Radians to Degrees Converter

Need to convert radians to degrees? This free online radians to degrees converter does it in your browser: type a value in rad and the ° answer appears as you type, alongside the same figure in every other angle unit. Radian and Degree describe the same quantity on two different scales, so the radians to degrees conversion is a single arithmetic step once you know the exact factor. Nothing is uploaded and there is no sign-up — the answer is computed on your device as fast as you can type.

The radians to degrees formula

One rad is 57.2958 °:

° = rad × 57.2958
rad = ° × 0.017453

That is the whole radians to degrees formula: multiply to go one way, divide — or multiply by the inverse — to come back. The factor is a defined constant rather than a measurement, so a radians to degrees conversion done this way carries no uncertainty of its own; the only open question is how many decimal places to display, which is covered further down.

Worked example

10 rad = 572.9578 °. Enter 10 in the box above and you will see exactly that, plus the value carried across the rest of the angle scale so you can sanity-check it against a unit you already recognise. It is the quickest way to convert radians to degrees when the answer has to be exact rather than estimated.

How to convert radians to degrees by hand

1. Write the value down in rad — 25 rad is used here.
2. Multiply it by 57.2958, because 1 rad = 57.2958 °.
3. Read the answer: 25 rad = 1,432.39 °.
4. To come back, divide by 57.2958, or multiply by 0.017453 instead — 1 ° = 0.017453 rad.

Radians to Degrees conversion table

Every figure below comes from the same engine as the box at the top of this page, shown at its Automatic precision, so each row is exactly what you would see after typing that value in. Treat it as a ready-made radians to degrees chart for the values people reach for most.

Why convert radians to degrees?

radians to degrees questions rarely arrive alone: they show up when degrees meet radians — geometry class, CAD drawings, navigation and astronomy. In each case a rad reading has to become ° — or be checked against one — before it can be used, and a guessed conversion is how the wrong size gets ordered, the wrong setting gets dialled in or the wrong amount gets poured. This free angle converter exists for that moment: the radians to degrees answer is exact, the full angle table sits one glance away, and everything runs locally in the browser — no sign-up, and none of the values you type are uploaded anywhere.

One rad in every angle unit

The 57.2958 ° figure the converter shows for 1 rad is one row of this table — the row it defaults to. The others are here so a single reading can be checked against any further angle unit without running the conversion twice.

Estimating radians to degrees without a calculator

One habit worth keeping is to memorise two anchor points on the radians-to-degrees line: 10 rad is 572.9578 °, and 100 rad is 5,729.58 ° — both computed by the same engine as the converter above, not rounded by hand. With those anchors in mind, a mental radians to degrees estimate becomes a matter of proportion: a value between the anchors has an answer between them too, and a mental conversion that lands far outside them is a sign that the factor has almost certainly been inverted. The converter above is there for every time an estimate is not good enough.

Which direction the numbers move

Because 1 rad = 57.2958 °, converting radians to degrees increases the size of the number: 100 rad becomes 5,729.58 °, while 100 ° becomes 1.7453 rad. If a result moves the other way, the factor has been inverted — the two directions are reciprocals and never the same number.

How many decimals to keep

The relationship between rad and ° is a defined constant, but written out in decimal it runs past eight places, so every figure on screen is a rounding of it. Automatic shows 57.2958, which is within 0.000036% of the true quotient, and the menu (Automatic, whole numbers, or 2, 4, 6 and 8 decimal places) keeps more or fewer digits when a specification asks for a fixed count.

radians to degrees in the real world

Multiply by 180⁄π and remember the one anchor: π rad is exactly 180°, so everything is a proportion of it. 1 rad is 57.2958° — a hair over 57 — and π⁄3 rad is 60°, a sixth of a turn. Engineering maths switches between them constantly: torque, phase and angular frequency live in radians, while drawings, miter saws and navigation bearings are stamped in degrees. The 1897 New York note that quietly omitted the degree symbol from a contract's "5,000" is the most expensive radian-to-degree argument on record.

When people actually need radians to degrees

The calculator's mode switch is the trap: trig functions computed in radian mode give entirely different answers, and school results hinge on which mode was left set. Navigation and astronomy feed it too — orbital mechanics publishes in radians because the maths is cleaner, while every chart a human reads is signed in degrees of arc.

About these units

Angle conversions turn on π. A full turn is 360 degrees and 2π radians, so one radian is exactly 180⁄π degrees — an irrational number, which is why radian results are shown to a fixed number of decimals rather than exactly.

Converting the other way

Press Swap to turn this into a °-to-rad converter in place. The inverse factor, 1 ° = 0.017453 rad, is shown in the arithmetic panel so you can check the reverse calculation independently.