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Tangent Calculator

Tangent calculator finds tan of any angle in degrees instantly. Enter an angle to get the exact tangent value, with step-by-step working and quadrant identification. Common values: tan(0) = 0, tan(30) = 0.5774, tan(45) = 1, tan(60) = 1.7321. Tangent is undefined at 90 and 270 degrees. Used in trigonometry, surveying, slope calculations, roof pitch, and physics problems involving inclined planes.

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Angle (degrees)

Result

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Formula

Core Formula

\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}

How it works: Converts degrees to radians and evaluates tangent. Undefined when cosine equals zero (at 90, 270 degrees).

Worked Example

Find tan(48.59 degrees):

1Step 1: Convert to radians: 48.59 x (pi/180) = 0.8481 radians

2Step 2: Evaluate tan(0.8481) = sin(0.8481) / cos(0.8481) = 0.7501 / 0.6614

3Step 3: tan(48.59) = 1.1340

4Step 4: Quadrant: 48.59 is in Quadrant I (0-90), so tangent is positive

Result: tan(48.59 degrees) = 1.1340

Verification: arctan(1.1340) = 48.59 degrees

How the Tangent Function Works

Tangent is the ratio of sine to cosine. In a right triangle, tan(theta) equals the opposite side divided by the adjacent side.

tan(theta) = opposite / adjacent = sin(theta) / cos(theta) in a right triangle
Key values: tan(0) = 0, tan(30) = 0.5774, tan(45) = 1, tan(60) = 1.7321, tan(90) = undefined
Tangent is undefined at 90 and 270 degrees because cosine is zero at those angles, creating a division by zero
Unlike sine and cosine (period 360), tangent has a period of 180 degrees: tan(theta) = tan(theta + 180)
Tangent grows rapidly near 90 degrees: tan(80) = 5.67, tan(85) = 11.43, tan(89) = 57.29, tan(89.9) = 572.96. This steep curve is why tangent is undefined at exactly 90 degrees

This calculator accepts degrees and handles radian conversion internally. For inverse tangent (finding the angle from a ratio), use the arctan calculator.

You can also calculate changes using our Sine Calculator, Cosine Calculator or Arctan Calculator.

Common Tangent Values: 0 to 360 Degrees

Reference table of tangent values for commonly used angles. Tangent is positive in Quadrants I (0-90) and III (180-270), negative in Quadrants II (90-180) and IV (270-360).

Angle	tan(angle)	Exact Value	Quadrant
0	0	0	-
10	0.1763		I
15	0.2679	2 - sqrt(3)	I
20	0.3640		I
25	0.4663		I
30	0.5774	1/sqrt(3)	I
35	0.7002		I
40	0.8391		I
45	1.0000	1	I
50	1.1918		I
60	1.7321	sqrt(3)	I
70	2.7475		I
80	5.6713		I
90	Undefined	cos(90) = 0	-
120	-1.7321	-sqrt(3)	II
135	-1.0000	-1	II
150	-0.5774	-1/sqrt(3)	II
180	0	0	-
210	0.5774	1/sqrt(3)	III
225	1.0000	1	III
240	1.7321	sqrt(3)	III
270	Undefined	cos(270) = 0	-
300	-1.7321	-sqrt(3)	IV
315	-1.0000	-1	IV
330	-0.5774	-1/sqrt(3)	IV
360	0	0	-

Note: Tangent is undefined at 90 and 270 degrees (and any angle of the form 90 + 180n) because cosine equals zero at those angles. Notice that tangent values repeat every 180 degrees (period = 180), and the function grows rapidly near the undefined points. Bold values are the five standard angles to memorize (0, 30, 45, 60, 90).

Frequently Asked Questions

What is tan(45) degrees?

tan(45 degrees) = 1 exactly. This is because sin(45) and cos(45) are both 0.7071, and their ratio is 1. In a right triangle, this means the opposite and adjacent sides are equal, forming a 45-45-90 isosceles right triangle.

Why is tangent undefined at 90 degrees?

tan(theta) = sin(theta) / cos(theta). At 90 degrees, cos(90) = 0, which creates a division by zero. Tangent is also undefined at 270 degrees and any angle of the form 90 + 180n degrees. Near these angles, tangent approaches positive or negative infinity.

What are the common tangent values to memorize?

The five key values:

tan(0) = 0.

tan(30) = 0.5774 (or 1/sqrt(3)).

tan(45) = 1.

tan(60) = 1.7321 (or sqrt(3)).

tan(90) = undefined. Notice tangent increases rapidly as the angle approaches 90 degrees.

How do I use tangent to find the slope of a ramp or hill?

The slope grade equals tan(angle) x 100%. A 10-degree incline has slope = tan(10) x 100% = 17.6%. A 45-degree slope has a 100% grade. Road grades above 10% (about 5.7 degrees) are considered steep for vehicles.

What is the period of the tangent function?

Tangent has a period of 180 degrees, not 360 like sine and cosine. This means tan(theta) = tan(theta + 180). For example, tan(30) = tan(210) = 0.5774. Tangent is positive in quadrants I (0-90) and III (180-270), and negative in quadrants II (90-180) and IV (270-360).

What is the tangent of 20 degrees?

tan(20 degrees) = 0.3640. To calculate: convert 20 degrees to radians (20 x pi/180 = 0.3491), then evaluate tan(0.3491) = 0.3640. Other commonly searched values: tan(10) = 0.1763, tan(15) = 0.2679, tan(25) = 0.4663, tan(30) = 0.5774, tan(35) = 0.7002, tan(40) = 0.8391.

How can I put this Tangent Calculator on my blog or website?

Yes, the Tangent Calculator is fully embeddable. Tap "Embed" above to configure appearance and copy the code. It is free to use, works on any platform (HTML, WordPress, CMS), and adjusts to any screen size automatically. Visit calculory.com/services/embed-calculators for the complete guide.

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