Calculator
What the Radian Converter does
Radian Converter: 1 rad = 57.29577951 °, so multiply a radian value by 57.29577951 to get degree, or divide to go back. Example: 1 rad = 57.29577951 °.
Result, How it was calculated and Reverse conversion, derived from Value, From and To. You can nudge a single number and watch the effect straight away.
Most people who open the Radian Converter are anyone working across two measurement systems. Having the exact factor matters more than a rough mental estimate.
There is no account, no upload and no server round trip, because the page does the work itself.
If you want to check the arithmetic, the field table, the method and a worked example are further down.
What do the Radian Converter fields mean?
The Radian Converter uses 3 inputs. You do not have to fill everything in before seeing an answer; the starting values already produce one.
| Field | What to enter | Default |
|---|---|---|
| Value | required | 1 |
| From | choose from Degree (°), Radian (rad), Gradian (grad), Arcminute ('), Arcsecond (") or Turn (revolution) (turn) | Radian (rad) |
| To | choose from Degree (°), Radian (rad), Gradian (grad), Arcminute ('), Arcsecond (") or Turn (revolution) (turn) | Degree (°) |
How does the Radian 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.
Factors follow the internationally agreed definitions. The inch has been exactly 25.4 mm since 1959, and an exact definition is used wherever one exists. Where a unit is fixed by measurement rather than by agreement, the accepted CODATA or IAU value is used.
Worked example
These are the values the Radian Converter loads by default, and the result it produces from them. This is the worked example the page starts from, reproduced here so you can check the arithmetic.
| Value | 1 |
|---|---|
| From | Radian (rad) |
| To | Degree (°) |
| Result | 57.29577951 ° |
|---|---|
| How it was calculated | 1 rad = 57.29577951 °, so 1 × 57.29577951 = 57.29577951 ° |
| Reverse conversion | 0.017453293 rad (if you meant 1 °) |
The radian
A radian is defined geometrically, not by an arbitrary division of the circle: it’s the angle at which the arc length along a circle equals the circle’s radius, which means a full circle is exactly 2π radians (about 6.2832 radians), an irrational number rather than a round one.
Worth knowing
- Because it’s derived directly from the geometry of the circle rather than an arbitrary cultural convention (unlike the 360-degree system), the radian is the unit mathematics and physics formulas are built around: angular velocity, simple harmonic motion, and calculus involving trigonometric functions all assume radians unless stated otherwise.
- Most programming languages’ built-in trigonometric functions (sin, cos, tan) expect radians as input, not degrees: a very common source of bugs when a value in degrees is passed in directly without first converting it.
- Despite its mathematical elegance, the radian is rarely used in everyday, non-technical contexts, nobody gives directions or describes a turn using radians, which is why degrees remain the practical, human-facing default almost everywhere outside formal mathematics and physics.
Definitions: BIPM SI Brochure · NIST reference on units
How to use it
- Fill 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).
- Watch the results panel as you type: it recalculates on every keystroke.
- The panel reports Result, How it was calculated and Reverse conversion.
- Copy Link puts the current inputs in the URL, so bookmarking it brings the same numbers back.
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.
- The output is a number, not a judgement. Deciding what it means is still your job.
- The tool cannot tell whether a number was entered in the unit you intended, so double-check the labels.
Frequently asked questions
Just Value, From and To. Every box already holds a working value, meaning you can explore the calculation before committing to real figures.
With the values loaded when the page opens, result comes out as 57.29577951 °. The figure is derived from the inputs above, so it updates whenever they do.
Nothing leaves your machine. The only network traffic is loading the page itself.
No. There is no account, no usage cap and no trial period. The site is funded by advertising rather than by charging for the tools.
The output is deterministic. The same inputs always give the same answer, and the method is documented above so you can check it.