Angles are a fundamental concept in mathematics, physics, engineering, and surveying. While degrees are the most commonly used unit to measure angles, another unit called gradians is also widely used in specific applications such as surveying, civil engineering, and navigation.

What is a Degree?

A degree divides a full circle into 360 equal parts.

• 1 full circle = 360 degrees
• 90° = right angle
• 180° = straight angle

Degrees are intuitive for everyday measurements, navigation, and geometric calculations.

What is a Gradian?

A gradian (also called gon or grad) divides a full circle into 400 equal parts.

• 1 full circle = 400 gradians
• 100 gradians = right angle
• 200 gradians = straight angle

Gradians are commonly used in surveying, civil engineering, and some scientific applications because of their decimal-based structure, which makes calculations simpler in metric systems.

Formula for Conversion

The formula to convert degrees to gradians is:

Gradian = Degree × (400 / 360)
or simplified:
Gradian = Degree × 10 / 9

Examples:

1. Convert 180° to gradians:
   180 × (400 / 360) = 200 gradians
2. Convert 90° to gradians:
   90 × (400 / 360) = 100 gradians
3. Convert 45° to gradians:
   45 × (400 / 360) = 50 gradians

How to Use the Degree to Gradian Calculator

Using the calculator is straightforward:

1. Enter the angle in degrees.
2. Click the “Convert” button.
3. Instantly see the equivalent angle in gradians.

This tool eliminates manual calculations and provides accurate results, saving time for students and professionals alike.

Examples of Conversion

Here are some common degree-to-gradian conversions:

• 0° = 0 gradians
• 45° = 50 gradians
• 90° = 100 gradians
• 180° = 200 gradians
• 270° = 300 gradians
• 360° = 400 gradians

These examples illustrate how degrees scale to gradians and why gradians are convenient in certain applications.

Why This Conversion is Important

1. Surveying & Civil Engineering – Gradians are often used in land measurements and angle calculations.
2. Navigation – Some maps and compasses use gradians for precision.
3. Mathematics & Trigonometry – Gradians simplify decimal-based calculations.
4. Education – Helps students understand alternative angle units.
5. Professional Use – Engineers, surveyors, and architects benefit from quick and accurate conversions.

Understanding degree-to-gradian conversions ensures precision in professional and academic work.

Advantages of Using the Calculator

• Instant Results – Converts any degree value to gradians instantly.
• Accurate – Reduces errors compared to manual calculations.
• User-Friendly – Easy to use for beginners and professionals.
• Professional Tool – Useful for engineers, surveyors, and students.
• Educational Value – Helps learners grasp alternative angle measurements.

Additional Information

• Relationship Between Degrees and Gradians:
  360° = 400 gradians → 1° = 10/9 gradians → 1 gradian = 0.9°
• Practical Applications:
  • Surveying: land angle measurements
  • Civil engineering: construction planning
  • Map navigation: precise directional angles
• Decimal Convenience:
  Gradians are part of the metric system, which simplifies calculations compared to the sexagesimal degree system.

20 Frequently Asked Questions (FAQs)

Q1. What is 180 degrees in gradians?
180° = 200 gradians

Q2. How do I convert degrees to gradians manually?
Multiply degrees by 400/360 or 10/9.

Q3. What is 90° in gradians?
90° = 100 gradians

Q4. Why are gradians used in surveying?
They simplify decimal-based measurements and calculations.

Q5. How many gradians are in a full circle?
400 gradians

Q6. What is 45° in gradians?
45° = 50 gradians

Q7. Can the calculator handle decimal degrees?
Yes, it works with fractional values.

Q8. What is 30° in gradians?
30° = 33.33 gradians

Q9. Is 1 gradian smaller than 1 degree?
Yes, 1 gradian = 0.9 degrees

Q10. How do I convert gradians back to degrees?
Multiply gradians by 360/400 or 9/10.

Q11. What is 270° in gradians?
270° = 300 gradians

Q12. What is 360° in gradians?
360° = 400 gradians

Q13. Are gradians an SI unit?
Yes, they are recognized as an angular unit in the metric system.

Q14. What is 60° in gradians?
60° = 66.67 gradians

Q15. Why use gradians over degrees?
Decimal-based gradians simplify calculations in metric systems.

Q16. What is 120° in gradians?
120° = 133.33 gradians

Q17. Can this calculator be used for navigation?
Yes, it helps convert angles for maps and compasses.

Q18. How many degrees are in 1 gradian?
1 gradian = 0.9°

Q19. What is 135° in gradians?
135° = 150 gradians

Q20. Is this calculator suitable for students?
Yes, it helps learners quickly understand degree-to-gradian conversions.

Final Thoughts

The Degree to Gradian Calculator is a fast, reliable, and user-friendly tool for converting degrees into gradians. It is essential for students, engineers, surveyors, and professionals who need accurate angle measurements.