Radians to Degrees
Convert radian to degree instantly — type a value and read the result, with the exact formula shown.
Example
1 rad = 57.29578 °, 5 rad = 286.4789 °, 10 rad = 572.9578 °.
How it works
Degree = Radian × 57.29578. Every value is converted through a single degree base unit using internationally defined conversion factors, so any from/to pair stays consistent.
Good to know
Radians and degrees are the two languages for measuring angles, and converting between them is something you do constantly in trigonometry, physics, and any kind of programming that touches geometry. Nearly every math library — JavaScript's Math.sin(), Python's math module, C's libm — expects angles in radians, while protractors, compass bearings, CAD drawings, and everyday speech use degrees. So the typical real-world job is taking a radian result from code and translating it into a degree value a human can actually picture.
The degree is the older, more arbitrary unit: a full circle was split into 360 parts by Babylonian astronomers, a number that survives because it divides cleanly by 2, 3, 4, 5, 6, 8, 9, 10 and 12. The radian is the "natural" unit — one radian is the angle you sweep out when the arc length equals the circle's radius, which makes a full turn exactly 2π radians. Because both describe the same thing, the conversion is just a fixed ratio: 180 degrees per π radians.
The rule of thumb worth memorizing: one radian is a bit more than 57 degrees (57.29578°, or "57 and change"). For quick mental math, multiply radians by 57.3. The cleaner shortcut is to think in terms of π — π radians is a half-turn (180°), π/2 is a right angle (90°), and π/6 is 30°. If you can spot the π factor, you rarely need the decimal at all.
The most common mistake is mixing units without noticing: feeding degrees into a function that expects radians (or vice versa) produces answers that look plausible but are silently wrong by a factor of about 57. Watch the sign too — many calculators return values in the range −π to π, so a "negative" radian simply means an angle measured clockwise, and the converted degrees will be negative as well.
Frequently asked questions
How do you convert radian to degree?
Multiply the number of radians by 57.29578 to get degrees. For example, 1 rad = 57.29578 °.
What is 1 radian in degrees?
1 radian equals 57.29578 degrees (1 rad = 57.29578 °).
How many radians are in 1 degree?
There are 0.01745329 radians in 1 degree.
Is this converter free and private?
Yes. It runs entirely in your browser, so your inputs never leave your device, there is no sign-up, and it works offline once loaded.
Are the conversions exact?
Conversions use internationally defined factors and are exact where the definitions are exact (for example, 1 inch = 2.54 cm). Displayed results are rounded for readability.
People also ask
What is 2 radians in degrees?
2 radians equals about 114.59 degrees (2 × 57.29578). It is just over a 90-degree right angle but less than a straight 180-degree line.
How do I convert π radians to degrees?
π radians equals exactly 180 degrees, which is a half-turn or straight line. Likewise π/2 = 90°, π/3 = 60°, π/4 = 45°, and 2π = 360° (a full circle).
What is the formula to convert radians to degrees?
Multiply the radian value by 180/π, which equals about 57.29578. So degrees = radians × (180 ÷ π).
Why do calculators and programming languages use radians instead of degrees?
Radians are the natural unit because they make calculus and trigonometry formulas simpler — for example, the derivative of sin(x) is cos(x) only when x is in radians. That is why functions like sin(), cos(), and atan2() expect radian input.
How many degrees is 1 radian, roughly?
About 57.3 degrees (precisely 57.29578°). A handy approximation is to multiply any radian figure by 57.3 for a fast estimate.
Is 3.14 radians the same as 180 degrees?
Almost — 180 degrees is exactly π radians, and 3.14 is only a rounded value of π, giving about 179.9 degrees. Using more digits (3.14159) gets you closer to a true 180.
How do I convert a negative radian value to degrees?
Use the same factor: multiply by 57.29578 and keep the sign. For example, −1.5708 radians (−π/2) equals −90 degrees, meaning a right angle measured clockwise.
What is 1.5 radians in degrees?
1.5 radians is about 85.94 degrees (1.5 × 57.29578), just short of a 90-degree right angle.
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