How to Calculate Tan in Degrees in Excel

What is the tangent function?

The tangent function, often written as tan(θ), is one of the primary trigonometric functions. It's defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. The tangent of an angle is also equal to the sine of the angle divided by the cosine of the angle:

The tangent function has a period of π radians (180 degrees), meaning it repeats its values every 180 degrees. The function is undefined where the cosine is zero (at 90° and 270°).

In Excel, the tangent function is available through the TAN function, which works with radians by default. To calculate tan in degrees, we need to convert the angle from degrees to radians first.

Excel's TAN function

Excel provides the TAN function to calculate the tangent of an angle. However, this function expects the angle to be in radians, not degrees. The basic syntax is:

Where "number" is the angle in radians. For example, =TAN(1) calculates the tangent of 1 radian.

To calculate the tangent of an angle in degrees, you need to first convert the angle from degrees to radians using the RADIANS function:

This formula first converts the angle from degrees to radians and then calculates the tangent of that radian value.

How to calculate tan in degrees

To calculate the tangent of an angle in degrees using Excel, follow these steps:

1. Enter your angle in degrees in a cell (e.g., cell A1)
2. In another cell, use the formula: =TAN(RADIANS(A1))
3. Press Enter to calculate the result

This formula first converts the angle from degrees to radians using the RADIANS function, then calculates the tangent of that radian value.

Step-by-step example

1. Type "45" in cell A1 (this is your angle in degrees)
2. In cell B1, enter the formula: =TAN(RADIANS(A1))
3. Press Enter to see the result: approximately 1

You can also use this approach in more complex formulas where you need to calculate the tangent of a degree value.

Excel example calculation

Let's create a simple Excel worksheet to calculate the tangent of various angles in degrees:

1. Create a table with two columns: "Angle (degrees)" and "Tangent"
2. Enter degree values in the first column (e.g., 30, 45, 60, 90)
3. In the corresponding cells of the second column, enter the formula: =TAN(RADIANS(A2))
4. Copy the formula down to calculate the tangent for all angles

Notice that the tangent of 90 degrees results in an error (#NUM!) because the tangent function is undefined at 90 degrees (cosine is zero).

Common mistakes to avoid

When calculating tan in degrees in Excel, be aware of these common pitfalls:

1. Forgetting to convert degrees to radians: The TAN function expects radians, so you must use RADIANS() to convert your degree value first.
2. Using the wrong angle: Ensure you're using the correct angle value in degrees before conversion.
3. Undefined values: Remember that tan(90°) and tan(270°) are undefined, resulting in an error in Excel.
4. Incorrect formula placement: Make sure the formula references the correct cell containing your degree value.