Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Convert between degrees and radians instantly, in both directions.
3.141593
Degrees and radians are the two standard units for measuring angles. This tool converts between them in either direction.
Pick a direction, then enter a value. The converted value appears instantly.
Radians = Degrees × (π / 180)
Degrees = Radians × (180 / π)
The converter has two buttons, Degrees to Radians and Radians to Degrees, and each mode keeps its own input box. That means you can type a degree value, switch modes, type a radian value, and switch back without losing the first entry. Results are shown to six decimal places. The tool accepts any finite number, including negatives and values above a full turn, because angles are not limited to 0 through 360 in trigonometry, physics or programming. An empty field is read as zero, so you will see 0 rather than an error until you type something.
Common angles are worth memorising as fractions of pi, because you will see them constantly. Using made-up but standard values:
Going the other way, 1 radian is about 57.295780 degrees, and 2 radians is about 114.591559 degrees. The number 6.283185 radians is one full turn, so it converts to 360 degrees. A handy mental shortcut: one radian is a little under 60 degrees, so a result far from that ratio suggests you typed the wrong direction.
Radians measure an angle by the length of arc it cuts on a circle of radius one. That makes arc length simply radius times angle. As a hypothetical case, a wheel of radius 10 cm turning through 45 degrees first needs the angle in radians: 0.785398. The arc travelled is 10 × 0.785398 = 7.853982 cm. Try that same multiplication with 45 and you would get 450 cm, a clear sign the unit was wrong. The same applies to angular speed in physics, to sector area (half the radius squared times the angle), and to the derivatives of sine and cosine in calculus, which are only clean when the angle is in radians.
Most programming languages, including JavaScript, Python and spreadsheet functions like SIN and COS, expect radians. If you feed 90 to a sine function expecting degrees, you get a value near 0.894 instead of 1. Scientific calculators have a DEG/RAD switch, and forgetting which one is active is the classic source of trig homework errors. Use this converter to translate an angle before passing it into code or a formula, and confirm the direction with one known value such as 180 degrees equalling 3.141593 radians.
The conversion multiplies by pi divided by 180 using the computer's double precision value of pi, then displays six decimals. That is far more precision than measured angles in the real world carry. If you need an exact answer in terms of pi, for example 5 pi/6 for 150 degrees, work it out as a fraction: divide the degrees by 180 and simplify. The tool gives the decimal equivalent, not a symbolic fraction. Also note that the pre-filled radian entry of 3.14159265 is an approximation of pi, so it converts to 180.000000 only after rounding; a longer decimal would land even closer.
A value like 720 degrees converts to 12.566371 radians, which is two full rotations. The tool does not reduce it to an equivalent angle between 0 and 360, because that would change the number you asked about. If you need the reduced form, subtract multiples of 360 degrees (or 2 pi radians) yourself. This matters in animation, gear rotation counting and navigation, where the total turn, not just the final direction, can be important.
Radians are the "natural" unit for angles in calculus and physics -- many formulas (like arc length = radius × angle in radians) only work cleanly in radians.
One radian is approximately 57.295780 degrees, which is 180 divided by pi. It is the angle whose arc length equals the circle's radius.
Yes. The tool multiplies whatever number you enter, so -45 degrees gives about -0.785398 radians. The sign simply indicates rotation in the opposite direction.
Your calculator is probably in the other angle mode. Convert the angle with this tool and enter the radian value, or switch the calculator to degree mode, before evaluating trig functions.
No, it returns decimals to six places. To express a result in terms of pi, divide the degree value by 180 and simplify the fraction, such as 150 divided by 180 reducing to 5/6 pi.
Reference: NIST Weights and Measures