Degrees to Radians Converter

Need to convert degrees to radians? This free online degrees to radians converter does it in your browser: type a value in ° and the rad answer appears as you type, alongside the same figure in every other angle unit. Degree and Radian describe the same quantity on two different scales, so the degrees to radians 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 degrees to radians formula

One ° is 0.017453 rad:

rad = ° × 0.017453
° = rad × 57.2958

That is the whole degrees to radians 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 degrees to radians 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 ° = 0.174533 rad. 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 degrees to radians when the answer has to be exact rather than estimated.

How to convert degrees to radians by hand

1. Write the value down in ° — 25 ° is used here.
2. Multiply it by 0.017453, because 1 ° = 0.017453 rad.
3. Read the answer: 25 ° = 0.436332 rad.
4. To come back, divide by 0.017453, or multiply by 57.2958 instead — 1 rad = 57.2958 °.

Degrees to Radians 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 degrees to radians chart for the values people reach for most.

Why convert degrees to radians?

degrees to radians questions rarely arrive alone: they show up when degrees meet radians — geometry class, CAD drawings, navigation and astronomy. In each case a ° reading has to become rad — 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 degrees to radians 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 ° in every angle unit

The 0.017453 rad figure the converter shows for 1 ° 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 degrees to radians without a calculator

One habit worth keeping is to memorise two anchor points on the degrees-to-radians line: 10 ° is 0.174533 rad, and 100 ° is 1.7453 rad — both computed by the same engine as the converter above, not rounded by hand. With those anchors in mind, a mental degrees to radians 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 ° = 0.017453 rad, converting degrees to radians reduces the size of the number: 100 ° becomes 1.7453 rad, while 100 rad becomes 5,729.58 °. 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 ° and rad 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 0.017453, which is within 0.0017% 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.

degrees to radians in the real world

A full turn is 2π radians, so multiply degrees by π⁄180. The radian is the natural unit because one radian of arc equals exactly one radius of length — which is why calculus prefers it: the derivative of sin x is cos x only when x is in radians. Programming's classic trap is right here: Math.sin(90) is not 1, because it reads 90 radians. 45° is π⁄4, ≈ 0.7854 rad; a right angle is π⁄2, ≈ 1.5708.

When people actually need degrees to radians

Programming languages started this war: Math.sin(90) returns the wrong thing because the function wants radians, and 90° is π⁄2 — roughly 1.5708 — not 90. CAD and robotics keep the conversion running in production: drawings get read in degrees, servos commanded in radians, and every interface between the two is one ×π⁄180 multiplication that nobody should have to remember in the middle of the night.

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 rad-to-° converter in place. The inverse factor, 1 rad = 57.2958 °, is shown in the arithmetic panel so you can check the reverse calculation independently.