Angle conversion tool
Radians, Degrees, DMS, and Pi Values
Use the selected conversion type. Results appear above this form after calculation.
Formula used
Degrees to radians: radians = degrees × π ÷ 180
Radians to degrees: degrees = radians × 180 ÷ π
DMS to radians: radians = sign × (degrees + minutes ÷ 60 + seconds ÷ 3600) × π ÷ 180
Pi multiple: radians = coefficient × π, and coefficient = radians ÷ π
A full turn equals 360° and 2π radians. Therefore, 180° equals π radians, 90° equals π ÷ 2 radians, and 270° equals 3π ÷ 2 radians.
How to use this calculator
- Select the conversion type that matches your given angle.
- Choose your TI calculator family for a useful radians reminder.
- Enter one decimal angle or provide degree, minute, and second values.
- Choose the number of decimal places needed for your work.
- Press Convert angle. Review the result above the form.
- Download the CSV record or use Save as PDF from your browser.
For a TI-83 or TI-84 family calculator, choose Radian in the MODE menu. Other TI models may use a DRG or setup menu. The key names can vary by model.
Example conversion data
| Given angle | Decimal degrees | Decimal radians | Pi multiple | Common use |
|---|---|---|---|---|
| 30° | 30° | 0.523599 rad | π ÷ 6 | Special triangles |
| 90° | 90° | 1.570796 rad | π ÷ 2 | Quarter turns |
| 180° | 180° | 3.141593 rad | π | Straight angles |
| 45° 30′ 0″ | 45.5° | 0.794125 rad | 0.252778π | Survey and navigation |
Radian Mode Matters
Radian mode matters because trigonometric formulas use angular measure based on a circle. One radian measures an arc equal to the circle radius. A full rotation contains two pi radians. That same rotation contains 360 degrees. Your calculator must use the unit expected by the question. A correct expression can appear wrong when the mode is incorrect.
Check the TI Setting First
Many TI calculators keep the chosen angle mode until you change it. This can affect sine, cosine, tangent, inverse functions, graphing, and numerical tables. Before solving a problem, look for RAD or Radian on the display. Change the mode before entering the expression. Do not convert the final answer twice. The calculator should receive angles in the unit required by your formula.
Find the Radians Option
On many TI graphing models, press MODE. Move to the line that lists Degree and Radian. Highlight Radian, then press ENTER. Press 2nd and MODE to leave the settings screen. The top display should show RAD while you work. Some scientific models use a MODE, DRG, or setup key instead. Choose RAD from that menu. Labels can differ across model generations.
Convert the Form You Have
This tool converts several common formats. Enter a decimal degree value when you know an ordinary angle. Enter a radian value when a textbook gives a result with radians. Use degrees, minutes, and seconds for survey, navigation, or geographic angles. Use a pi coefficient when the angle is written as a multiple of pi. For example, 0.75 pi equals three quarters of pi radians.
Read Every Result Carefully
The result area gives more than one representation. It reports decimal degrees, decimal radians, a pi multiple, a normalized radian value, and a degree-minute-second value. Normalization places an angle within one positive full turn. That makes equivalent angles easier to compare. For example, negative pi over two normalizes to three pi over two. This does not change the terminal side.
Choose Helpful Precision
Use reasonable precision for your purpose. Six decimal places work for most classroom tasks. More places can help during engineering calculations. Fewer places may be easier to read. Keep extra digits until your final answer. Round only when the instructions request it. When a question needs an exact form, prefer the pi multiple result over a rounded decimal.
Avoid Common Unit Errors
Check whether an inverse trigonometric result needs radians. A function such as arctangent can return a different numeric value in each mode. Both values may describe the same direction, but their units differ. Graph windows and parametric equations also depend on the selected mode. Use the displayed unit label as a final safeguard.
Use It as a Verification Tool
This calculator does not replace the TI setting. It helps verify conversions and explain the values you enter. Set your device to radians first. Then use this page to compare forms, export a record, or review the method. Careful unit handling prevents common trigonometry mistakes and makes calculator work easier to trust. It provides a simple record for later study and checking.
Frequently asked questions
1. How do I set a TI-84 calculator to radians?
Press MODE. Find the angle setting line. Highlight Radian and press ENTER. Then press 2nd followed by MODE to exit. Confirm that RAD appears on the home screen before using trigonometric functions.
2. Why does my sine answer look wrong?
Your calculator may be using the wrong angle mode. A value entered as degrees produces a different result in radian mode. Check the question, then check the display for DEG or RAD before calculating.
3. What is the formula for degrees to radians?
Multiply the degree value by π and divide by 180. For example, 180 × π ÷ 180 equals π radians. This relationship comes from one full circle being 360 degrees or 2π radians.
4. What is the formula for radians to degrees?
Multiply the radian value by 180 and divide by π. For example, π ÷ 2 multiplied by 180 ÷ π equals 90 degrees. Use this when a result is supplied in decimal radians.
5. What does a pi multiple mean?
A pi multiple writes an angle as a coefficient times π. For example, 0.5π means one half of π radians. It is often preferred because it preserves exact values for special angles.
6. Can I enter negative angles?
Yes. Enter a negative decimal value for degree or radian conversions. For DMS input, place the negative sign in the degrees field. Keep minutes and seconds nonnegative and below sixty.
7. What are normalized radians?
Normalized radians describe an equivalent angle between zero and 2π. The calculator adds or subtracts full turns as needed. This helps compare terminal sides without changing the actual direction.
8. Does radian mode affect graphing?
Yes. Trigonometric graphing uses the current angle mode. Radian mode is usually expected for functions involving π, calculus, period formulas, and many advanced mathematics problems.
9. How many radians are in a full circle?
A full circle contains 2π radians, which is about 6.283185 radians. Half a circle contains π radians. A quarter turn contains π ÷ 2 radians.
10. Can I save my calculated result?
Yes. After a successful calculation, use Download CSV for a spreadsheet-friendly file. Use Save as PDF to open your browser print dialog and select its PDF saving option.
11. Which precision should I choose?
Choose six decimal places for typical homework. Use more places for technical work or later calculations. Use fewer places for a cleaner display. Keep full precision until your final required rounding step.