Switch between decimal degrees and DMS with ease. Review formulas, tables, and normalized angle outputs. Export clean results quickly for classes, reports, and practice.
| Degrees | Radians | Decimal Radians |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.523599 |
| 45° | π/4 | 0.785398 |
| 60° | π/3 | 1.047198 |
| 90° | π/2 | 1.570796 |
| 180° | π | 3.141593 |
| 270° | 3π/2 | 4.712389 |
| 360° | 2π | 6.283185 |
Decimal degree formula: radians = degrees × π / 180
DMS formula: decimal degrees = degrees + minutes / 60 + seconds / 3600
Then convert: radians = decimal degrees × π / 180
Turns: turns = degrees / 360
Grads: grads = degrees × 10 / 9
A degree to radian calculator helps convert common angle measurements into the unit used in higher mathematics. Degrees are familiar in school, drafting, and daily geometry. Radians are better for algebra, calculus, trigonometry, and graph analysis. This calculator handles both decimal degrees and degrees, minutes, seconds input. It also normalizes values, controls decimal precision, and shows results in several useful forms.
Radians connect angles directly to circle geometry. One full turn equals 2π radians and 360 degrees. Because of that relationship, radians simplify many formulas. Arc length, sector area, derivatives of trigonometric functions, and periodic modeling all rely on radian measure. When students move from basic geometry into advanced maths, quick and accurate conversion becomes essential.
This page converts decimal degrees to radians instantly. It also accepts DMS values for more detailed angle entry. You can choose rounding precision, normalize angles to a standard range, and view a symbolic π based expression when possible. Extra outputs such as turns and grads make comparison easier. These features are useful for homework, engineering checks, coding tasks, and exam practice.
The main conversion formula is simple: radians = degrees × π / 180. When DMS input is used, minutes are divided by 60 and seconds by 3600 before adding them to the degree value. If normalization is selected, the calculator shifts the angle into a standard interval while preserving the same direction on the circle.
This tool saves time and reduces manual errors. It also helps users learn the structure behind angle conversion instead of memorizing isolated answers. The example table shows common degree values with radian equivalents. The table gives a quick visual reference. CSV and PDF export options make classroom review, documentation, and revision much easier.
Students can verify textbook problems quickly. Teachers can prepare examples for lessons. Engineers can confirm angle inputs before deeper calculations. Developers can convert values for graphics, simulations, and scientific code. Anyone working with trigonometric functions, unit circles, or rotational measurements can benefit from a reliable conversion workflow that explains both the process and the final result clearly today.
Multiply the degree value by π and divide by 180. This changes angle measure from degrees into radians, which is the standard unit in many maths formulas.
Radians connect angles naturally to circles, arc length, and trigonometric behavior. They make many formulas cleaner in calculus, graphing, physics, and advanced trigonometry.
Yes. Choose DMS mode, then enter whole degrees, whole minutes, and numeric seconds. The calculator converts that input to decimal degrees before finding radians.
Normalization moves the same angle into a standard interval. You can keep angles inside [0, 360) or inside (-180, 180] for easier comparison.
The π form shows the radian answer as a multiple or fraction of π. For example, 90° becomes π/2 and 180° becomes π.
Turns show the fraction of a full rotation. Grads, also called gon, divide a full circle into 400 equal parts instead of 360.
Use decimal mode when your source value already appears as one number, such as 22.5°, 135°, or -47.25°. It is faster for direct conversion.
Yes. After conversion, use the CSV button for spreadsheet friendly output or the PDF button for a clean file you can save or share.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.