This degrees to radians calculator converts a numeric degree value into a numeric radian result instantly. It is useful for trigonometry homework, JavaScript or Python angle handling, graphics rotation values, and engineering workflows where formulas expect radians. The page explains the familiar degree-to-radian relationship with pi for context, but the tool itself returns a decimal number rather than a symbolic value such as pi/2.
The exact relationship is radians = degrees x (pi / 180). Since 180 degrees equals pi radians, every degree contributes a fixed share of pi. For browser-based conversion, the result is shown as a decimal radian value so you can copy it directly into code, calculators, or numeric workflows.
If you convert 90 degrees, the exact math is 90 x pi / 180, which equals pi/2. The calculator shows the decimal result 1.5707963268. If you convert 45 degrees, the exact math is pi/4 and the decimal output is 0.7853981634. This is why the page is useful for both classroom understanding and real numeric input into programming tools.
Common long-tail queries are easy to check against the formula. 30 degrees equals 0.5235987756 radians. 60 degrees equals 1.0471975512 radians. 120 degrees equals 2.0943951024 radians. A negative angle keeps its sign, so -45 degrees becomes -0.7853981634 radians. The conversion is linear, which means doubling the degree input doubles the radian result.
Most programming languages and math libraries expect radians for trigonometric functions. In JavaScript, for example, Math.sin(), Math.cos(), and Math.tan() read radian input. That means if a design spec says rotate by 30 degrees, the numeric value you feed into the trig function is 0.5235987756 rather than 30. This is one of the main reasons people search for deg to rad calculators.
One common use case is geometry and precalculus work, where a worksheet or class problem gives an angle in degrees but the next step needs radians. Another is front-end or game development, where animation and rotation code often expects radians even when designers talk in degrees. CAD, robotics, and physics work also use radian-based formulas for angular velocity, wave motion, and circular motion.
If you need the reverse workflow after reading output from a code library or scientific calculator, our radians to degrees converter handles the opposite direction. If you are working with surveying-style angle units instead, our degrees to gradians converter covers the gradian system, and our full angle unit converter lets you move across the wider angle family.
This page is a numeric converter only. It does not simplify output into symbolic pi fractions, it does not parse degree-minute-second text such as 30 degrees 15 minutes, and it does not evaluate sine, cosine, tangent, or inverse trig results for you. If you need a conversion here, enter a decimal degree value and use the decimal radian result the tool returns.
A lot of users arrive for deg to rad, 90 degrees in radians, 45 degrees to radians, or a dependable deg to rad calculator before pasting values into code, spreadsheets, or calculators. This page answers those exact questions while staying truthful about one important boundary: the output is a decimal radian result, not symbolic classroom notation.
If the session expands into gradians, turns, or mixed angle systems, switch to the shared angle conversion tool. If the next task is simply reversing a numeric result, continue to the radians to degrees converter. That keeps degrees to radians narrow, practical, and well linked to the surrounding cluster.
| Degrees | Decimal radians | Common query |
|---|---|---|
| 0 | 0 | 0 degrees to radians |
| 15 | 0.2617993878 | 15 degrees to radians |
| 30 | 0.5235987756 | 30 degrees to radians |
| 45 | 0.7853981634 | 45 degrees to radians |
| 60 | 1.0471975512 | 60 degrees to radians |
| 90 | 1.5707963268 | 90 degrees to radians |
| 120 | 2.0943951024 | 120 degrees to radians |
| 180 | 3.1415926536 | 180 degrees to radians |
| 270 | 4.7123889804 | 270 degrees to radians |
| 360 | 6.2831853072 | 360 degrees to radians |
The exact formula is radians = degrees x (pi / 180). This page uses that relationship and returns the result as a decimal number.
180 degrees equals 3.1415926536 radians, which is the decimal form of pi.
90 degrees equals 1.5707963268 radians. In exact math notation that is pi/2, but this tool displays the decimal result.
No. The page may mention exact math relationships for explanation, but the converter itself outputs decimal radians only.
Yes. The sign is preserved, so a negative degree input produces a negative radian result.
No. Enter a decimal degree value only. This page does not parse DMS text input.
Radians are the standard unit used by most trig libraries because they fit the underlying math directly. That is why deg to rad conversion is so common in code and engineering workflows.
Use this route when the source angle is already in degrees and the next workflow expects numeric radians. That is the common case for trig formulas, graphics programming, physics homework, and rotation values in code where the destination is a decimal radian result rather than another degree-based representation.
If the job involves several angle units or surveying-style values, the shared angle conversion tool is more flexible. This page is most useful when the direct degree-to-radian step is the only real question.
Remember that this page returns decimal radians, not symbolic pi fractions. That matters if the next consumer is a textbook solution versus a calculator or code library. For the reverse route, use Radians to Degrees Converter. If the destination is the gradian system instead, go to Degrees to Gradians Converter.
This is why the page stays useful. It gives one practical numeric radian answer and leaves symbolic math or alternate angle systems to the neighboring tools.
Convert degrees to decimal radians for trig formulas, coding libraries, and rotation values.
Use these workflow guides when you need more context before or after running this tool.