Gradian to Quadrant Converter
Convert gradians to quadrants with our free online angle converter.
Quick Answer
1 Gradian = 0.01 quadrants
Formula: Gradian × conversion factor = Quadrant
Use the calculator below for instant, accurate conversions.
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All conversion formulas on UnitsConverter.io have been verified against NIST (National Institute of Standards and Technology) guidelines and international SI standards. Our calculations are accurate to 10 decimal places for standard conversions and use arbitrary precision arithmetic for astronomical units.
Gradian to Quadrant Calculator
How to Use the Gradian to Quadrant Calculator:
- Enter the value you want to convert in the 'From' field (Gradian).
- The converted value in Quadrant will appear automatically in the 'To' field.
- Use the dropdown menus to select different units within the Angle category.
- Click the swap button (⇌) to reverse the conversion direction.
How to Convert Gradian to Quadrant: Step-by-Step Guide
Converting Gradian to Quadrant involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
quad = grad × 0.01Example Calculation:
1 grad = 0.01 quad
Disclaimer: For Reference Only
These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.
Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.
Need to convert to other angle units?
View all Angle conversions →What is a Gradian and a Quadrant?
1 gradian = 1/400 of a full circle = 0.9 degrees = 0.01571 radians
Key conversions:
- 100 gradians = 90 degrees (right angle)
- 200 gradians = 180 degrees (straight angle)
- 400 gradians = 360 degrees (full circle)
- 1 gradian = 0.9° = π/200 radians
Symbols: grad, gon, or superscript "g" (e.g., 100ᵍ)
1 quadrant = 1/4 of a full circle = 90 degrees = π/2 radians ≈ 1.5708 radians
Key conversions:
- 1 quadrant = 90 degrees
- 1 quadrant = π/2 ≈ 1.5708 radians
- 1 quadrant = 100 gradians (or gons)
- 4 quadrants = 360 degrees (full circle)
- 2 quadrants = 180 degrees (straight angle)
Symbol: quad or Q (sometimes written as "right angle")
Note: The Gradian is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Quadrant belongs to the imperial/US customary system.
Common Uses and Applications: gradians vs quadrants
Explore the typical applications for both Gradian (imperial/US) and Quadrant (imperial/US) to understand their common contexts.
Common Uses for gradians
Surveying: Primary angle unit in France, Germany, Switzerland, and Scandinavia for land surveys. Civil Engineering: Building construction, road design, slope measurements in Europe. Military: Artillery calculations and targeting in European armed forces. Geodesy: Precise Earth measurements and coordinate systems in metric countries.
When to Use quadrants
Coordinate Systems: Cartesian plane divided into four quadrants (I, II, III, IV). Navigation: Compass quadrants (NE, SE, SW, NW) for direction description. Astronomy: Celestial sphere divided into quadrants for star mapping. Geometry: Right angles and perpendicular measurements in construction and design.
Additional Unit Information
About Gradian (grad)
How do I convert gradians to degrees?
Formula: Degrees = Gradians × 0.9 (or Gradians × 9/10)
Examples:
- 100 gradians = 90°
- 200 gradians = 180°
- 400 gradians = 360°
- 50 gradians = 45°
- 25 gradians = 22.5°
Gradians to Degrees converter →
How do I convert gradians to radians?
Formula: Radians = Gradians × (π/200) ≈ Gradians × 0.01571
Examples:
- 100 gradians = π/2 ≈ 1.571 radians
- 200 gradians = π ≈ 3.142 radians
- 400 gradians = 2π ≈ 6.283 radians
- 50 gradians = π/4 ≈ 0.785 radians
Gradians to Radians converter →
What's the difference between gradians and gons?
No difference - they're the same unit:
- Gradian: Traditional name, widely recognized
- Gon: Modern ISO standard term (ISO 31-1)
- Grad: Common abbreviation used on calculators
- Grade: French name (le grade)
All represent 1/400 of a circle. "Gon" is preferred in modern technical standards to avoid confusion with other meanings of "grade" (road grade, academic grade, etc.).
Why were gradians created?
Decimal system alignment: Part of French Revolution's metrication effort to create base-10 measurements.
Historical context:
- Created in 1795 alongside metric system
- Right angle = 100 (easier than 90 degrees)
- Full circle = 400 (divisible by 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200)
- Percentage calculations simpler: 25 gradians = 25% of right angle
Advantages over degrees:
- Pure decimal arithmetic (no sexagesimal base-60 calculations)
- Easier mental math: 50 gradians = half right angle
- Better integration with metric measurements
- Simpler for computing and digital systems
Modern usage: While degrees dominate globally, gradians remain standard in European surveying, civil engineering, and cadastral work. France, Switzerland, and Germany extensively use gradians in official surveying.
