors and civil engineers, mostly across continental Europe, like that decimal tidiness. One gradian is 0.9 degrees, and if your calculator answers are off by that exact factor, you've knocked it into GRA mode by accident.

A turn is simply one full spin, 360 degrees, the way engineers describe gear ratios and anything that rotates ("give it a quarter turn"). Go smaller than a degree and you hit arcminutes and arcseconds. A degree splits into 60 arcminutes, each arcminute into 60 arcseconds, the same base-60 scheme as the minutes and seconds on a clock. Astronomers and navigators live in these, the full moon is about 30 arcminutes wide, and one arcminute of latitude is a nautical mile. A coordinate written 48°37′52″ is degrees, arcminutes, arcseconds, each one a sixtieth of the unit before it.