TAN in Collabora Office: Relate Angles to Slopes Without Unit Errors

• Introduced: documented in Collabora Office 26.04 Help; the original introduction version is not established by the reviewed history.
• Availability: the official TAN reference documents support in Calc’s 26.04 desktop manual.
• Scope: this evidence does not establish identical behavior in Collabora Online, mobile clients or older releases.
• Checked: October 14, 2026 against the captured 26.04 manual. Examples were calculated independently; no native Collabora execution was performed.

=TAN(number)

The single argument is the angle in radians. For a right triangle, tangent is the opposite side divided by the adjacent side. In a coordinate model, it can represent rise divided by horizontal run when the angle is measured from the horizontal.

The ratio is dimensionless when rise and run use the same unit. It is not itself an angle or a distance. Store the angle’s unit explicitly before choosing a formula.

Enter 0, 30, 45, −45 in A2:A5. In B2 enter and fill down:

=TAN(RADIANS(A2))

Expected results: approximately 0, 0.577350269, 1, −1. At 45 degrees, rise and run have equal magnitudes; at −45 degrees the signed rise is negative for a positive run.

The RADIANS guide explains the conversion. A formula such as TAN(45) uses 45 radians and does not represent a 45-degree slope.

For a mathematical triangle with horizontal run 12 units and angle 30 degrees:

=12*TAN(RADIANS(30))

Expected rise: approximately 6.928203230 units. The tangent ratio is about 0.57735, and multiplying it by 12 gives the opposite-side length.

This is a geometry example, not a construction or safety specification. Real measurements and design requirements need their own validation. Do not mix meters of run with centimeters of rise unless you convert them to a common unit.

A signed rise of 3 and horizontal run of 12 gives the ratio 3/12 = 0.25. To find its principal angle:

=DEGREES(ATAN(3/12))

Expected angle: approximately 14.036243468 degrees. ATAN converts the ratio to radians; DEGREES changes the output unit.

A 25% rise/run ratio is not an angle of 25 degrees. Keep the percentage ratio and angular measure in separately labeled fields.

Put runs 4, 8, 12 in D2:D4 and the angle 30 in F1. In E2 enter and fill down:

=D2*TAN(RADIANS($F$1))

Expected E2:E4: approximately 2.309401077, 4.618802154, 6.928203230. The absolute reference fixes the common angle while the run changes.

Doubling the run doubles the rise in this fixed-angle model. If your results do not scale that way, inspect the reference to F1 and confirm that the source values are numeric.

=TAN(RADIANS(45))
=TAN(RADIANS(225))

Both expected results are approximately 1. Tangent repeats every 180 degrees, so its value does not identify a unique direction around a full circle.

If two signed coordinates define a direction, use ATAN2 to retain quadrant information. Dividing y by x and applying ATAN can lose it, and division fails when x is zero.

Mathematically, tangent is undefined at 90 degrees plus whole multiples of 180 degrees. Do not use TAN(PI()/2) as if it had a finite geometric answer. An approximate input can produce an enormous finite number or application-specific behavior near the singularity; this guide does not assign a native error code there.

Values near these angles are extremely sensitive to small input changes. That is a property of the function, not something repaired by merely formatting fewer decimals.

The identity TAN(angle) = SIN(angle)/COS(angle) is useful where cosine is nonzero, but evaluating the quotient near zero has the same underlying problem. Use SIN and COS to understand the relationship, not to bypass domain limits.

Test a known angle, a negative angle and your expected working range. Independent calculations establish these examples’ mathematical intent; native target-application behavior remains a separate verification step.

• Collabora Office 26.04 Help: TAN — direct product-specific definition and syntax.
• Editorial testing standards.

The examples use semicolon argument separators. Displayed decimals are rounded expected values, not exact native outputs. Mathematical identities are explanatory calculations; product support is limited to the cited documentation scope.