Quadrant Calculator

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The x- and y-axes split the plane into four quadrants, numbered counterclockwise from the upper right. The point (−3, 4) has a negative x and a positive y, so it is in Quadrant II. An angle of 200° ends in Quadrant III.

FreeStep by stepPoints and angles

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Location

Quadrant II

x is negative and y is positive: signs (−, +).

The point on the coordinate plane.

Signs (x, y)	(−, +)
Distance from the origin	5
Angle from the positive x-axis	126.8699°

Show steps

Quadrant I: (+, +). Quadrant II: (−, +). Quadrant III: (−, −). Quadrant IV: (+, −).
x is negative and y is positive: signs (−, +).

How to use the quadrant calculator

Choose a point or an angle.
Enter the coordinates, or the angle in degrees or radians.
Press Find to see the quadrant, the signs and a graph.

Quadrant rules

Quadrant	Signs (x, y)	Angles	Positive trig functions
I	(+, +)	0° to 90°	all
II	(−, +)	90° to 180°	sin
III	(−, −)	180° to 270°	tan
IV	(+, −)	270° to 360°	cos

Memory aid: “All Students Take Calculus” (All, Sin, Tan, Cos, counterclockwise from Quadrant I).

Points on the axes

If x = 0 or y = 0, the point lies on an axis and is not in any quadrant. Angles that are multiples of 90° (quadrantal angles) also lie on an axis.

Angles larger than 360° or negative

Add or subtract 360° until the angle is between 0° and 360°, then use the table. −45° + 360° = 315°, which is in Quadrant IV.

Quadrants practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you know which quadrant a point is in?

Look at the signs: (+, +) is I, (−, +) is II, (−, −) is III and (+, −) is IV.

What if a coordinate is zero?

The point lies on an axis and is not in any quadrant.

How do I find the quadrant of an angle?

Reduce it to between 0° and 360°, then 0°–90° is I, 90°–180° is II, 180°–270° is III and 270°–360° is IV.

Which trig functions are positive in each quadrant?

All in I, sine in II, tangent in III and cosine in IV.

Can I enter radians?

Yes. Choose Radians and type values like 5pi/4.

Sources

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