How do I convert degrees to radians?

Multiply the number of degrees by π and divide by 180. So 90 degrees becomes 90 × π ÷ 180 = π/2, roughly 1.5708 radians.

How many degrees is one radian?

About 57.29578 degrees, which is 180 divided by π. It is deliberately not a round number: a radian is defined by the geometry of the circle, not by convention.

Why do programming languages use radians?

Trigonometric functions in almost every language, including JavaScript's Math.sin and Python's math.sin, expect radians. Passing degrees produces plausible-looking but wrong answers, which makes it a common and hard-to-spot bug. Convert first.

A gradian, or gon, divides a full turn into 400 parts, so a right angle is exactly 100 gradians. It was introduced alongside the metric system and is still used in some European surveying work.

What are arcminutes and arcseconds used for?

Navigation, surveying and astronomy, where angles are small and precision matters. One arcminute is 1/60 of a degree and one arcsecond is 1/3600. Latitude and longitude are traditionally written in degrees, minutes and seconds.

Angle Converter - Degrees to Radians, Gradians & Arcminutes

Angle Converter Tool

Value

From

Result

Milliradian (mrad)

Degrees, radians and the formula

A full turn is 360 degrees, 2π radians, or 400 gradians. Converting between degrees and radians is a single multiplication:

radians = degrees × π ÷ 180
degrees = radians × 180 ÷ π

Radians are the natural unit in mathematics because they measure arc length on a unit circle: an angle of one radian subtends an arc exactly one radius long. Every trigonometric function in JavaScript, Python and virtually every other language expects radians, which is the single most common source of wrong-looking trigonometry results.

Degrees subdivide into arcminutes and arcseconds, sixtieths and three-thousand-six-hundredths of a degree, still used in navigation, surveying and astronomy. Gradians divide the right angle into a round 100 and survive mainly in European surveying. Milliradians are used in optics and ballistics.

Quick reference

Common angle conversions

Angle	Equivalent
1 turn	360° = 2π rad = 400 gon
180°	π radians (3.14159 rad)
90°	π/2 radians (1.570796 rad)
60°	π/3 radians (1.047198 rad)
45°	π/4 radians (0.785398 rad)
30°	π/6 radians (0.523599 rad)
1 radian	57.29578°
1 degree	0.0174533 radians
1 degree	60 arcminutes
1 degree	3600 arcseconds

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Questions

Frequently Asked Questions

How do I convert degrees to radians?: Multiply the number of degrees by π and divide by 180. So 90 degrees becomes 90 × π ÷ 180 = π/2, roughly 1.5708 radians.
How many degrees is one radian?: About 57.29578 degrees, which is 180 divided by π. It is deliberately not a round number: a radian is defined by the geometry of the circle, not by convention.
Why do programming languages use radians?: Trigonometric functions in almost every language, including JavaScript's Math.sin and Python's math.sin, expect radians. Passing degrees produces plausible-looking but wrong answers, which makes it a common and hard-to-spot bug. Convert first.
What is a gradian?: A gradian, or gon, divides a full turn into 400 parts, so a right angle is exactly 100 gradians. It was introduced alongside the metric system and is still used in some European surveying work.
What are arcminutes and arcseconds used for?: Navigation, surveying and astronomy, where angles are small and precision matters. One arcminute is 1/60 of a degree and one arcsecond is 1/3600. Latitude and longitude are traditionally written in degrees, minutes and seconds.