Radians to Degrees Converter
1 radian = 57.2957795°. Type in either box.
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180 over pi
A full turn is 360 degrees or 2π radians, so half a turn is 180 degrees or π radians. That gives the conversion factor directly.
degrees = radians × 180 / π = radians × 57.2957795
A radian is the angle you get when the arc length equals the radius. That definition is why it is the natural unit in mathematics: the derivative of sine is cosine only when the angle is measured in radians, and the small angle approximation sin x ≈ x only holds in radians too.
Degrees are the older and more intuitive unit. The 360 is Babylonian, chosen because it divides evenly by so many numbers, which makes fractions of a turn come out whole.
Worth memorising: π/6 is 30°, π/4 is 45°, π/3 is 60°, π/2 is 90°, π is 180°.
The radian
The angle subtended at the centre of a circle by an arc equal in length to the radius. A full turn is 2π radians, which is why π appears everywhere in trigonometry.
Radians are the natural unit for angle in mathematics: the derivative of sine is cosine only when the angle is in radians. Every programming language's trigonometric functions expect them.
The degree
A 360th of a full turn. The 360 is Babylonian, chosen because it divides cleanly by so many numbers — 2, 3, 4, 5, 6, 8, 9, 10, 12 and more.
Degrees are easier to picture than radians, which is why navigation, surveying and everyday geometry use them, while mathematics and programming use radians.
The working, step by step
Every line updates with whatever you type above. The point is the method, which is the same for any pair of units in this family.
The same quantity, two different numbers
One physical amount, read off two scales. The tick marks do not line up, and the gap between them is the conversion factor made visible.
Your turn
Reading a method and being able to use it are different things. Answer within half a per cent and it counts as correct.
Score: 0 of 0
How to use this converter
- Type into either box. The other side updates as you go; there is no button to press.
- Swap the direction with the button between the boxes, carrying your value across.
- Set the decimals if the default is more or less precision than you need.
- Copy the answer with its unit, ready to paste.
- Use the shortcut buttons for the values that come up most often.
- Share the result. The address bar tracks what you type, so the link you copy opens on the same number.
Common uses and tips
Where this comes up
- Coursework and lab work, where quantities are measured with a convenient prefix and calculated in base SI units.
- Datasheets, which pick whichever prefix keeps the numbers readable and leave the reader to convert.
- Spreadsheets and code, where mixing prefixes silently is one of the easier ways to be wrong by a factor of a thousand.
The prefix ladder
Every SI prefix is a power of ten, and the common ones step by three:
- nano — a thousand-millionth, 10−9
- micro — a millionth, 10−6
- milli — a thousandth, 10−3
- kilo — a thousand, 103
- mega — a million, 106
- giga — a thousand million, 109
Converting between neighbours on this ladder is always a shift of three decimal places, never a lookup. Unlike data storage, SI prefixes have no binary alternative: mega always means exactly a million here.
Tips worth knowing
- Capitalisation matters. M is mega and m is milli — a factor of a thousand million apart.
- Work in base units inside a calculation and apply the prefix only when reporting the answer. Most prefix errors happen in the middle of a multi-step sum.
- Check the order of magnitude. If an answer is out by a factor of exactly 1,000 or 1,000,000, a prefix has been dropped.
Values people look up most
Each one opens the converter with the number already in it.
- 0.1 rad to °
- 0.25 rad to °
- 0.5 rad to °
- 0.5236 rad to °
- 0.7854 rad to °
- 1 rad to °
- 1.0472 rad to °
- 1.5708 rad to °
- 2 rad to °
- 2.0944 rad to °
- 2.3562 rad to °
- 3 rad to °
- 3.1416 rad to °
- 4 rad to °
- 5 rad to °
- 6.2832 rad to °
Quick reference
The odd-looking inputs are π/6, π/4, π/3, π/2, π and 2π.
| Radians | Degrees |
|---|---|
| 0.5236 rad | 30.00007 ° |
| 0.7854 rad | 45.000105 ° |
| 1 rad | 57.29578 ° |
| 1.0472 rad | 60.00014 ° |
| 1.5708 rad | 90.00021 ° |
| 2 rad | 114.591559 ° |
| 3.1416 rad | 180.000421 ° |
| 4.7124 rad | 270.000631 ° |
| 6.2832 rad | 360.000842 ° |
Questions people ask
What is the formula for radians to degrees?
Multiply by 180/π, which is about 57.2957795.
How many degrees is π radians?
Exactly 180.
How many degrees is 1 radian?
57.2957795°, which is not a round number in either system.
Why does mathematics use radians?
Because calculus works out cleanly in them. The derivative of sin x is cos x only if x is in radians; in degrees a factor of π/180 appears in every derivative.
Which do programming languages use?
Radians, almost universally. Passing degrees to a sine function is a common bug.