Convert an angle and choose the correct mode
Use numeric values only. The tool also provides decimal degrees, DMS notation, calculator-mode guidance, CSV export, and print-ready results.
Example conversion data
| Radians | Degrees | DMS notation | Typical graphing use |
|---|---|---|---|
| π / 6 ≈ 0.523599 | 30° | 30° 0′ 0″ | Reference angle |
| π / 4 ≈ 0.785398 | 45° | 45° 0′ 0″ | Equal sine and cosine |
| π / 2 ≈ 1.570796 | 90° | 90° 0′ 0″ | Quarter rotation |
| π ≈ 3.141593 | 180° | 180° 0′ 0″ | Half rotation |
| 2π ≈ 6.283185 | 360° | 360° 0′ 0″ | Full rotation |
Formula used
Radians to degrees: Degrees = Radians × 180 ÷ π
Degrees to radians: Radians = Degrees × π ÷ 180
Gradians to degrees: Degrees = Gradians × 0.9
One full turn contains 2π radians, 360 degrees, or 400 gradians. The formulas compare equivalent parts of the same full rotation.
How to use this calculator
- Enter the angle shown in your question or calculator.
- Choose the unit that describes the entered angle.
- Select degrees when your graphing task needs degree measure.
- Choose the calculator menu style closest to your device.
- Set a precision level, then select Convert angle.
- Read the result above the form and update your calculator mode.
- Export the values as CSV or print the result when needed.
Angle mode and graphing accuracy
Why the setting matters
Graphing calculators interpret trigonometric inputs through an angle mode. That mode can be degrees, radians, or gradians. A correct expression can produce an unexpected number when the selected mode is wrong. The graph may also look unfamiliar. A sine curve can appear compressed or stretched across a chosen window.
Degrees and radians describe the same turn
Degrees divide one complete rotation into 360 equal parts. Radians measure an angle through arc length and radius. One full turn equals 360 degrees and 2π radians. Therefore, π radians equals 180 degrees. The conversion factor 180 divided by π changes radians into degrees accurately.
Change the calculator mode before evaluating functions
Converting a number does not automatically change your device setting. Open the mode or settings screen. Choose Degree when entering degree values into sine, cosine, tangent, inverse trigonometric functions, or polar graphs. Choose Radian when formulas include π, calculus conventions, unit-circle analysis, or radian-based periodic models.
Check a familiar reference angle
A fast check avoids many errors. In Degree mode, sin(30) should equal 0.5. In Radian mode, sin(π/6) should equal 0.5. If you type 30 while the calculator expects radians, the result differs. This simple test confirms that the displayed mode matches your intended input.
Use the graph window thoughtfully
Angle mode affects values, while window settings affect visibility. After changing modes, review the horizontal scale. Degree graphs often use values such as 0 to 360. Radian graphs often use 0 to 2π. A mismatched window can hide important cycles even after the calculator mode is corrected.
Keep enough precision
Rounding is helpful for reading results. It can create small differences in later calculations. Retain more decimal places for engineering, science, or chained trigonometric work. Use fewer places for classroom answers when the required rounding is clear. The calculator displays decimal degrees and DMS notation to support both situations.
Avoid common conversion mistakes
Do not multiply degrees by 180 divided by π. That formula goes in the wrong direction. Do not replace π with 3 unless an estimate is requested. Do not assume a calculator remembers your last intended mode. Verify the on-screen indicator before every important calculation or graph.
Enter angles in the intended form
Use parentheses when a calculation contains several operations. Enter negative angles with a leading minus sign. Preserve π symbols on your device when an expression includes exact values. Convert only after deciding whether the original problem gives radians or degrees. This order reduces accidental double conversions. It also keeps inverse trigonometric answers consistent with the required unit. Review any stored variables before reusing a previous graph.
Document settings in shared work
When you share a graph, label the angle unit in notes or captions. Another person may reproduce the same function using a different mode. Stating Degree or Radian prevents confusion. This is useful in lab reports, engineering worksheets, and saved calculator files. Small checks at the beginning protect later calculations, tables, and conclusions. Clear labels also help when you return to a project later. Check labels before submitting work. This habit prevents avoidable errors during later reviews and revisions.
Frequently asked questions
1. How do I change radians to degrees?
Multiply the radian value by 180 and divide by π. For example, π/2 radians becomes 90 degrees. Then set your calculator’s angle mode to Degree before entering degree-based trigonometric expressions.
2. Why does my calculator give a different sine value?
Your calculator may be using the wrong angle mode. sin(30) means 30 degrees in Degree mode, but 30 radians in Radian mode. Check the on-screen mode indicator before calculating.
3. Does converting an angle change calculator mode automatically?
No. A conversion changes the number only. You must open the calculator mode or setup menu and select Degree, Radian, or Gradian manually.
4. What is π radians in degrees?
π radians equals 180 degrees. This represents half of a full turn. Two π radians equals 360 degrees, which represents one complete rotation.
5. Should I use degrees or radians for graphing?
Use the unit required by the problem. Degrees are common for geometry and navigation. Radians are common for calculus, advanced trigonometry, and formulas involving π. Match the calculator mode to the input unit.
6. What are gradians?
Gradians divide a full turn into 400 parts. A right angle equals 100 gradians. They appear in some surveying and technical settings, but degrees and radians are more common in graphing work.
7. How many degrees are in one radian?
One radian is approximately 57.2958 degrees. The exact relationship is 180 divided by π degrees. This value helps estimate conversions, although the full formula provides better accuracy.
8. Can I enter π directly in this calculator?
This web calculator accepts numeric values. Enter a decimal approximation, such as 3.141592654 for π. On a graphing calculator, use its π key whenever available for better precision.
9. Why does my graph look compressed after changing modes?
Your graph window may still use the previous unit scale. Degree graphs often cover 0 through 360. Radian graphs often cover 0 through about 6.283. Adjust the window after changing angle mode.
10. Is decimal degree notation the same as DMS notation?
They represent the same angle differently. Decimal degrees use a fractional degree, such as 45.5°. DMS uses degrees, minutes, and seconds, such as 45° 30′ 0″.
11. Can I save the results?
Yes. Use the Download CSV button for a spreadsheet-friendly file. Use Print / Save PDF in the result panel for a printable record. Both options preserve the calculated angle values.