How to use the RADIANS function
What is the RADIANS function?
The RADIANS function converts degrees to radians.
Table of Contents
1. Introduction
What is radian?
Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2π multiplied by the circle's radius (2πr).
Since the circumference goes all the way around a circle, that means the full circle measures 2π radians. Half a circle would be π radians (half of 2π). A quarter circle is 2π/4 = π/2 radians. An eighth of a circle is 2π/8 = π/4 radians.
Excel has a function that returns the number pi: PI function
What is the number pi?
Pi is a irrational number meaning it cannot be expressed as a ratio of two integers. In other words, it has an infinite number of decimal places with no repeating pattern. It is calculated by the ratio of the circumference of a circle to its diameter.
circumference = diameter * π
or
circumference = 2 * π * radius
this means that the diameter = 2 x radius.
What is the circumference of a circle?
The circumference is the linear distance enclosing the circle.
What is the diameter of a circle?
The diameter of a circle is the straight line distance that passes through the center of the circle connecting one point on the circumference to another, going all the way across the circle.
What is the radius of a circle?
The radius of a circle is the distance from the center point to any point on the circle's edge or circumference.
Why is the PI function useful?
The trigonometric functions in Excel accept radians as the angular measurement. The basic trigonometry ratios like sine, cosine and tangent come from the ratios of sides in a right triangle. Sine, cosine and tangent ratios relate the lengths of sides to angles in a right triangle. If you know one side and angle, you can use these ratios to find the other sides. The ratios link geometry and angles together.
What is the relationship between the number pi and radians?
Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2π multiplied by the circle's radius (2πr).
Since the circumference goes all the way around a circle, that means the full circle measures 2π radians. Half a circle would be π radians (half of 2π). A quarter circle is 2π/4 = π/2 radians. An eighth of a circle is 2π/8 = π/4 radians.
What is an arc in a circle?
The arc in a circle is a segment of the circle's circumference. Arcs are an angle measured in degrees or radians.
What is a segment in a circle?
A segment (also called chord) connects two points on a circle's edge by a straight line, and can be used to analyze geometric aspects of the circle like angles, area, and tangents.
What is a sector?
A sector of a circle is the section enclosed by two radii and an arc.
What is radii?
The plural form of the word "radius".
What is the connection between a circle and trigonometry?
The geometry of the circle underlies the theory, definitions, models, identities, and applications of trigonometry. The circle and trigonometry are deeply mathematically connected.
What is the relationship between radians and degrees?
The circumference of a circle is 360 degrees or 2π radians.
360 degrees = 2π radians
which is
degrees = radians x (180 / π)
This is what the RADIANS function does:
Radians = Degrees * PI() / 180
2. Syntax
RADIANS(angle)
| angle | Required. The degree you want to convert. |
3. Example 1
Convert the following values in degrees [0, 45, 90, 135, 180, 225, 270, 315, 360] to radians?
The degrees are specified in cell range B16:B24.
Formula in cell D16:
The formula returns the following radians in cell range D16:D24 in decimal form, they are [0, π/4, π/2, 3π/4, π, 5/4π, 3/2π, 7/4π, 2π] in fractions of pi.
The image above displays a chart that illustrates the relationship between angles expressed in radians and their corresponding values in degrees. The chart consists of two main sections: a graphical representation and a tabular data section.
The graphical representation shows a unit circle divided into quadrants, with angles represented in both radians and degrees. The angles are marked along the circumference of the circle, with their radian values indicated below and their degree values indicated above. For example, the angle π/4 radians is equivalent to 45 degrees, and the angle 3π/2 radians is equivalent to 270 degrees.
The tabular data section consists of two columns:
- DEGREES: This column lists various angle values in degrees, including 0, 45, 90, 135, 180, 225, 270, 315, 360
- Radians: This column shows the corresponding radian values for the degree values in the previous column, calculated using the RADIANS function in Excel. The RADIANS function converts an angle value from radians to degrees.
- Radians: This column lists various angle values in radians based on fractions of π (pi), including 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4, and 2π.
For example, the radian value π/4 corresponds to 45 degrees, π/2 corresponds to 90 degrees, and 2π corresponds to 360 degrees.
The chart serves as a visual aid and reference for understanding the conversion between radian and degree measurements of angles which is essential in various mathematical and scientific applications.
4. Example 2
In a right-angled triangle, find the length of the opposite side if A = 30 degrees and the hypotenuse is 5 units?
What we know:
- Right-angled triangle meaning one angle is 90 degrees or π/2
- c = 5 units (hypotenuse)
- A = 30 degrees
Steps to build the Excel formula:
- Convert degrees to radians.
- Calculate the ratio between a and c (a/c) using the SIN function and the provided angle converted to radians.
- Multiply result by 5 to get the length of the opposite side.
Formula in cell C20:
The fomrula in cell C20 returns 2.5 which represents the length of the opposite side in units.
The RADIANS function allows us to convert 30 degrees to radians which is π/4. The SIN function calculates the ratio between opposite side and the hypotenuse using an angle as the input value.
SIN A = a/5
a = 5 * SIN A
a = 5 * SIN π/4
a = 5 * 0.5
a = 2.5
The length of the opposite side is 2.5 units. The image above shows a chart displaying a right triangle in blue color, angle A is 30 degrees and the hypotenuse is 5. Cell C18 contains the number of degrees which represents the angle A.
5. Function not working
The RADIANS function returns a
- #VALUE! error if the argument angle is non-numeric.
- #NAME? error if you misspelled the function.
5.1 Troubleshooting the error value
When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.
- The first line describes the error if you press with left mouse button on it.
- The second line opens a pane that explains the error in greater detail.
- The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
- This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
- The fifth line lets you edit the formula in the Formula bar.
- The sixth line opens the Excel settings so you can adjust the Error Checking Options.
Here are a few of the most common Excel errors you may encounter.
#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.
#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.
#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.
#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.
#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.
#NAME error - The #NAME error happens if you misspelled a function or a named range.
#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.
#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.
#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.
5.2 The formula returns an unexpected value
To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:
- Select the cell containing the formula you want to examine in detail.
- Go to tab “Formulas” on the ribbon.
- Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control. - Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
- Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
- Press "Close" button to dismiss the dialog box.
There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..
- Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
- Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
- Press F9: This will calculate and display the result of just that selected portion.
- Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
- Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.
The image above shows cell reference B3 converted to hard-coded value using the F9 key. The RADIANS function requires numerical values which is not the case in this example. We have found what is wrong with the formula.
Tips!
- View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
- Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
- Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.
Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button
5.3 Other errors
Floating-point arithmetic may give inaccurate results in Excel - Article
Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.
'RADIANS' function examples
Table of Contents How to use the IMABS function How to use the IMAGINARY function How to use the IMARGUMENT […]
Functions in 'Math and trigonometry' category
The RADIANS function function is one of 62 functions in the 'Math and trigonometry' category.
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