rad to deg Converter
Turn radian values into clear degree angles
Radians to degrees FAQ
How do you convert radians to degrees exactly?
The core fact is that a full circle is 2π radians = 360°. That means π rad = 180°, so 1 rad = 180°/π ≈ 57.29577951°. To convert from radians to degrees, you multiply the radian value by 180/π. For example, π/6 rad becomes 30°, π/4 rad becomes 45°, and about 1.5708 rad corresponds to 90°. The calculator uses this exact relationship and handles the rounding automatically.
Why do calculators and websites give slightly different degree values?
Small differences usually come from how many digits of π are used and how the final result is rounded. Some tools approximate π as 3.14, others as 3.1416 or more digits. Over large angles or when you chain several operations, that can shift the last decimal place or two. This converter relies on your browser’s high-precision value of π and then formats the answer consistently so it’s easy to paste into homework, spreadsheets or code comments.
What’s 1 radian in degrees?
Exactly, 1 rad = 180°/π, which is approximately 57.2958°. Remembering that 1 rad is a bit less than 60° gives you a good mental anchor for estimating other radian values in degrees. The converter uses the full precision of 180/π so repeated conversions stay consistent.
Why do many math and physics formulas give answers in radians?
Radians are the natural unit for angles in calculus, trigonometry and much of
physics. When angles are measured in radians, derivatives and series for
sine, cosine and other functions become simple, which is why many formulas
assume radian input. Programming languages follow the same convention:
functions like sin() and cos() typically expect
radians. This converter helps you translate those radian-based outputs into
degrees that feel more intuitive when you explain or visualize results.
Can I use this for angles coming from sensors, simulations or code?
Yes. Many sensors, robotics libraries, simulations and game engines report angles in radians. You can paste the raw radian value, convert it to degrees, and instantly see something like “1.0472 rad = 60°”. That makes it much easier to sanity-check motion, steering, camera rotation or phase angles against your expectations in everyday degree terms.
Is there a quick mental shortcut for radians to degrees?
A simple rule of thumb is to multiply by 60 and subtract a bit, because 1 rad is a little under 60°. For example, 1.0 rad ≈ 57°, 1.5 rad is a bit under 90°, and 3.0 rad is a bit under 180°. Another shortcut is to multiply by 180/π ≈ 57.3 using 57 or 57.5 in your head. The converter uses the exact 180/π factor every time so you can compare your rough mental estimate with a precise numerical answer.
From radian-based formulas to everyday degree angles
This rad to deg converter is designed for the common situation where your calculator, textbook, code or sensor gives you an angle in radians, but you want to interpret or present it in degrees. That happens in math homework, physics problems, engineering design, robotics, control systems and computer graphics. Instead of re-typing a formula into a spreadsheet or interpreter every time, you enter the radian value, press convert and see a clear statement such as “1.5708 rad = 90°”.
1. Simple single-box interface for any angle
The interface is deliberately minimal: one input field for radians and one result card. It works for tiny angles like 0.01 rad, standard values such as π/6 or π/2, and large angles that wrap around the circle many times. You can paste decimal radians directly from code, calculator history or data logs. The converter applies the exact 180/π factor and formats the result in degrees in a way that’s easy to read and copy.
When you need to go in the opposite direction, the “Swap Units” button takes you straight to the dedicated deg to rad page. That lets you move back and forth between degrees and radians without reconfiguring settings in a hardware calculator or a larger conversion tool.
2. Exact relationship: 1 rad = 180°/π
The converter follows the standard definitions used in mathematics and the SI system. A full turn is 360° or 2π rad. Dividing by 2 shows that 180° corresponds to π rad, and dividing again by π gives 1 rad = 180°/π ≈ 57.2958°. Using this exact relationship keeps your radians to degrees conversions aligned with scientific calculators, programming libraries and reference tables.
If you need to move between other angle units, such as gradians, turns or milliradians, you can step up to the full angle conversion calculator. It delivers the same clean style of results while covering more unit combinations in one place.
3. Common radian to degree values at a glance
Here are some frequently used radian measures and their degree equivalents. They match what the calculator produces and are great checkpoints when you debug calculations or verify exam answers:
| Radians (rad) | Degrees (°) |
|---|---|
| π/6 ≈ 0.5236 | 30° |
| π/4 ≈ 0.7854 | 45° |
| π/3 ≈ 1.0472 | 60° |
| &pi/2 ≈ 1.5708 | 90° |
| 2π/3 ≈ 2.0944 | 120° |
| π ≈ 3.1416 | 180° |
| 3π/2 ≈ 4.7124 | 270° |
| 2π ≈ 6.2832 | 360° |
A quick mental check is to remember that π rad is 180° and 1 rad is a bit under 60°. If your radian value is around half of π, the degree result should be near 90°, and so on. The converter helps turn that intuition into a precise numerical answer with one click.
4. Where the rad to deg converter shines
You will often reach for this tool when you:
- Interpret math and physics results — turn radian answers from exams, textbooks or CAS systems into degrees you can visualise.
- Debug code that uses trig functions — convert radian angles from
sin,cosor rotation matrices into degrees for easier reasoning. - Work with robotics and control systems — translate sensor readings, joint angles or heading from radians into degrees for dashboards and logs.
- Analyse simulations and animations — convert radian-based rotation outputs into degrees when reviewing motion or camera paths.
- Prepare teaching material or documentation — show both radian and degree values side-by-side in diagrams, tables and worked examples.
Because the underlying conversion is fixed by the relationship between degrees, radians and the full turn of a circle, this radians to degrees converter will always give the same result for the same input. It becomes a dependable bridge between radian-based formulas and the degree angles people use in diagrams, explanations and everyday thinking.
References and further reading on radians and degrees
These references explain how radians and degrees are defined and why radians are widely used in mathematics and science:
- Radian — describes the radian as the SI derived unit of angle and how it relates to arc length and the circle.
- Degree (angle) — covers the degree as a unit of plane angle and its common uses in navigation, surveying and everyday geometry.
- SI Brochure — Plane angle and the radian (NIST) — provides the formal SI treatment of the radian and its role in scientific work.
For exams, standards or published work, always follow the notation and rounding rules required by your teacher, institution or style guide when converting between radians and degrees.