SEC in Excel: Calculate Secant with Correct Radian Units

• Introduced: Microsoft marks the function as introduced in Excel 2013. Version-marker reference.
• 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 SEC reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=SEC(number)

Microsoft specifies radians and an absolute input below 2^27. It documents #NUM! outside the bound and #VALUE! for nonnumeric input. For degrees, use PI()/180 or RADIANS before SEC.

The current help table describes SEC(45) and SEC(30) as degree examples, but their displayed numbers correspond to radian inputs. Follow the explicit syntax and conversion guidance rather than those inconsistent labels. This guide writes the conversion into every degree-based formula.

Enter 0, 30, 60, 120, 180 degrees in A2:A6 and fill =SEC(A2*PI()/180) down. Expected results are approximately 1, 1.154700538, 2, −2, −1.

Secant is the reciprocal of cosine, so its magnitude is at least one wherever the real ratio is defined. A negative result can be valid for an oriented angle even though a basic triangle’s side lengths are positive.

For a stated acute right triangle with adjacent side 8 and angle 35 degrees:

=8*SEC(35*PI()/180)

Expected hypotenuse: approximately 9.766196710. The adjacent side is the one next to the specified angle, excluding the hypotenuse itself.

Multiplying the unrounded result by COS of the same radian angle reconstructs approximately 8. If that check fails substantially, inspect the angle unit, side definition and copied reference before changing the formula.

At 60 degrees, =1/COS(60*PI()/180) also gives approximately 2. For a separate 45-degree control:

=SEC(PI()/4)^2-TAN(PI()/4)^2

Expected result: approximately 1, since the squared terms are 2 and 1. TAN and SEC share cosine in their denominators, explaining the corresponding identity.

These are ordinary-input checks. Algebraic equivalence is not a promise that expanded formulas have identical native error behavior or floating-point accuracy in every corner case.

At 120 degrees, cosine is −0.5 and SEC is −2. Multiplying SEC by cosine gives approximately 1, but replacing the secant with ABS(SEC(…)) would give −1 in that product. Decide whether a workflow needs signed orientation or only a positive magnitude before removing signs.

Mathematically SEC is undefined at pi/2 plus an integer multiple of pi. PI()-based formulas approximate those angles, so a very large finite result is not evidence that the exact singularity has a valid finite secant.

The dedicated page does not establish every singular-input native error code. Keep that uncertainty separate from the documented magnitude and type restrictions. Avoid comparing identities by exact stored equality near a singularity, and retain the original angles for diagnosis.

• Microsoft SEC 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.