What is the syntax for TAN in Excel?

The syntax for TAN is: =TAN(number)

What are common errors with TAN?

Undefined at 90, 270 degrees etc.. Argument must be in radians

How do I calculate slope using TAN?

Slope = TAN(angle). If a ramp rises at 30°: =TAN(RADIANS(30)) = 0.577, meaning it rises 0.577 units for every 1 unit horizontal. Conversely, to find angle from slope: =DEGREES(ATAN(slope)).

Why does TAN return very large numbers at certain angles?

TAN approaches infinity at 90°, 270°, etc. (where COS = 0). At exactly 90°, TAN is undefined. Excel returns very large numbers near these angles. This is mathematically correct - the tangent line becomes vertical.

What is the relationship between TAN, SIN, and COS?

TAN(x) = SIN(x)/COS(x). This is why TAN is undefined when COS = 0. You can verify: =SIN(RADIANS(45))/COS(RADIANS(45)) equals =TAN(RADIANS(45)), both returning 1.

Math & Trig

TAN Function in Excel

Returns the tangent of an angle specified in radians.

Syntax

=TAN(number)

Arguments

number (required): Angle in radians

Examples

=TAN(PI()/4) - Tangent of 45 degrees - Result: 1
=TAN(RADIANS(45)) - Tangent of 45 degrees - Result: 1

TAN in reporting workflows

Use absolute references when copying formulas across rows.
For conditional totals see [SUMIF](/functions/sumif/) and [SUMIFS](/functions/sumifs/).
Filtered lists may need [SUBTOTAL](/functions/subtotal/) instead of SUM on visible cells only.

Common errors

Undefined at 90, 270 degrees etc.
Argument must be in radians

Use cases

Slope calculations
Angle problems
Engineering

Frequently asked questions

How do I calculate slope using TAN? Slope = TAN(angle). If a ramp rises at 30°: =TAN(RADIANS(30)) = 0.577, meaning it rises 0.577 units for every 1 unit horizontal. Conversely, to find angle from slope: =DEGREES(ATAN(slope)).
Why does TAN return very large numbers at certain angles? TAN approaches infinity at 90°, 270°, etc. (where COS = 0). At exactly 90°, TAN is undefined. Excel returns very large numbers near these angles. This is mathematically correct - the tangent line becomes vertical.
What is the relationship between TAN, SIN, and COS? TAN(x) = SIN(x)/COS(x). This is why TAN is undefined when COS = 0. You can verify: =SIN(RADIANS(45))/COS(RADIANS(45)) equals =TAN(RADIANS(45)), both returning 1.

Editorial review

Reviewed by Excel.Directory Editorial Team. Updated May 2026.