ATAN in Google Sheets: Turn Slope Ratios into Angles

• Introduced: original service launch date is not established by the official history reviewed; Sheets has no corresponding numbered desktop release in this guide.
• Availability: documented in the rolling Google Sheets service; examples use an ordinary web spreadsheet and numeric cells.
• Checked: October 14, 2026; official ATAN reference. Documentation and independent calculations, without native Sheets execution or broader client certification.

=ATAN(value)

The argument is the ratio whose inverse tangent is wanted. Google says the chosen angle is between −PI()/2 and PI()/2. For ordinary finite real inputs, the ideal values lie strictly inside those vertical limits.

Use DEGREES or multiply by 180/PI() for degree output. Do not convert the ratio as though it were a degree angle before calling ATAN. The examples use English function names and decimal-point numbers.

Enter −1, −0.75, 0, 0.75, 1 in A2:A6. In B2 enter and fill down:

=ATAN(A2)*180/PI()

Expected angles, approximately: −45, −36.869897646, 0, 36.869897646, 45 degrees. A ratio of one corresponds to a 45-degree principal angle, not one degree.

For the ratio 0.75, the direct radian value is approximately 0.643501109. Retain that radian value when passing the angle to TAN; converting it to degrees and then using it directly would mix units.

Suppose a constructed rise is 6 units over a horizontal run of 8 units. Its ratio is 0.75, or 75 percent. Use:

=ATAN(6/8)*180/PI()

Expected result: approximately 36.869897646 degrees, not 75 degrees. A rise of −6 with the same positive run gives the negative of that angle.

Both source lengths must use compatible units. A stored number of 75 is not the same as a cell storing 0.75 and displaying 75%. Keep the rise and run visible so a reviewer can see which quantity was converted.

=ATAN(6/8)*180/PI()
=ATAN(-6/-8)*180/PI()

Both expected answers are approximately 36.869897646 degrees because both divisions produce 0.75. Yet the two coordinate pairs point in opposite directions. Dividing first discarded their separate signs.

ATAN2 accepts both coordinates and is the appropriate function to investigate when an actual direction is required. If the horizontal run is zero, forming a ratio fails even though the vector can have a vertical direction; retain the original coordinates instead.

Replace A2:A4 with 0.2, 0.75, 1.5. In B2 enter =ATAN(A2) and fill down. Put =B2*180/PI() in C2 and fill down, giving expected angles approximately 11.309932474, 36.869897646, 56.309932474 degrees.

In D2 enter =TAN(B2) and fill down. Expected recovered ratios are approximately 0.2, 0.75, 1.5. TAN receives B’s radians, while C is only a converted view for the reader.

This separation makes a unit error easier to locate than a long nested expression. Keep full stored values rather than retyping the displayed rounded degrees for the inverse calculation.

Check whether the source is a ratio, a degree angle or a percent-scale integer. Review whether a principal slope angle is sufficient or whether separate coordinate signs are needed. These are modelling choices that ATAN cannot infer.

The official reference identifies the principal branch but does not provide a full native coercion/error matrix. Extreme ratios approach vertical limits and can amplify numerical concerns. The small finite examples here do not certify every imported type or native precision boundary.

• Google ATAN help.
• Editorial testing standards.

Worked inputs are fictional and outputs independently calculated. Approximate values are rounded mathematical expectations, not captured native results. Imported types, extreme magnitudes and a complete error/coercion matrix remain outside the tests.