deg to rad Converter
Convert degree angles into precise radian values
Degrees to radians FAQ
How do you convert degrees to radians exactly?
The key relationship is that a full circle is 360° = 2π rad. That means 180° = π rad, so 1° = π/180 rad ≈ 0.01745329252 rad. To convert from degrees to radians, you multiply the degree value by π/180. For example, 45° becomes π/4 rad (about 0.7854 rad) and 90° becomes π/2 rad (about 1.5708 rad). The calculator uses this exact relationship internally and handles the rounding for you.
Why do calculators and websites sometimes give slightly different radian values?
Most differences come from how many decimals of π are used and how the final result is rounded. Some tools round π to 3.14, others to 3.1416 or more digits. Over large angles this can shift the final decimal places. This converter relies on your browser’s built-in value of π, which is very accurate, and then formats the result in a consistent way so it is ready to paste into homework, code or documentation.
What’s 180 degrees in radians?
By definition, 180° = π radians. Numerically that is about 3.1415926536 rad. This is the anchor for all other deg to rad conversions: once you remember that 180° corresponds to π rad, it’s easy to scale other angles up or down.
Why do math and programming often use radians instead of degrees?
Radians are the natural unit for angles in calculus and many formulas. When angles are measured in radians, trigonometric functions have clean derivatives and limits, and many physics equations simplify. That is why most programming languages’ math libraries expect angles in radians. With this converter you can keep thinking in degrees while still giving your code the radian values it needs.
Can I use this for rotating graphics, animations or game coordinates?
Yes. When you work with 2D or 3D graphics libraries, rotation functions usually expect radians. You can type the familiar degree angle (like 30°, 45° or 270°), convert it to radians, and then paste the result directly into your transform, shader or physics code. This reduces mistakes compared with trying to remember “rough” radian values off the top of your head.
Is there a quick mental shortcut for degrees to radians?
A handy rule of thumb is to multiply by π and divide by 200, which slightly underestimates the answer but is easy to do in your head. For example, 60° → (60 × π)/200 ≈ 0.94 rad, which is close to the exact 1.0472 rad. Another common shortcut is to remember a few key angles like 30°, 45°, 60° and 90° in radians and then judge other angles relative to those. The converter uses the exact π/180 factor every time so you can sanity-check your mental estimates.
From everyday degrees to radian-friendly angles
This deg to rad converter is designed for the moment when you think in degrees but your formulas, calculator or code want radians instead. That happens a lot in trigonometry, calculus, signal processing, graphics, robotics and game development. Rather than typing a custom formula into a spreadsheet or a console every time, you enter the degree measure, press convert and immediately see the matching radian value in a clean format such as “45° = 0.785398 rad”.
1. Simple single-box interface for any angle
The interface is intentionally minimal: one input field for degrees, one result card underneath. It works for tiny angles like 0.5°, standard angles such as 30° and 90°, and large angles beyond a full turn. You can paste values directly from code, notes or a calculator, including decimal degrees such as 12.75°. The converter applies the exact π/180 factor behind the scenes and formats the radian value so that it is easy to read and copy.
If you later need to reverse the process, the “Swap Units” button takes you straight to the dedicated rad to deg page. That makes it easy to move between both directions without reconfiguring an all-in-one tool or digging through menus on a calculator.
2. Exact relationship: 1° = π/180 rad
The converter is based on the standard angle definitions used in mathematics and the SI system. A full revolution is 360°, which corresponds to an angle of 2π radians. Half a turn, 180°, is therefore π radians. Dividing both sides by 180 gives 1° = π/180 rad ≈ 0.01745329252 rad. Using this exact ratio keeps your degrees to radians conversions consistent with textbooks, scientific calculators and programming libraries.
When you need to work with other angle units like gradians, turns or milliradians, you can step up to the full angle conversion calculator. It uses the same style of clear outputs while handling more combinations in one place.
3. Common degrees to radians values at a glance
Here are some of the most frequently used angles and their radian equivalents. They match what the calculator produces and make useful checkpoints when checking homework or debugging code:
| Degrees (°) | Radians (rad) |
|---|---|
| 30° | π/6 (≈ 0.5236 rad) |
| 45° | π/4 (≈ 0.7854 rad) |
| 60° | π/3 (≈ 1.0472 rad) |
| 90° | π/2 (≈ 1.5708 rad) |
| 120° | 2π/3 (≈ 2.0944 rad) |
| 180° | π (≈ 3.1416 rad) |
| 270° | 3π/2 (≈ 4.7124 rad) |
| 360° | 2π (≈ 6.2832 rad) |
A simple mental check is to remember that 180° corresponds to π rad. If your degree angle is roughly half of 180°, the radian result should be close to π/2, and so on. The converter lets you lean on that intuition while still giving an exact numeric value.
4. Where the deg to rad converter shines
You will often reach for this tool when you:
- Do trigonometry or calculus — convert degree angles into radians so formulas, derivatives and integrals behave as expected.
- Write code that uses sin, cos or tan — supply radians to programming language math libraries while thinking in degrees.
- Work with physics and engineering problems — translate angular velocities, phase shifts and oscillations from degrees to radians.
- Rotate sprites, cameras or meshes — convert intuitive degree rotations into radians for graphics or game engines.
- Prepare documentation and teaching material — show both degree and radian versions of the same angle on diagrams and examples.
Because the underlying conversion is fixed by the relationship between the circle and π, this degrees to radians converter will always give the same result for the same input. It becomes a reliable reference as you move between mental pictures in degrees and the radian-based world of math, physics and programming.
References and further reading on degrees and radians
These references explain how degrees and radians are defined and why radians are so common in mathematics and science:
- Degree (angle) — describes the degree as a unit of plane angle and its relationship to radians and other angle units.
- Radian — explains the radian as the SI derived unit of angle and why it is preferred in most mathematical work.
- SI Brochure — Plane angle and the radian (NIST) — gives the formal SI definition of the radian and its role as the coherent unit for plane angle.
For exams, specifications or published work, always follow the notation and rounding rules required by your teacher, institution or publishing style when converting between degrees and radians.