DEGREES in Excel: Convert Radians and Interpret Inverse-Trig Results

• Introduced: First introduction version is not established by the official history reviewed.
• Availability: official help 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; official DEGREES reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=DEGREES(angle)

The required input angle is in radians. The mathematical conversion multiplies by 180/π. RADIANS performs the reverse conversion.

The function returns a number, not a formatted label carrying a degree symbol or a normalized compass bearing. Keep the input and output units in worksheet headings. The finite numeric examples below do not establish a complete text-coercion, imported-locale or extreme-angle error matrix.

Enter formulas for -PI(), -PI()/2, 0, PI()/6, PI()/3, PI(), 2*PI() in A2:A8, then fill =DEGREES(A2) down.

Expected degree values are -180, -90, 0, 30, 60, 180 and 360. The sign is preserved and a full turn remains 360, rather than automatically becoming zero.

For a non-special angle, =DEGREES(3) has expected result approximately 171.887338539. The argument is three radians, not three degrees; no display convention can substitute for that unit requirement.

=ATAN(1)
=DEGREES(ATAN(1))

Expected results are approximately 0.785398163 radians and 45 degrees. ATAN produces the angle in radians, and DEGREES changes its numeric representation.

This angle is the principal inverse-tangent result for slope one. A slope alone does not identify a full two-dimensional quadrant; a line rising one unit per horizontal unit can be traversed in different directions. Use coordinates and an appropriate directional function when the quadrant matters.

For coordinates x=3 and y=4:

=DEGREES(ATAN2(3,4))

Expected angle: approximately 53.130102354 degrees, measured from the positive x-axis under the ordinary mathematical convention. Excel’s ATAN2 takes x first and y second; do not copy another programming language’s y-first call without checking its signature.

Changing y to -4 gives expected angle approximately -53.130102354 degrees. Changing x to -3 with positive y=4 gives approximately 126.869897646 degrees. DEGREES converts the returned angle but does not change ATAN2’s quadrant selection.

For x=3 and y=-4, a report may want a nonnegative orientation in a 360-degree cycle:

=MOD(DEGREES(ATAN2(3,-4)),360)

Expected result: approximately 306.869897646 degrees. The conversion alone would retain the signed -53.130102354 result; MOD adds the chosen normalization.

This remains an angle from the positive x-axis, not automatically a navigation bearing measured clockwise from north. Defining a different reference axis or orientation is a separate transformation. State the convention before comparing the result with another system.

An arc length of six units on a circle of radius four has angle s/r=1.5 radians. Convert it with:

=DEGREES(6/4)

Expected angle: approximately 85.943669270 degrees. Both length and radius must use compatible units. Dividing centimeters by meters without conversion would make the ratio and resulting angle wrong even though the formula syntax is valid.

This formula concerns an arc, not a straight chord. A chord length requires a different geometric relationship, so confirm the meaning of the measured distance before converting it.

=RADIANS(DEGREES(1.5)) has mathematical expectation 1.5. Keep the underlying calculated value for the reverse conversion rather than retyping its rounded display.

The scale-factor identity is a model check. It does not certify exact native equality for every floating-point value, and it cannot detect an input that was mistakenly labeled radians when it was already in degrees.

If a result is unexpectedly large, inspect whether a degree-valued input was converted again as radians. If an angle has an unexpected sign, inspect the inverse-trig input or coordinate convention before changing the conversion formula.

No native Excel execution is claimed. The source defines the conversion direction; exact malformed-input errors and accuracy for very large multi-turn values require additional evidence beyond these small finite controls.

• Microsoft DEGREES reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.