Degrees to Radians Converter

How to convert degrees to radians

Converting degrees to radians is a single multiplication. The formula is degrees × (π / 180) = rad, which means one degree equals 0.0174533 rad. Going the other way, one radian equals 57.29578 °.

The calculator above applies this automatically as you type, but it is worth knowing the arithmetic if you need to sanity-check a figure or work one out without a device to hand.

Worked examples

7 ° to rad: multiply 7 by 0.0174533, which gives 0.122173 rad.

45 ° to rad: multiply 45 by 0.0174533, which gives 0.785398 rad.

250 ° to rad: multiply 250 by 0.0174533, which gives 4.3633231 rad.

Degrees to Radians conversion table

The values below are calculated with the same function as the converter above, so they agree to the digit. Use it as a quick reference when you need a rough figure without typing anything.

What is a degree?

A degree is one three-hundred-and-sixtieth of a full rotation. Degrees subdivide into 60 minutes of arc, and each minute into 60 seconds of arc.

Where the degree came from

The 360-degree circle comes from Babylonian astronomy and its base-60 number system, chosen partly because 360 divides evenly by so many numbers, which makes fractions of a circle easy to express as whole degrees.

Where degrees are used today

Degrees are what people use in practice: navigation bearings, latitude and longitude, construction angles, and the angle settings in design software. Mathematics and physics use radians instead, so conversion between the two is routine.

• A right angle is 90 degrees
• A full circle is 360 degrees
• A clock hand moves 30 degrees per hour

What is a radian?

One radian is the angle subtended at a circle's center by an arc equal in length to the radius. A full circle is 2 pi radians, which is why radian values so often carry a factor of pi.

Where the radian came from

The concept dates to 18th-century work on circular motion, and the name radian appeared in print in 1873. It became standard because it makes the calculus of trigonometric functions clean: the derivative of sin(x) is cos(x) only when x is in radians.

Where radians are used today

Radians are the standard angular unit in mathematics, physics, and every major programming language. JavaScript's Math.sin, Python's math.sin, and their equivalents all expect radians, which is the usual reason a developer needs this conversion.

• A full circle is 2 pi radians, about 6.283
• A right angle is pi/2 radians, about 1.571
• 1 radian is about 57.3 degrees

When you actually need this conversion

degrees belong to the other system and radians to the metric (si) system, so this conversion turns up whenever information crosses between countries that measure differently.

Accuracy, precision, and rounding

The factor used here (degrees × (π / 180) = rad) is the standard accepted value. The results above are shown to about eight significant figures, which is more precision than almost any practical use requires.

The sensible rule is to round the answer to roughly the same precision as the number you started with. If you measured to the nearest degree, an answer carrying six decimal places is not more accurate, it just looks more accurate. For most everyday purposes one or two decimal places is plenty.

Common mistakes to avoid

Converting in the wrong direction

Multiplying when you should divide is by far the most common error, and it is easy to miss because the result is still a number in a believable range. A quick check: since one degree is 0.0174533 rad, a degree value should get smaller when converted.

Using a rounded factor for a long calculation

Rounding the conversion factor before multiplying, then repeating that across many values, compounds the error. Convert with the full factor and round only the final answer.

Converting degrees to radians in a spreadsheet or in code

A one-off answer is what the calculator above is for. When you have a whole column of figures, or you are writing something that has to do the conversion repeatedly, it is worth putting the formula in the tool you are already working in.

Excel and Google Sheets

With your degree value in cell A1, put this in B1 and fill it down the column:

=A1 * 0.0174533

Excel also ships a built-in CONVERT function that handles many unit pairs directly, but it does not cover every unit and its unit codes are easy to mistype. An explicit formula like the one above is harder to get wrong and shows its working.

Python

def from_to_rad(value):
    return value * 0.0174533

print(from_to_rad(10))

JavaScript

const fromToRad = (value) => value * 0.0174533;

console.log(fromToRad(10));

Store the factor as a named constant rather than typing 0.0174533 at each call site. When a figure appears in three places it will eventually be updated in two of them.

The two measurement systems behind this conversion

This conversion sits on the fault line between the two measurement systems still in everyday use. The metric system was designed in one go in the 1790s as a coherent decimal scheme, where every unit relates to the next by a power of ten. The imperial and US customary systems grew instead by accretion over centuries, which is why their relationships are numbers like 12, 16, 5,280, and 43,560 rather than round ones.

Only three countries have not formally adopted the metric system: the United States, Liberia, and Myanmar. In practice the picture is messier than that, since the US uses metric units throughout science, medicine, and the military, while metric countries still buy screens and tires by the inch. That overlap is exactly why conversions like this one stay necessary.

More questions about degrees and radians

Is the conversion exact or approximate?

The underlying definition is exact, and the factor shown here (0.0174533) is that definition expressed to the precision this page displays. For any everyday purpose the result is exact; only at very high precision would you need more digits of the factor.

Why does the answer have so many decimal places?

The converter shows a high-precision result so that it is never the limiting factor in your calculation. It is up to you to round to something sensible. A measurement taken with a tape measure does not become more accurate because the conversion carried six decimals.

Can I convert in the opposite direction on this page?

Yes. The swap button in the calculator reverses the conversion and carries the current result across as the new input, so you do not have to navigate anywhere or retype anything. The second table above also lists the reverse conversion directly.

Does anything get sent to a server?

No. The arithmetic runs in your browser with a few lines of JavaScript. Nothing you type is uploaded, logged, or stored, which also means the converter keeps working if your connection drops after the page has loaded.

Which figure should I use on an official form?

Use whatever precision the form asks for, and if it does not say, match the precision of the original measurement. For height, weight, and similar personal details, one decimal place is almost always sufficient and often more than is wanted.

Related angle conversions

If you need to go the other way as a starting point rather than as a swap, the Radians to Degrees converter is the mirror of this page: same factor, same tables, opposite direction. It is the more natural place to start when most of your figures are already in radians.

This is a small category, so the list below reaches into the other measurement families as well:

• CM to Inches - Convert centimeters to inches instantly. Enter any value and get the exact result in decimal inches.
• KG to LBS - Convert kilograms to pounds instantly. Perfect for fitness, cooking, and shipping calculations.
• Celsius to Fahrenheit - Convert Celsius to Fahrenheit instantly. Essential for weather, cooking, and science.
• Liters to Gallons - Convert liters to US gallons quickly. Great for fuel economy, cooking, and tank sizes.
• MPH to KPH - Convert miles per hour to kilometers per hour instantly. Perfect for travel and speed limits.
• Acres to Square Feet - Convert acres to square feet instantly. Ideal for real estate, land surveying, and property measurements.

For anything not listed here, the full converter directory covers over a hundred pairs across length, weight, temperature, volume, area, speed, pressure, energy, and more.

Quick reference

Why Use Our Degrees to Radians Converter?

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