What this calculator does
Reference & coterminal angle works out reduces any angle to its 0–360° coterminal angle, quadrant and reference angle. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulacoterminal = ((θ mod 360) + 360) mod 360; reference angle measures the gap to the nearest x-axis
The inputs explained
| Field | What to enter |
|---|---|
| Angle (degrees, any value) | A number. Starts at -750. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with angle (degrees, any value)
Every other input is held at the calculator’s starting values while angle (degrees, any value) varies. Select any row to load that scenario into the calculator.