RADIANS in Excel: Convert Degrees Before Trigonometric Calculations

• 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 RADIANS reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=RADIANS(angle)

The required argument is the angle in degrees. The mathematical conversion is degrees×π/180. Microsoft defines the direction explicitly: this function converts degrees into radians, while DEGREES converts back.

The examples use English function names and comma separators. They cover ordinary finite numeric angles, not every text, error, extreme-value or imported-locale boundary. RADIANS changes the numeric representation; it does not attach an angle-unit type to the result.

Put -180, -90, 0, 30, 60, 180, 360 in A2:A8 and fill =RADIANS(A2) down in B2:B8.

Negative angles keep their sign. A full turn becomes 2π radians; the conversion does not force it to zero. Preserve a heading naming the input unit so a later user does not accidentally convert an already-radian value again.

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

Expected results are 0.5 and approximately -0.988031624. SIN reads its input in radians, so the second formula asks a different question: sine of 30 radians.

A degree-looking cell format cannot change that argument meaning. Put numeric 30 in C2 with a Degrees heading, then use =SIN(RADIANS(C2)) to make the conversion explicit. Avoid typing a degree-symbol string into a cell expected to hold a number unless a separate conversion rule has been verified.

A circle of radius 8 units subtends a central angle of 75 degrees. The arc-length formula is radius×angle in radians:

=8*RADIANS(75)

Expected length: approximately 10.471975512 units. Multiplying 8×75 directly would give 600, because it would omit the required degree-to-radian factor.

This is arc length, not the straight chord between the endpoints. The chord for the same geometry is =2*8*SIN(RADIANS(75)/2), with independently expected length approximately 9.740182864 units. The two lengths differ because they trace different paths.

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

Expected radians are approximately 7.853981634 and 1.570796327. The first retains the full 450-degree angle; the second explicitly normalizes the degree value to 90 before converting.

MOD supplies the normalization policy in this control. Whether turns should be discarded depends on the workbook: a rotation-total log may need 450, while a displayed orientation may use 90. RADIANS itself does not decide that policy.

For an ordinary input of 75, =DEGREES(RADIANS(75)) has mathematical expectation 75. The two scale factors cancel. This is a useful small-input consistency check, not a promise of exact bit-for-bit equality at every native floating-point magnitude.

Keep intermediate values at their available precision. If you manually replace the radian result with a rounded decimal, the reverse conversion can differ slightly because you changed the numeric input.

Check the heading and provenance of every angle before applying the function. A radian value converted as if it were degrees is scaled a second time, which can produce a plausible but wrong small angle.

The conversion is linear and preserves signs; periodicity belongs to the trigonometric operation or an explicit normalization step. Exact error codes for nonnumeric arguments and extreme-angle numerical accuracy remain unverified in this guide.

• Microsoft RADIANS 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.