Interactive Degree Calculator
Convert between degrees, radians, gradians, and turns. You can also convert DMS (degrees-minutes-seconds) to decimal degrees.
1) Angle Unit Converter
2) DMS to Decimal Degrees
What is a degree calculator?
A degree calculator is a quick tool for working with angles. In math class, engineering drawings, navigation, and computer graphics, angles show up everywhere. Sometimes you are given an angle in degrees, while a formula or software package expects radians. Other times, you need the same number in DMS format (degrees, minutes, seconds). A reliable calculator saves time and helps avoid conversion mistakes.
The calculator above is designed for practical use: simple inputs, fast conversion, and useful extra output like decimal-degree equivalents and trigonometric values.
Common degree conversions (with formulas)
Degrees to radians
Use this formula:
radians = degrees × π / 180
Example: 45° = 45 × π / 180 = π/4 ≈ 0.785398 rad
Radians to degrees
degrees = radians × 180 / π
Example: 1 rad ≈ 57.2958°
Degrees to gradians and turns
- gradians = degrees × 10 / 9
- turns = degrees / 360
These are useful in some surveying tools and CAD systems.
Decimal degrees vs DMS
Angles are often represented in one of two ways:
- Decimal degrees: 73.9856°
- DMS: 73° 59' 8.16"
Both represent the same angle. DMS is common in geography and mapping, while decimal degrees are easier for calculations. If you work with GPS coordinates, you'll frequently switch between the two.
How to use this calculator
Unit conversion workflow
- Enter your numeric angle value.
- Choose the input unit (from).
- Choose the output unit (to).
- Select precision and click Convert.
DMS conversion workflow
- Enter degrees, minutes, and seconds.
- Choose positive or negative sign.
- Click Convert DMS.
The output includes decimal degrees and radians for quick reference.
Real-world examples
1) Trigonometry homework
Many trig functions in programming languages use radians. If your problem gives 30°, convert first to radian form (π/6) before evaluating sine, cosine, or tangent.
2) Surveying and bearings
Survey data can use DMS angles while mapping software expects decimal degrees. The DMS converter helps move cleanly between formats without manual arithmetic.
3) Robotics and simulation
Mechanical systems may be defined in degrees for readability, but physics engines often run in radians. A quick conversion step avoids errors in motion calculations.
Tips to avoid angle conversion mistakes
- Always check your unit before calculating.
- Keep enough decimal precision in intermediate steps.
- Use negative signs consistently for direction-sensitive problems.
- For DMS, remember minutes and seconds should normally be less than 60.
- Verify with a known value (e.g., 180° = π rad).
Final thoughts
A degree calculator is one of those small tools that make a big difference. Whether you're studying math, building software, analyzing maps, or solving engineering problems, quick and accurate angle conversion keeps your work clean and consistent. Bookmark this page and use it whenever you need a fast, dependable conversion.