Radians Converter & Mode Check
Need quick help before homework or an exam? Use this mini calculator to convert angles and confirm whether you should be in Radians or Degrees.
Tip: If your assignment uses sin, cos, or tan with π (pi), your calculator should usually be in RAD mode.
Why calculators have degree and radian modes
Most scientific calculators support two angle systems: degrees and radians. Degrees divide a full circle into 360 parts. Radians measure angle using arc length, where one full circle is 2π radians. In algebra and geometry you may use degrees frequently, but in higher-level math (especially calculus and physics), radians are often required.
If your calculator is in the wrong mode, trig answers can look totally incorrect even when your steps are right. For example, entering sin(30) gives 0.5 in degree mode, but gives about -0.988 in radian mode, because the calculator interprets 30 as 30 radians, not 30°.
How to change your calculator to radians (quick instructions)
TI-83 / TI-84 series
- Press MODE.
- Use arrow keys to highlight RADIAN.
- Press ENTER so RADIAN is selected.
- Press 2nd then MODE (QUIT) to return.
Casio scientific calculators (fx-991, fx-115, similar)
- Press MODE or SETUP (depends on model).
- Find Angle Unit or Deg/Rad/Gra.
- Select Rad.
Desmos
- Open settings (wrench icon).
- Under angle settings, choose Radians.
Phone calculator apps
- Rotate phone to scientific mode (if needed).
- Look for DEG/RAD toggle and switch to RAD.
How to tell if you are already in radian mode
Most calculators display RAD somewhere on screen. If you do not see it, test with a known value:
- Compute
sin(π/2)— in radians it should equal 1. - Or compute
sin(90)— if this gives 1, your calculator is in degrees, not radians.
Fast conversion rules you should memorize
- Degrees to radians: multiply by π/180
- Radians to degrees: multiply by 180/π
Common angles:
- 30° = π/6
- 45° = π/4
- 60° = π/3
- 90° = π/2
- 180° = π
- 360° = 2π
When should you use radians?
Use radians whenever your class, problem set, or calculator expression includes:
- π directly in angle values
- calculus topics (derivatives/integrals of trig functions)
- physics equations involving angular velocity or harmonic motion
- unit-circle-based trig identities
Troubleshooting wrong trig answers
1) Correct formula, wrong number
The most common cause is wrong mode. Verify DEG vs RAD before reworking your math.
2) You switched mode mid-problem
Some students use degree mode for one class and radian mode for another. Add a habit: check the screen indicator before every trig question.
3) Using graphing calculator defaults
After reset, many calculators return to degree mode. Re-check setup after battery change or memory reset.
Final takeaway
Changing your calculator to radians is usually a 10-second settings update, but it prevents major errors in trigonometry, calculus, and physics. If answers look strange, check angle mode first. Use the converter above any time you need a quick degree↔radian value while studying.