SIN in Excel: Calculate Sine with Explicit Angle Units

• Introduced: original introduction release and first numeric build are not established by the official history reviewed.
• Availability: the official SIN 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.

=SIN(number)

The argument is required. Microsoft specifies radians; degree inputs must be converted with PI()/180 or RADIANS. Label the input unit in the worksheet instead of relying on the appearance of a number. The sine result is a dimensionless ratio, not an angle in either unit.

Examples use English names, comma separators and decimal points. Keep the full formula result for later calculations; the reported decimals below are for readability.

Enter degree values 0, 30, 90, 150, 270 in A2:A6 and Degree angle in A1. In B1 enter Sine; in B2 enter and fill down:

=SIN(A2*PI()/180)

Expected B2:B6, within numerical precision: 0, 0.5, 1, 0.5, −1. The 30- and 150-degree rows intentionally share a result. A sine value alone does not identify a unique full-circle angle.

As a unit control, =SIN(30) is approximately −0.988031624. That is not the sine of 30 degrees. Formatting the input to show a degree symbol does not automatically convert the numeric argument.

Suppose a constructed vector has magnitude 12 and an angle measured counterclockwise from the positive horizontal axis. Its vertical component is:

=12*SIN(30*PI()/180)

Expected result: 6. With −30 degrees, the component becomes −6. The sign communicates direction; wrapping the result in ABS would discard that information.

The magnitude and resulting component have the same physical unit. This example assumes the coordinate convention just stated; measuring the angle from the vertical instead changes which trigonometric relationship is appropriate. COS supplies the horizontal component under this convention.

An illustrative signal is defined as baseline 10 plus amplitude 4 times the sine of a degree phase. Enter 0, 90, 180, 270, 360 in D2:D6. In E2 enter:

=10+4*SIN(D2*PI()/180)

Fill down. Expected outputs are approximately 10, 14, 10, 6, 10. The sampled maximum and minimum are four units from the baseline. This is a specified mathematical model, not evidence that an observed process is sinusoidal.

If the phase is instead time-dependent, state the period and convert elapsed time into a dimensionless cycle fraction before multiplying by 2*PI(). Confusing a time quantity with an angle can produce a smooth-looking but meaningless curve.

=ASIN(SIN(150*PI()/180))*180/PI()

Expected result: approximately 30, not 150. ASIN returns its principal angle; both source angles have sine 0.5. Preserve the original angle or additional quadrant information if reconstruction matters.

Mathematically, SIN(PI()) is zero. Microsoft’s example describes its result as approximately zero, so do not treat the last displayed digit of every computed multiple of pi as a universal exact-zero guarantee. Use a justified tolerance when comparing calculated coordinates.

Check the stored angle, its unit and any scale or offset separately. This guide does not certify arbitrary text coercion, huge-angle reduction accuracy or behavior at every platform limit. The table, signed component and inverse control provide small reproducible checks before adapting the model.

• Microsoft SIN 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.