Calculator
What the Angle Converter does
Angle 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.
Enter Value, From and To and the Angle Converter reports Result, How it was calculated and Reverse conversion. Edit a field and the answer updates in place.
Typical users are anyone working across two measurement systems. Having the exact factor matters more than a rough mental estimate.
There is no back end here. The calculation runs where you are sitting, not on a server somewhere.
The meaning of each field, the formula in use, and a worked example that starts from the default inputs are all further down.
What do the Angle Converter fields mean?
The Angle Converter uses 3 inputs. You can work from the defaults, or clear them and start fresh, both work.
| 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 Angle 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.
Definitions are taken from the SI system where one exists, and from CODATA or the IAU where a unit is established by measurement. No factor is rounded before the calculation.
Worked example
These are the values the Angle Converter loads by default, and the result it produces from them. Here is the calculation as it stands the moment the page loads.
| 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) |
Degrees, radians and other angle units
A full circle is exactly 360 degrees or exactly 2π radians, two completely different-looking numbers describing the identical rotation, because they come from two different traditions: degrees from ancient Babylonian base-60 astronomy, radians from the purely mathematical relationship between a circle’s radius and its circumference.
Worth knowing
- Radians are the unit calculus and most higher mathematics actually require: trigonometric derivatives and many physics formulas only take their simple, familiar forms when angles are measured in radians, not degrees.
- The 360-degree circle likely traces back to Babylonian astronomers, who used a base-60 number system and noticed that 360 is conveniently close to the number of days in a year while also dividing evenly by many small numbers (2, 3, 4, 5, 6, 8, 9, 10, 12...), making it practical for the era’s calculations.
- Beyond degrees and radians, a handful of specialised angle units exist for particular fields (gradians for some surveying equipment, mils for military artillery, arcminutes and arcseconds for astronomy) each covered in their own converters on this site.
Definitions: BIPM SI Brochure · NIST reference on units
How to use it
- Enter 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).
- The result appears as you type. There is no button to press.
- You get Result, How it was calculated and Reverse conversion back.
- Copy Link is the quickest way to send the exact scenario to someone else.
What this tool does not do
- Repeated conversions compound rounding, so convert once from the original value where possible.
- Factors use the internationally agreed definitions; some industries round them differently.
- It cannot flag an input that is technically valid but wrong for your case.
- It validates ranges, not intent. A value can be accepted and still be the wrong one to use.
Frequently asked questions
3 things: Value, From and To. Nothing starts empty, meaning you can explore the calculation before committing to real figures.
With the values loaded when the page opens, result comes out as 0.017453293 rad. Any edit re-runs the calculation, so there is no stale number on screen.
Not at all: the whole thing runs offline once the page has loaded, which tells you nothing is being sent.
Nothing at all. There is no registration, no paywall and no per-use quota.
It implements the published definition directly, without shortcuts or approximations.