How do you convert degrees to radians?

Multiply the angle in degrees by pi and divide by 180. For example, 90 degrees is 90 times pi over 180, which is pi over 2, about 1.5708 radians.

How do you convert radians to degrees?

Multiply the angle in radians by 180 and divide by pi. For example, pi radians is 180 degrees, and one radian is about 57.296 degrees.

Why are there two units for angles?

Degrees split a full turn into 360 parts and are common in everyday use. Radians measure angle by arc length and are the natural unit in calculus and physics, where a full turn is two pi.

Degrees to Radians Calculator

This calculator converts angles between degrees and radians in both directions, and shows the radian value in exact terms of pi as well as a decimal. Degrees and radians are two ways of measuring the same thing, the size of an angle, and being able to move between them quickly is essential once you reach trigonometry, calculus and physics. Degrees split a full circle into 360 equal parts, a system inherited from ancient astronomy that suits everyday angles, navigation and construction. Radians instead measure an angle by the length of the arc it cuts on a unit circle, so a full turn is two pi radians, a half turn is pi, and a right angle is pi over 2. Radians are the natural choice in higher maths because the calculus of sine and cosine comes out cleanly only when angles are in radians. To convert degrees to radians you multiply by pi and divide by 180, and to go the other way you multiply by 180 and divide by pi. The calculator does both at once, so you can type into either box, and it expresses the radian answer as a simple multiple of pi where possible. Enter an angle in either unit to see the conversion update as you type.

Degrees to radians

Angle in degrees

1.570796 rad (π/2)

Radians to degrees

Angle in radians

180 degrees

How it works

To convert degrees to radians the calculator multiplies by pi over 180. It then checks whether the result is a simple multiple of pi, such as pi over 2 or two pi over 3, and shows that exact form next to the decimal. To convert radians to degrees it multiplies by 180 over pi.

Worked example

90 degrees times pi over 180 is pi over 2, which is about 1.5708 radians. Going the other way, pi radians times 180 over pi is exactly 180 degrees.

Related calculators

Trig Calculator: all six trig functions.
Sine Cosine Tangent Calculator: sin, cos, tan.
Hypotenuse Calculator: right triangles.
Circle Calculator: arcs and circles.

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