Gradian to Radian Converter
Convert gradians to radians with our free online angle converter.
Quick Answer
1 Gradian = 0.015708 radians
Formula: Gradian × conversion factor = Radian
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 Radian Calculator
How to Use the Gradian to Radian Calculator:
- Enter the value you want to convert in the 'From' field (Gradian).
- The converted value in Radian 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 Radian: Step-by-Step Guide
Converting Gradian to Radian involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
rad = grad × 0.015708Example Calculation:
1 grad = 0.015708 rad
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 Radian?
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)
A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. 1 radian ≈ 57.2958 degrees.
Key values:
- π radians = 180°
- 2π radians = 360°
- 1 radian = 180/π ≈ 57.296°
Why Radians Matter
The radian is unique because it's dimensionless:
- Definition: Arc length ÷ Radius = Angle in radians
- Dimensionless: Ratio of two lengths (meters ÷ meters = just a number)
- Natural for math: Calculus formulas work perfectly with radians (no messy constants)
- SI standard: The official unit for angles in physics and engineering
- Degrees are arbitrary: Based on Babylonian base-60 system (historical accident)
Note: The Gradian is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Radian belongs to the imperial/US customary system.
Common Uses and Applications: gradians vs radians
Explore the typical applications for both Gradian (imperial/US) and Radian (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 radians
Mathematics: Required unit for calculus (derivatives, integrals of trig functions only work with radians). Physics: Angular velocity (rad/s), rotational motion, oscillations, wave propagation. Engineering: Computer graphics, robotics, signal processing, control systems. Programming: All major languages (Python, JavaScript, C++) use radians for sin(), cos(), tan().
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 Radian (rad)
How do I convert radians to degrees?
Formula: degrees = radians × (180/π) = radians × 57.2958
Examples:
- 1 rad = 57.3°
- π/2 rad = 90°
- π rad = 180°
- 2π rad = 360°
How many radians in 180 degrees?
180° = π radians ≈ 3.14159 radians
This is the fundamental relationship between degrees and radians.
Why use radians instead of degrees?
Mathematical simplicity: d/dx[sin(x)] = cos(x) ONLY when x is in radians. Physics advantage: Angular velocity formulas are much simpler with radians. Programming standard: All programming languages default to radians for trig functions.
Conversion Table: Gradian to Radian
| Gradian (grad) | Radian (rad) |
|---|---|
| 0.5 | 0.008 |
| 1 | 0.016 |
| 1.5 | 0.024 |
| 2 | 0.031 |
| 5 | 0.079 |
| 10 | 0.157 |
| 25 | 0.393 |
| 50 | 0.785 |
| 100 | 1.571 |
| 250 | 3.927 |
| 500 | 7.854 |
| 1,000 | 15.708 |
People Also Ask
How do I convert Gradian to Radian?
To convert Gradian to Radian, 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 Radian?
The conversion factor depends on the specific relationship between Gradian and Radian. 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 Radian back to Gradian?
Yes! You can easily convert Radian back to Gradian by using the swap button (⇌) in the calculator above, or by visiting our Radian to Gradian converter page. You can also explore other angle conversions on our category page.
Learn more →What are common uses for Gradian and Radian?
Gradian and Radian 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.
Helpful Conversion Guides
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📚 How to Convert Units
Step-by-step guide to unit conversion with practical examples.
🔢 Conversion Formulas
Essential formulas for angle and other conversions.
⚖️ Metric vs Imperial
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⚠️ Common Mistakes
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All Angle Conversions
Other Angle Units and Conversions
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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