ATAN in Excel: Convert a Slope Ratio into a Principal Angle

• Introduced: original introduction release and first numeric build are not established by the official history reviewed.
• Availability: the official ATAN reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026. Documentation and independently calculated finite-value examples; no native Excel execution or broader platform certification.

=ATAN(number)

Supply the tangent ratio, not an angle already measured in degrees. Microsoft documents a principal radian result in the −PI()/2 to PI()/2 range. For ordinary finite real inputs, the mathematical values lie strictly between the two vertical limits; increasing the input magnitude approaches rather than reaches them.

Convert the result with 180/PI() or DEGREES when you need degrees. Examples use English function names and decimal-point numeric notation. A percentage is a ratio on a different display scale, not a degree measure.

Enter −1, −0.5, 0, 0.5, 1 in A2:A6. In B2 enter and fill down:

=ATAN(A2)*180/PI()

Expected results, approximately: −45, −26.565051177, 0, 26.565051177, 45 degrees. The signed result preserves which side of zero the ratio lies on within the chosen principal branch.

For input 1, the radian result is approximately 0.785398163. Multiplying that by 180/PI() changes units; it does not change which angle branch is selected.

Suppose a constructed rise is 3 units over a horizontal run of 12 units. The ratio is 0.25, or 25 percent. Use:

=ATAN(3/12)*180/PI()

Expected angle: approximately 14.036243468 degrees, not 25 degrees. A negative rise of −3 with the same positive run gives approximately −14.036243468 degrees.

Both lengths must have the same unit. The ratio becomes invalid when the run is zero, even though a vertical direction may exist geometrically. Use ATAN2 with the original signed coordinates for that situation rather than dividing first.

=ATAN(4/4)*180/PI()
=ATAN(-4/-4)*180/PI()

Both expected results are 45 because both ratios equal one. However, the coordinate points (4,4) and (−4,−4) point in opposite directions. Division discarded the separate signs that identify the quadrant.

ATAN2(−4,−4) instead gives a principal direction of approximately −135 degrees. This is not a contradiction: it answers a coordinate-aware question using two inputs. Keep both components until you know whether a plain slope or a full direction is required.

Replace A2:A4 with input ratios 0.25, 0.5, 2, then enter the following in B2 and fill down to apply TAN to the principal radian angles:

=TAN(ATAN(A2))

The expected reconstructed ratios are approximately 0.25, 0.5, 2. Their degree angles are approximately 14.036243468, 26.565051177, 63.434948823. TAN expects the radian angle directly; do not pass a degree-converted intermediate without converting it back.

These moderate controls are useful for checking units. They do not establish unlimited numerical round-trip precision near vertical limits or for extreme magnitudes.

Inspect whether the cell contains a ratio, a percent display, an angle or a pair of coordinates combined too early. A value stored as 25 rather than 0.25 represents a very different slope. Keep the source rise and run visible to distinguish a calculation error from a misunderstood input convention.

The direct reference defines the function and principal interval but does not provide a complete coercion/error matrix. Native checks remain necessary for unusual imported types and precision-critical boundary cases.

• Microsoft ATAN reference.
• Editorial testing standards.

Numerical outputs are independent mathematical expectations, rounded where stated. Product-specific syntax and scope come from the cited reference. Native error/coercion matrices and extreme-value precision remain untested.