Angle Converter
Use our angle converter to switch between degrees, radians, gradians, and mils instantly. Great for math, engineering, and quick checks.
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SIMILAR TOOLS
What this converter does
An angle can be written several ways, and which one you reach for says a lot about your field. Degrees rule everyday life and navigation, radians run mathematics and physics, gradians turn up in surveying, and mils belong to the military. This converter moves an angle between all four.
How to use it
Enter the angle, choose the unit it is in under From and the unit you want under To, then press Calculate. It starts on degrees to radians, the pair people need most. Swap reverses the direction, Reset clears the field, and the answer is shown to nine significant figures.
How it works
Internally the radian is the reference, and the factors are built on π. A full circle is 2π radians, which is also 360 degrees, 400 gradians, and 6,400 mils, so every unit is just that circle sliced a different number of ways. The tool converts your value to radians and then out to the unit you want.
Common angle conversions
The ones that come up most:
| Conversion | Value |
|---|---|
| 1 full circle | 360° = 2π rad = 400 grad = 6,400 mil |
| 1 radian | about 57.296° |
| 90° (right angle) | π/2 rad ≈ 1.5708 rad (100 gradians) |
| 1 degree | π/180 rad ≈ 0.01745 rad |
| 1 gradian | 0.9° |
| 1 mil (6,400 per circle) | 0.05625° |
Four units, four fields
The same angle, four different traditions.
Degrees split the circle into 360, a choice inherited from the ancient Babylonians (360 is close to the number of days in a year and divides neatly). They are the everyday unit, used in weather, navigation, and most of daily life.
Radians are the mathematician's choice, because they are tied to the circle itself: one radian is the angle whose arc length equals the radius, and a full circle is 2π of them, so one radian is about 57.3 degrees. Trigonometry and calculus come out cleaner in radians, which is why scientific calculators have a "rad" mode.
Gradians, also called gons or grades, divide the circle into 400, so a right angle is a tidy 100 gradians and one gradian is 0.9 degrees. Born alongside the metric system, they survive mainly in surveying and civil engineering, where decimal grades are convenient.
Mils divide the circle into 6,400 in the convention used by this tool. The appeal is a handy approximation: at 1,000 metres, an angle of one mil spans about one metre, which makes range and adjustment estimates quick in the field.
Questions people ask
How many degrees are in a radian?
About 57.296 degrees. A full circle is 2π radians, which equals 360 degrees, so one radian is 180 divided by π.
How do I convert degrees to radians?
Multiply by π and divide by 180. So 180 degrees is π radians, and 90 degrees is π/2, about 1.571 radians.
What is a gradian?
A metric angle unit that splits the circle into 400 parts, so a right angle is 100 gradians and one gradian is 0.9 degrees. It is used mostly in surveying and civil engineering.
What is a mil?
A military angle unit. In the NATO standard there are 6,400 mils in a circle. It is popular for artillery because, at 1,000 metres, one mil covers roughly one metre, which simplifies range estimates.
Why do calculators have a "rad" mode?
Because trigonometric functions are defined in radians. If your angle is in degrees, the calculator needs to be set to degrees, or the angle converted first, or the sine and cosine values will be wrong.
References
- National Institute of Standards and Technology (NIST), Office of Weights and Measures. The International System of Units (SI) and the radian. https://www.nist.gov/pml/owm/metric-si/si-units
Okan Atalay is a results driven senior operations manager and a graduate of Industrial Engineering from Bilkent University. With over 22 years of experience in textile manufacturing and integrated operations, he has led large scale business process improvements and strategic planning initiatives. Currently, he serves as a top mathematics expert for a global ed tech platform, where he applies his analytical expertise to solve complex mathematical problems. At Eon Tools, he reviews converter and maths tools.