DEGREES in Google Sheets: Convert Radians and Display Directions
Convert Sheets radians to degrees with inverse-trigonometric examples, quadrant checks and explicitly separate normalization.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: DEGREES converts radians to degrees. =DEGREES(PI()) represents a half turn and has expected result 180. Apply it to a radian value, including an inverse-trigonometric result, rather than to a value already measured in degrees.
Availability and version history
- Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
- Availability: documented in the rolling Google Sheets service. Examples target ordinary web-spreadsheet cells; mobile clients and imported file modes are not separately certified.
- Checked: October 14, 2026; official DEGREES reference. Documentation and independently calculated examples, without native Sheets execution.
Syntax and conversion direction
=DEGREES(angle)
The required argument is a radian angle. The mathematical conversion is angle*180/PI(). The function changes units without deciding whether the angle should be positive, wrapped to one turn or measured from a different axis.
Google’s dedicated reference documents the direction of conversion but does not supply a full input-conversion or error-code matrix. The worked cases use explicit real numeric inputs and English function names.
Example 1: familiar radian landmarks
Enter the formulas for the radian inputs in A2:A8. Put =DEGREES(A2) in B2 and fill down:
| Input in column A | Expected degrees |
|---|---|
| =-PI() | -180 |
| =-PI()/2 | -90 |
| =0 | 0 |
| =PI()/6 | 30 |
| =PI()/3 | 60 |
| =PI() | 180 |
| =2*PI() | 360 |
Keep enough decimal precision in the input when using an approximate radian constant. Rounding pi to 3.14 before conversion is a different input, not a defect in DEGREES.
For a non-landmark control, =DEGREES(3) has mathematical expectation approximately 171.887338539. Three radians and three degrees are very different angles.
Example 2: display an inverse tangent
=ATAN(1)
=DEGREES(ATAN(1))
Independent expected values are approximately 0.785398163 radians and 45 degrees. ATAN returns a radian angle, so the conversion is appropriate here.
This does not change ATAN’s selected inverse branch. A conversion between units cannot recover extra revolutions or quadrant information that the input calculation never supplied.
Advanced example: preserve the quadrant of a coordinate direction
Google Sheets ATAN2 uses the argument order x, y. With x=3 and y=4:
=DEGREES(ATAN2(3,4))
The expected direction from the positive x-axis is approximately 53.130102354 degrees. For x=3, y=-4 it is approximately -53.130102354; for x=-3, y=4 it is approximately 126.869897646.
These three controls distinguish quadrants. Swapping the arguments or replacing ATAN2 with ATAN(y/x) without handling signs can answer a different direction question. The origin is not part of these nonzero-coordinate examples.
Advanced example: normalize only when the report requires it
=MOD(DEGREES(ATAN2(3,-4)),360)
The independent expectation is approximately 306.869897646 degrees. The underlying direction is the same as the negative angle above, but this display is in a nonnegative one-turn interval.
DEGREES alone did not perform that normalization; MOD did. This direction is measured counterclockwise from the positive x-axis, not automatically as a compass bearing measured clockwise from north. Changing the axis convention requires a separate model.
Advanced example: recover a central angle from arc length
For a circular arc 6 meters long with radius 4 meters, the radian angle is length divided by radius:
=DEGREES(6/4)
The expected angle is approximately 85.943669270 degrees, from a radian input of 1.5. The length and radius must use the same unit so their ratio is dimensionless.
A chord length is not an arc length. Substituting a straight endpoint distance into this ratio would not represent the same geometry. The unit conversion cannot correct a wrongly chosen geometric formula.
Reverse checks and common mistakes
=RADIANS(DEGREES(1.5)) has mathematical expectation 1.5. RADIANS is the reverse conversion and belongs before a radian-based sine or cosine when the starting value is in degrees.
Do not apply DEGREES to an already-degree input of 90 and expect it to remain 90. It would treat 90 as radians. Store unit labels outside the numeric cells and inspect the preceding calculation when an angle looks implausible.
The displayed decimals are rounded independent expectations. Native round-trip precision, huge angles, numeric text and client-specific error displays remain untested; no zero-tolerance identity is promised for every spreadsheet input.
References and verification
Inputs are fictional. Approximate answers are independent mathematical expectations rounded to nine places, not captured native results. Complete type/error matrices, extreme-magnitude accuracy and cross-client behavior remain untested.