RADIANS in Google Sheets: Convert Degrees for Trigonometry

• 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 RADIANS reference. Documentation and independently calculated examples, without native Sheets execution.

=RADIANS(angle)

Supply an angle measured in degrees. The conversion is angle*PI()/180. The result is a radian measure; it does not choose a direction convention or reduce the angle to a particular interval.

Google documents this single required argument. It does not give a complete Boolean, text, blank or native error matrix on the dedicated page. These examples use explicitly numeric angles and English function names.

Enter the degree values below in A2:A8. In B2 enter =RADIANS(A2) and fill down.

The negative signs remain negative, and a full turn becomes two pi radians. Label both input and output columns with their units rather than relying on the displayed number to reveal the distinction.

The independent algebraic control =A2*PI()/180 represents the same conversion. Tiny numerical differences in an actual client are not measured here; the listed values are rounded mathematical expectations.

=SIN(RADIANS(30))
=SIN(30)

Expected values are 0.5 and approximately -0.988031624. The second formula gives the sine of thirty radians, because SIN takes radians. Both formulas are syntactically meaningful, so the wrong unit may not produce a visible error.

If your source cell already contains a radian measure, do not apply RADIANS again. The function does not inspect a unit label in another column and decide whether conversion is necessary.

For a circle with radius 8 meters and central angle 75 degrees:

=8*RADIANS(75)

The expected arc length is approximately 10.471975512 meters. The radius-times-angle formula requires a radian angle. Using =8*75 instead gives 600, which is not the intended arc length in meters.

This model assumes a circular arc and a central angle. It does not describe a straight-line distance between endpoints. Keep the geometric meaning of the input distinct from the unit conversion.

For the same radius and angle:

=2*8*SIN(RADIANS(75)/2)

The expected chord length is approximately 9.740182864 meters, smaller than the arc. Converting 75 degrees and then halving its radian measure is equivalent to converting 37.5 degrees.

A useful check is =2*8*SIN(RADIANS(37.5)), which has the same expectation. Halving the radius instead of the angle would describe a different calculation.

=RADIANS(450)
=RADIANS(MOD(450,360))

Expected results are approximately 7.853981634 and 1.570796327. The first preserves the extra full revolution; the second deliberately reduces the degree value to 90 before converting.

The two directions have the same sine and cosine in the ideal mathematical model, but they are different accumulated rotations. Normalization can lose useful information when counting turns, so apply MOD only when the reporting question calls for it.

=DEGREES(RADIANS(75)) has mathematical expectation 75. The reverse function DEGREES is useful when displaying a radian calculation in familiar degree units.

Do not enter a degree symbol as part of a numeric string and assume it is converted. Store the number separately from its unit label. For a decimal comma locale, adapt formula punctuation rather than silently changing the intended numeric value.

No extreme-angle precision, native coercion or universal formatting behavior is certified. These finite examples check the conversion direction and units, which are the main causes of plausible but incorrect trigonometric results.

• Google RADIANS help.
• Editorial testing standards.

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.