Angles look innocent until two tools disagree on the unit. A CAD rotation field shows 90. A trig library wants 1.5708. A survey note mentions 100 gradians. Someone on the team still thinks in compass degrees while the postprocessor prints radians. The converter above is the quick handshake: enter what you have, pick what the next step expects, copy the result into the script or the setup sheet.
Plenty of classroom mistakes are just a wrong mode on the calculator—45 entered as degrees when the grading script assumed radians, or the reverse. Before you blame the formula, run a single conversion and read the detail line. A check people use constantly: 90 degrees expressed in radians should land near 1.57, not anywhere near 90.
Software is the same story with different symptoms. Spreadsheets and drawing tools usually speak degrees. Many programming math functions expect radians unless the docs say otherwise. Pasting a degree value into code without converting is how you get a gentle slope when you meant a vertical line.
Turns, gradians, and the pi habit
A full rotation is 360 degrees, 2π radians, 400 gradians, or one turn depending on who wrote the spec. When a CAM file lists 0.25 turn, that is a quarter rotation—a quarter turn in degrees is the sanity pass before you override a fixture offset.
Gradians show up in surveying and some European drawing traditions more often than in everyday homework. If a note says 50 grad and your head only thinks degrees, convert once instead of scaling by guesswork.
Swap the from/to units if you typed the comparison backwards—the control beside the fields fixes direction faster than redoing mental π arithmetic. Negative angles and values above one full turn still convert; normalize in your own process if the downstream tool only accepts 0–360°.
Before the number goes into code or metal
Round for display, not twice in a chain. Convert the authoritative value once, then format for the UI or the printout. If you need a bearing on a map, that is still an angle—but it is not a length, so do not route compass headings through a length converter by habit.
- Match the unit the next tool's docs name explicitly.
- Confirm whether the source meant degrees or radians before debugging trig.
- Keep the original value beside the converted one in tickets.
The degrees and radians workflow note walks CAD and homework mixes without turning this page into a trig course. For bigger unit confusion across a project, the unit conversion checklist still starts with naming the dimension.
Reference conversions for plans and code, not certified surveying. When rotation matters, paste both figures so the next person does not inherit the wrong mode.