Quadrant to Radian Converter
Convert quadrants to radians with our free online angle converter.
Quick Answer
1 Quadrant = 1.570796 radians
Formula: Quadrant × conversion factor = Radian
Use the calculator below for instant, accurate conversions.
Our Accuracy Guarantee
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.
Quadrant to Radian Calculator
How to Use the Quadrant to Radian Calculator:
- Enter the value you want to convert in the 'From' field (Quadrant).
- 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 Quadrant to Radian: Step-by-Step Guide
Converting Quadrant to Radian involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
rad = quad × 1.5708Example Calculation:
1 quad = 1.570796 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 Quadrant and a Radian?
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")
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 Quadrant 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: quadrants vs radians
Explore the typical applications for both Quadrant (imperial/US) and Radian (imperial/US) to understand their common contexts.
Common Uses for 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.
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 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°).
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: Quadrant to Radian
| Quadrant (quad) | Radian (rad) |
|---|---|
| 0.5 | 0.785 |
| 1 | 1.571 |
| 1.5 | 2.356 |
| 2 | 3.142 |
| 5 | 7.854 |
| 10 | 15.708 |
| 25 | 39.27 |
| 50 | 78.54 |
| 100 | 157.08 |
| 250 | 392.699 |
| 500 | 785.398 |
| 1,000 | 1,570.796 |
People Also Ask
How do I convert Quadrant to Radian?
To convert Quadrant to Radian, enter the value in Quadrant 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 Quadrant to Radian?
The conversion factor depends on the specific relationship between Quadrant 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 Quadrant?
Yes! You can easily convert Radian back to Quadrant by using the swap button (⇌) in the calculator above, or by visiting our Radian to Quadrant converter page. You can also explore other angle conversions on our category page.
Learn more →What are common uses for Quadrant and Radian?
Quadrant 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
Learn more about unit conversion with our comprehensive guides:
📚 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
Understand the differences between measurement systems.
⚠️ Common Mistakes
Learn about frequent errors and how to avoid them.
All Angle Conversions
Other Angle Units and Conversions
Explore other angle units and their conversion options:
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