Tangent CalculatorFree online math calculator — instant results, no sign-up
Calculate the tangent of an angle in degrees.
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About the Tangent Calculator
The Tangent Calculator calculates the tangent of an angle entered in degrees. It converts the angle to radians before evaluating the trigonometric function and returns a dimensionless result. With the default angle of 45 degrees, the result is 1.
- Angle (degrees)
- The angle whose tangent you want to calculate, measured in degrees and defaulting to 45.
Formula and method
r = θ × π / 180; t = tan(r) = sin(r) / cos(r), provided cos(r) ≠ 0. For θ = 45: r = π / 4 and t = tan(π / 4) = 1.
- θThe input angle in degrees.
- rThe input angle converted to radians.
- tThe tangent value returned as Result, with no units.
- πThe mathematical constant pi; π radians equals 180 degrees.
Multiply the entered degree value by π / 180 to convert it to radians, then evaluate its tangent. Tangent is the ratio of sine to cosine and is undefined wherever cosine is zero. For the default input, 45 × π / 180 = π / 4; sine and cosine are equal at this angle, so their ratio is 1.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Angle (degrees)45
Results
- Result1
How to use the Tangent Calculator
- 1Enter your angle in the Angle (degrees) field, or leave the default value of 45.
- 2Confirm that your input is in degrees rather than radians.
- 3Run the calculation to evaluate the tangent of the entered angle.
- 4Read the Result row: for the default input of 45 degrees, Result = 1.
Reading your result
The Result row gives the tangent of the input angle as a dimensionless number. For an acute angle in a right triangle, this is the length of the opposite side divided by the length of the adjacent side. Result = 1 for 45 degrees means those two sides have equal lengths.
Limitations
This tool assumes degree input; entering a radian value without converting it will calculate a different angle's tangent. Tangent is undefined at θ = 90° + 180° × k, where k is any integer. At or very near these angles, floating-point computation may produce an error or a very large finite value; a finite display at an exact undefined angle is not a valid mathematical tangent. Display rounding and numerical precision may also affect the last digits, especially for very large input angles.
Common questions
Why does the default angle of 45 degrees give Result = 1?+
At 45 degrees, sine and cosine are equal and nonzero. Since tangent equals sine divided by cosine, tan(45°) = 1.
Can I enter an angle in radians for the tangent function?+
The input is interpreted only as degrees. Convert a radian angle to degrees by multiplying it by 180 / π before entering it.
Why is tangent undefined at odd multiples of 90 degrees?+
Cosine is zero at those angles. Because tangent equals sine divided by cosine, evaluating tangent there would require division by zero.
Can tangent be negative, and does it repeat?+
Yes. Tangent is negative when sine and cosine have opposite signs, which occurs in quadrants II and IV. It repeats every 180 degrees wherever it is defined, so tan(θ + 180°) = tan(θ).
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.