Calculator
What the Degree Converter does
Degree Converter: 1 ° = 0.017453293 rad, so multiply a degree value by 0.017453293 to get radian, or divide to go back. Example: 1 ° = 0.017453293 rad.
The inputs are Value, From and To; the output is Result, How it was calculated and Reverse conversion. There is no submit step; the numbers move as you adjust them.
It is mostly used by students converting units for homework. Unit mistakes are quietly expensive. They have wrecked spacecraft and ruined recipes alike.
Nothing leaves the tab. You can watch your browser network panel while you use it and see for yourself.
The field reference, the method and a worked example using the default inputs follow the tool itself.
What do the Degree Converter fields mean?
The Degree Converter uses 3 inputs. The starting figures are ordinary, not edge cases, so they make a sensible baseline.
| Field | What to enter | Default |
|---|---|---|
| Value | required | 1 |
| From | choose from Degree (°), Radian (rad), Gradian (grad), Arcminute ('), Arcsecond (") or Turn (revolution) (turn) | Degree (°) |
| To | choose from Degree (°), Radian (rad), Gradian (grad), Arcminute ('), Arcsecond (") or Turn (revolution) (turn) | Radian (rad) |
How does the Degree Converter work?
Both units are converted through angle's base unit (rad), so any of the 7 units in the dropdowns can be paired in either direction without loss of accuracy.
Where a unit has an exact legal definition, that exact value is used rather than a rounded one. The 1959 international agreement fixing the inch at 25.4 mm is the best-known example; the same principle applies throughout.
Worked example
These are the values the Degree Converter loads by default, and the result it produces from them. The defaults produce the result shown here; change any of them and the answer moves.
| Value | 1 |
|---|---|
| From | Degree (°) |
| To | Radian (rad) |
| Result | 0.017453293 rad |
|---|---|
| How it was calculated | 1 ° = 0.017453293 rad, so 1 × 0.017453293 = 0.017453293 rad |
| Reverse conversion | 57.29577951 ° (if you meant 1 rad) |
The degree
A degree is defined as 1/360th of a full circle: a division with no fundamental mathematical necessity behind it, unlike the radian, but deeply convenient historically because 360 divides evenly by so many small whole numbers.
Worth knowing
- Degrees are further divided into 60 arcminutes, and each arcminute into 60 arcseconds: the same base-60 (sexagesimal) system used for hours, minutes and seconds of time, both inherited from ancient Babylonian mathematics.
- Navigation, surveying, geography (latitude and longitude) and everyday contexts (compass headings, protractors) almost universally use degrees rather than radians, precisely because whole and simple fractional degree values are easier for people to reason about intuitively.
- Converting to radians for a calculation is straightforward (multiply degrees by π/180), but it’s easy to forget this step when moving from an everyday degree-based context into a formula (especially in programming, where trigonometric functions almost always expect radians, not degrees).
Definitions: BIPM SI Brochure · NIST reference on units
How to use it
- Key in Value.
- Pick a value for From: the options are Degree (°), Radian (rad), Gradian (grad), Arcminute ('), Arcsecond (") or Turn (revolution) (turn).
- Pick a value for To: the options are Degree (°), Radian (rad), Gradian (grad), Arcminute ('), Arcsecond (") or Turn (revolution) (turn).
- There is nothing to click. The answer keeps pace with your edits.
- Read Result, How it was calculated and Reverse conversion in the results panel.
- If you need a record, Copy Link saves the inputs and Print produces a clean page.
What this tool does not do
- Factors use the internationally agreed definitions; some industries round them differently.
- Repeated conversions compound rounding, so convert once from the original value where you can.
- Values outside the documented ranges are rejected rather than approximated.
- A plausible-looking answer from the wrong input is still the wrong answer: verify the fields first.
Frequently asked questions
3 things: Value, From and To. A starting value is in place for each, so the quickest approach is to replace the one number you actually care about.
With the values loaded when the page opens, result comes out as 0.017453293 rad. Edit any input and that figure moves with it.
No. There is no upload step, no database, and nothing to delete afterwards.
No cost and no account. Use it as often as you like.
It is exact within the stated method. Anything the method does not model is simply out of scope.