About Quadrant (quad)
How do I convert quadrants to degrees?
Formula: Degrees = Quadrants × 90
Examples:
- 1 quadrant = 90°
- 2 quadrants = 180°
- 3 quadrants = 270°
- 4 quadrants = 360°
- 0.5 quadrants = 45°
Quadrants to Degrees converter →
How do I convert quadrants to radians?
Formula: Radians = Quadrants × (π/2) ≈ Quadrants × 1.5708
Examples:
- 1 quadrant = π/2 ≈ 1.571 radians
- 2 quadrants = π ≈ 3.142 radians
- 3 quadrants = 3π/2 ≈ 4.712 radians
- 4 quadrants = 2π ≈ 6.283 radians
- 0.5 quadrants = π/4 ≈ 0.785 radians
Quadrants to Radians converter →
What are the four quadrants in a coordinate plane?
Quadrant system divides the Cartesian plane using x and y axes:
Quadrant I (First): x > 0, y > 0
- Angles: 0° to 90° (or 0 to π/2 radians)
- Example point: (3, 4)
Quadrant II (Second): x < 0, y > 0
- Angles: 90° to 180° (or π/2 to π radians)
- Example point: (-3, 4)
Quadrant III (Third): x < 0, y < 0
- Angles: 180° to 270° (or π to 3π/2 radians)
- Example point: (-3, -4)
Quadrant IV (Fourth): x > 0, y < 0
- Angles: 270° to 360° (or 3π/2 to 2π radians)
- Example point: (3, -4)
Axes: Points on x or y axes are not in any quadrant.
Why is a right angle called a quadrant?
Etymology: "Quadrant" comes from Latin "quadrans" meaning "fourth part."
Historical context:
- A right angle is 1/4 of a full circle rotation
- Ancient navigational instruments called "quadrants" were quarter-circle shaped
- The term emphasizes the fractional relationship: 1 quadrant = 1/4 circle
Modern usage: While "right angle" is more common in everyday geometry, "quadrant" is still used in:
- Coordinate systems (Quadrant I, II, III, IV)
- Navigation and surveying
- Astronomy and celestial mechanics
- Mathematical analysis and calculus
The term "quadrant" emphasizes the measurement as a fraction of a circle, while "right angle" emphasizes the geometric perpendicularity (90°).
Conversion Table: Gradian to Quadrant
| Gradian (grad) | Quadrant (quad) |
|---|---|
| 0.5 | 0.005 |
| 1 | 0.01 |
| 1.5 | 0.015 |
| 2 | 0.02 |
| 5 | 0.05 |
| 10 | 0.1 |
| 25 | 0.25 |
| 50 | 0.5 |
| 100 | 1 |
| 250 | 2.5 |
| 500 | 5 |
| 1,000 | 10 |
People Also Ask
How do I convert Gradian to Quadrant?
To convert Gradian to Quadrant, enter the value in Gradian in the calculator above. The conversion will happen automatically. Use our free online converter for instant and accurate results. You can also visit our angle converter page to convert between other units in this category.
Learn more →What is the conversion factor from Gradian to Quadrant?
The conversion factor depends on the specific relationship between Gradian and Quadrant. You can find the exact conversion formula and factor on this page. Our calculator handles all calculations automatically. See the conversion table above for common values.
Can I convert Quadrant back to Gradian?
Yes! You can easily convert Quadrant back to Gradian by using the swap button (⇌) in the calculator above, or by visiting our Quadrant to Gradian converter page. You can also explore other angle conversions on our category page.
Learn more →What are common uses for Gradian and Quadrant?
Gradian and Quadrant are both standard units used in angle measurements. They are commonly used in various applications including engineering, construction, cooking, and scientific research. Browse our angle converter for more conversion options.
For more angle conversion questions, visit our FAQ page or explore our conversion guides.
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Verified Against Authority Standards
All conversion formulas have been verified against international standards and authoritative sources to ensure maximum accuracy and reliability.
National Institute of Standards and Technology — Fundamental physical constants and unit conversions
Bureau International des Poids et Mesures — International System of Units (SI) definitions and standards
International Organization for Standardization — Quantities and units international standards series
Last verified: February 19, 2026