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°).

Quadrant (quad) - Unit Information & Conversion

Symbol:quad

Plural:quadrants

Category:Angle

🔄 Quick Convert Quadrant

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What is a Quadrant?

Quadrant is 1/4 of a full circle, equal to 90 degrees or π/2 radians. Used in coordinate systems, navigation, and geometry to describe quarter-circle sections. 4 quadrants = 360 degrees = full circle.

History of the Quadrant

Named from Latin "quadrans" (quarter). Used since ancient times in astronomy, navigation, and cartography. Essential for coordinate plane systems and compass directions (NE, SE, SW, NW quadrants).

Quick Answer

What is a Quadrant? A quadrant is one-quarter of a full circle, equal to 90 degrees or π/2 radians. Used to divide coordinate planes, compass directions, and circular measurements into four equal sections. 1 quadrant = 90° = π/2 rad = 100 gradians. Use our angle converter for instant conversions.

Key Facts: Quadrant

Property	Value
Symbol	quad
Quantity	Angle
System	Metric/SI Derived
Derived from	Radian
Category	Angle
Standard Body	NIST / ISO

Definition

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")

Common Uses

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.

Real-World Examples

Coordinate System Quadrants: Detailed Breakdown

How the Cartesian plane divides into four sections:

Quadrant	X Sign	Y Sign	Angle Range	Examples
I (First)	Positive	Positive	0° to 90°	(5, 3), (1, 1), (10, 7)
II (Second)	Negative	Positive	90° to 180°	(-5, 3), (-1, 1), (-10, 7)
III (Third)	Negative	Negative	180° to 270°	(-5, -3), (-1, -1), (-10, -7)
IV (Fourth)	Positive	Negative	270° to 360°	(5, -3), (1, -1), (10, -7)
On Axes	0 or varies	0 or varies	0°, 90°, 180°, 270°	(5, 0), (0, 3), (-4, 0)

Rule: Points ON the axes themselves belong to NO quadrant (axis points only)

Trigonometric Function Signs by Quadrant

How sine, cosine, and tangent change signs:

Quadrant	Sine	Cosine	Tangent	Remember
I (0°-90°)	+	+	+	All positive
II (90°-180°)	+	-	-	Sine positive
III (180°-270°)	-	-	+	Tangent positive
IV (270°-360°)	-	+	-	Cosine positive

Mnemonic: "All Students Take Calculus" = Quadrants 1-4 with + functions

Historical Quadrant Navigation Instrument

The astronomical quadrant used for celestial navigation:

Feature	Description	Measurement
Shape	Quarter-circle (90° arc)	1 quadrant = 90°
Arm length	Sighting arm (radius)	Typically 60-120 cm
Scale	Degree marks along arc	0° to 90° divisions
Plumb bob	Hanging weight for vertical	Gravity reference
Peep sights	Holes for star alignment	Two sighting points
Purpose	Measure star altitude	Above horizon angle
Navigation use	Determine latitude	Using North Star

Historical note: Used by explorers and navigators from 1300s-1700s; superseded by sextant

Compass Navigation: Cardinal Quadrants

Traditional navigation using quadrant directions:

Direction	Compass Bearing	Quadrant	In Degrees	In Radians
North	N	0°	0° or 360°	0 or 2π
Northeast	NE	I	45°	π/4
East	E	I/II	90°	π/2
Southeast	SE	II/III	135°	3π/4
South	S	III	180°	π
Southwest	SW	III/IV	225°	5π/4
West	W	IV/I	270°	3π/2
Northwest	NW	IV/I	315°	7π/4

Application: Traditional navigation references bearings in terms of quadrants (e.g., "East-Southeast")

Architectural Applications

Where quadrants appear in building design:

Application	Quadrant Use	Example
Right angles	1 quadrant = 90°	Square room corners
Arched doorways	Quarter-circle arch	Semicircle = 2 quadrants
Domes	Hemispherical = 2 quadrants	Half-sphere structure
Spiral stairs	Each turn ≈ 1 quadrant	Full turn = 4 quadrants
Circular gardens	Divided into 4 sections	Quadrant lawn areas
Rotundas	4-quadrant sections	Octagonal/circular buildings

Unit Conversion Reference

Quick conversions between quadrants and other angle units:

Quadrants	Degrees	Radians	Gradians	Revolutions
0.5	45°	π/4	50	1/8
1	90°	π/2	100	1/4
1.5	135°	3π/4	150	3/8
2	180°	π	200	1/2
3	270°	3π/2	300	3/4
4	360°	2π	400	1

Quadrant Conversion Formulas

To Degree:

1 quad = 90 °

Example: 5 quadrants = 450 degrees

To Radian:

1 quad = 1.570796 rad

Example: 5 quadrants = 7.853982 radians

To Gradian:

1 quad = 100 grad

Example: 5 quadrants = 500 gradians

To Arcminute:

1 quad = 5400 ′

Example: 5 quadrants = 27000 arcminutes

To Arcsecond:

1 quad = 324000 ″

Example: 5 quadrants = 1620000 arcseconds

To Turn:

1 quad = 0.25 turn

Example: 5 quadrants = 1.25 turns

To Revolution:

1 quad = 0.25 rev

Example: 5 quadrants = 1.25 revolutions

To Gon:

1 quad = 100 gon

Example: 5 quadrants = 500 gons

To Mil:

1 quad = 1600 mil

Example: 5 quadrants = 8000 mils

Frequently Asked Questions

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 →

Convert Quadrant

Need to convert Quadrant to other angle units? Use our conversion tool.

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