Enter a value in any field (degrees, radians or slope %). The other two units update automatically.
About this angle converter (degrees, radians and slope %)
This free angle converter helps you convert instantly between degrees (°), radians (rad), and slope percentage (%) (also called grade). These three notations describe the same concept—an angle or a steepness—but they are used in different fields. Degrees are the most common unit for everyday geometry, navigation, and general measurements. Radians are widely used in mathematics, physics, and programming, especially in trigonometry, calculus, simulations, and graphics. Slope percentage is a practical way to describe how steep a road, ramp, roof, or terrain is in engineering and construction.
The relationship between these units is straightforward. Degrees and radians are linked by the circle: rad = deg × π / 180 and deg = rad × 180 / π. Slope percentage is based on the tangent function: slope% = tan(rad) × 100. That means a 45° angle corresponds to a 100% slope (because tan(45°) = 1). As the angle approaches 90°, the tangent grows extremely fast, so slope percentage becomes very large. This tool is designed to help you quickly verify those conversions without switching between calculators or searching formulas.
The converter is interactive: type a value in any field and the other two fields update automatically. This is convenient when you work with mixed inputs—for example, a technical document might specify an angle in degrees, while your software requires radians, or a road specification might use slope percentage while you want the corresponding angle. All calculations run locally in your browser: no account, no uploads, and your values are not stored by the page.
Tip: for small angles, slope% is close to (rad × 100), but the exact conversion always uses tan().
What is this angle converter used for?
This angle converter allows you to convert an angle between degrees, radians, and slope percentage (grade). These representations describe the same geometric concept but are used in different technical, scientific, and practical contexts.
Who is this tool useful for?
- Students learning geometry, trigonometry, or physics
- Engineers and technicians working with slopes or angles
- Developers converting degrees to radians for code and formulas
- Construction and civil works professionals dealing with gradients
Concrete examples
- Converting degrees to radians before using trigonometric functions in software
- Finding the slope percentage of a ramp or road from its angle
- Checking that a roof or staircase respects maximum slope constraints
Common mistakes to avoid
- ❌ Mixing degrees and radians in mathematical formulas
- ❌ Assuming slope percentage and degrees are directly proportional
- ❌ Forgetting that slope grows extremely fast near 90°
This tool applies the correct trigonometric relationships automatically, reducing the risk of conversion errors.
Limits and possible alternatives
This converter focuses on static angle values. It does not handle bearings, compass directions, or 3D vector angles. Extremely steep slopes may produce very large percentage values.
- Scientific calculators for advanced trigonometry
- Engineering software for terrain or structural analysis
Educational summary
In summary, this angle converter helps you translate an angle between degrees, radians, and slope percentage quickly and accurately. It is especially useful when switching between mathematical theory and real-world applications such as construction or engineering.