Radians to Degrees Calculator

Formula used

The conversion formula is degrees = radians × 180 ÷ π.

One full turn contains 2π radians and 360 degrees. Therefore, each radian equals approximately 57.295779513 degrees.

How to use this calculator

1. Enter a decimal radian value or a supported π expression.
2. Optionally select a preset angle for a standard conversion.
3. Choose decimal precision, rounding, normalization, and display settings.
4. Press Convert radians to view the result above this form.
5. Use CSV or PDF export after reviewing the displayed result.

Example conversion data

Radians and degrees explained

Understanding radians and degrees

Radians and degrees describe the same angle in different ways. Degrees divide a full turn into 360 equal parts. Radians measure angles through the relationship between an arc and radius. One complete rotation equals 2π radians. It also equals 360 degrees. This calculator changes the representation without changing the actual angle. It helps with classroom work, technical drawings, programming, and scientific calculations. A clear conversion helps prevent confusing angle units during important work.

Why the conversion matters

Many formulas use radians by default. Trigonometry, calculus, physics, and software often follow radian measurement. People may still need degrees for reports, plans, or familiar visual references. Conversion keeps numbers understandable across different contexts. For example, π/2 radians represents a right angle. The same angle is 90 degrees. A value of π radians is 180 degrees. Using the correct unit avoids mistaken sine, cosine, rotation, and slope calculations. Always check the required angle unit before entering a value.

Using precision and rounding

Real-world conversions can create long decimal results. The degree value for one radian is approximately 57.295779513 degrees. Precision settings control how many decimal places appear. Standard rounding gives the nearest selected value. Floor rounding moves downward. Ceiling rounding moves upward. Truncation removes extra decimal digits. Choose a method that matches your instructions or measurement practice. Engineering tasks often state required precision. Classroom answers may need fewer digits. Keep extra decimals while working, then round the final reported answer.

Working with normalized angles

Angles can extend beyond one rotation or move below zero. Normalization changes their display range while preserving their direction on a circle. The 0 to 360 option is useful for bearings and complete rotations. The minus 180 to 180 option suits signed turns and coordinate systems. For instance, 450 degrees normalizes to 90 degrees. Negative 270 degrees normalizes to 90 degrees in the first range. The calculator can leave values unchanged when the original total rotation matters. Select the range before calculating.

Reading the result

Results show supplied radians, formula, and converted degree value. It can also show degrees, minutes, and seconds. This format is helpful for navigation, astronomy, and mapping. One degree contains 60 minutes. One minute contains 60 seconds. The decimal result remains best for most mathematical functions. Compare both displays when you need a careful verification. Use the copyable values in your worksheet, report, or design notes. The export buttons create a compact record for later reference.

Common checks

Use π symbols carefully. The entry π/6 should produce 30 degrees. The entry 3π/2 should produce 270 degrees. Negative inputs normally produce negative degree values. Normalization can show a matching positive angle. Do not confuse radians with revolutions. One revolution equals 2π radians, not 360 radians. Test a known angle when reviewing unfamiliar results. Clear results support checking during practical work. Save exported data only after confirming the selected options. Good unit habits make every conversion faster, safer, and easier to explain. This approach supports dependable answers during every careful technical conversion task.