Convert Between Degrees, Radians & Gradians
Angle unit conversions are essential in mathematics, physics, engineering, and everyday applications. While degrees are familiar to most people, radians are the standard in calculus and advanced mathematics. Gradians (also called grads) are used in surveying and some specialized fields. Convert between these angular units instantly and accurately. All values are current as of 2026 and reviewed regularly.
When to use this calculator
- Physics and engineering calculations requiring angle conversions
- Trigonometry and calculus homework and assignments
- Programming and computer graphics development
- Surveying, navigation, and geospatial applications
- Quick reference checks before applying calculations to real projects
Example Conversion
- 90° → radians
- π/2
How it works
1 min readUnderstanding Angle Units
Angle conversions are fundamental in mathematics, physics, engineering, and many practical applications. The three primary units are:
How the Conversion Works
This calculator applies standard mathematical formulas to convert between any of the three angular units. Enter your value, select the unit you're converting from and to, and get the result instantly. The tool checks for valid input ranges and alerts you to unusual values.
Key Conversion Formulas
Important Notes
This calculator provides reference results using internationally validated formulas. For critical applications in engineering, physics, or navigation, verify results with professional tools or consult a specialist.
Frequently asked questions
Why use radians instead of degrees?
Radians are the natural unit in calculus and physics because they simplify formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. Most scientific calculators and programming languages use radians as the default.
How do I convert degrees to radians?
Multiply the degree value by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 radians.
What's a full rotation in each unit?
A complete rotation = 360° = 2π radians (≈ 6.283 rad) = 400 gradians. This relationship is constant across all angle measurements.
When are gradians used?
Gradians (grads) are primarily used in surveying, geospatial sciences, and some European technical fields. They divide a right angle into 100 units, making calculations in those fields more convenient.
What are common angle values in radians?
Common conversions: 45° = π/4, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π. Learning these helps with mental math and understanding circular functions.
Can I use this calculator for programming?
Yes. Most programming languages (Python, JavaScript, C++) use radians for trigonometric functions. Use this converter to check your angle conversions before implementing mathematical calculations.
Is this calculator free?
Yes, all Hacé Cuentas calculators are completely free and require no registration or sign-up.
How accurate are the results?
Results use standard mathematical formulas validated internationally. For general reference and learning, the accuracy is excellent. For critical engineering or scientific work, use professional-grade tools and consult a specialist.
Is my data stored or shared?
No. All calculations happen in your browser. We don't send data to any server or store your inputs.