Excel SIN, COS & TAN — Why =SIN(30) Isn't 0.5 (the Radians Trap)

TL;DR — SIN, COS and TAN take an angle and return a ratio, but they measure that angle in radians, not degrees. =SIN(30) is not 0.5 — it reads 30 as radians and returns -0.988, with no error to warn you. The single rule that fixes it: wrap every degree value in RADIANS() — =SIN(RADIANS(30)) gives 0.5. Everything else about these functions is easy; the radians mismatch is the only thing that actually goes wrong.

=SIN(30)            ' 30 read as RADIANS -> -0.988   (the trap)
=SIN(RADIANS(30))   ' 30 degrees, done right -> 0.5
=COS(RADIANS(60))   ' cosine of 60 degrees -> 0.5
=TAN(RADIANS(45))   ' tangent of 45 degrees -> 1

Search "SIN function in Excel" and you'll find a hundred pages that tell you =SIN(number) returns the sine of an angle — and stop right there. But the one thing that trips up nearly everyone isn't the syntax; it's that the "number" is in radians. That mismatch is why a formula returns -0.988 when you expected 0.5, and why nothing looks broken. This page leads with it.

What you'll learn

The mental model: these functions think in radians, you think in degrees
Why =SIN(30) returns -0.988 and no error appears
The one fix — RADIANS() — and where it goes
Why TAN blows up to a huge number near 90° instead of #DIV/0!
Building a right-triangle calculation (SOH-CAH-TOA) that actually works
The judgment call: pick one angle unit and hold it across the sheet

The mental model: Excel is a radian-native triangle calculator

SIN, COS and TAN are the three basic ratios of a right triangle — opposite over hypotenuse, adjacent over hypotenuse, opposite over adjacent. Feed one an angle and it hands back the ratio. That part matches what you learned in school.

The catch is the unit of the angle. Mathematics — and therefore Excel — measures angles in radians, where a full circle is 2π (about 6.283) rather than 360. Degrees are a human convention; radians are the native language of trigonometry. Excel speaks only radians. It will never ask which unit you meant, and it will never warn you when you guess wrong — it simply assumes the number you typed is already in radians and computes accordingly.

Hold that one idea and every "wrong" trig answer explains itself.

Why =SIN(30) returns -0.988, not 0.5

Here's the trap in its purest form:

=SIN(30)   ' -> -0.988   (you wanted 0.5)

You meant 30 degrees, whose sine is exactly 0.5. Excel read 30 radians. Thirty radians is nearly five full trips around the circle (30 ÷ 2π ≈ 4.77 laps), landing at about 279° — whose sine really is -0.988. Excel did the math perfectly; it just answered a different question than the one you asked.

The reason this is so dangerous is that it produces a plausible-looking number, not an error. A #VALUE! you'd catch immediately. A -0.988 sits quietly in your model, flows into the next calculation, and corrupts everything downstream while looking completely normal. There is no red flag — which is exactly why the radians rule has to become a reflex.

The fix: RADIANS() on the way in

RADIANS() converts degrees to radians. Wrap your degree value in it before handing it to any trig function, and the answers snap to what you expect:

=SIN(RADIANS(30))   ' -> 0.5
=COS(RADIANS(60))   ' -> 0.5
=TAN(RADIANS(45))   ' -> 1
=COS(RADIANS(0))    ' -> 1
=SIN(RADIANS(90))   ' -> 1

If your angles already live in radians (common when they come out of another formula, like an inverse-trig result), skip RADIANS() and pass them straight in. The rule isn't "always use RADIANS" — it's "know which unit your angle is in, and convert only at the boundary between degrees and radians." Most of the time your data is in degrees and Excel wants radians, so RADIANS() at the input is the norm. (The PI() route works too — =SIN(PI()/6) is 0.5 — but RADIANS() reads better and is the function built for exactly this job. See the RADIANS & DEGREES guide.)

TAN near 90°: a huge number, not an error

Tangent is sine ÷ cosine, and at 90° the cosine is zero — so TAN(90°) is mathematically undefined (it shoots off to infinity). You might expect #DIV/0!. You don't get it:

=TAN(RADIANS(90))   ' -> 16331239353195370   (not #DIV/0!)

The reason is subtle and worth understanding. RADIANS(90) is Excel's best floating-point approximation of π/2, but it isn't exactly π/2 — it's a hair off. So the cosine underneath isn't exactly zero; it's a microscopic non-zero number, and dividing by it yields an enormous but finite result. Treat any trig output in the quadrillions as a flag that you're sitting on an asymptote (90°, 270°, …), not as a real value. If a downstream formula could land there, guard it rather than trusting the number.

A worked example: the height of a triangle

Trig earns its keep in geometry, surveying, physics and engineering. Say a ramp rises at a 15° incline over a 20-foot run, and you want the vertical rise. That's opposite = adjacent × tan(angle):

=20*TAN(RADIANS(15))    ' rise of a 15-degree ramp over 20 ft -> 5.36 ft
=20*SIN(RADIANS(15))    ' if 20 ft were the hypotenuse instead -> 5.18 ft

The only thing standing between "textbook-correct" and "silently wrong" here is the RADIANS() wrapper. Drop it and the ramp's rise comes back as -30.9 — nonsense that no error message would ever announce.

The three core ratios have a full supporting cast, and they all obey the same radians rule:

ASIN, ACOS, ATAN, ATAN2 — the inverse functions, which run the other way: give them a ratio (or a pair of coordinates) and they return the angle. Crucially they return radians, so you wrap the output in DEGREES(). They're the subject of the inverse-trig guide.
SINH, COSH, TANH — the hyperbolic versions, used in engineering and statistics; different math, but the same call pattern.
RADIANS, DEGREES, PI — the unit converters that make all of the above usable with human angles. Covered in the RADIANS & DEGREES guide.

The judgment call: one unit per sheet

The cleanest trig models decide up front whether their stored angles are in degrees or radians, and never mix. If your inputs are degrees (they usually are), keep them as degrees in the cells, and convert inside the formula with RADIANS() at the moment you call a trig function. Don't scatter half-converted angles around the sheet, and don't hardcode × π/180 in ten places when one named converter says what you mean. An angle column with no label saying "degrees" or "radians" is a bug waiting to happen — write the unit in the header.

How ExcelMaster helps

The radians trap is invisible until a number looks wrong, and by then it's often three formulas downstream. Ask ExcelMaster "why is my SIN giving a negative number?" and it spots the missing RADIANS(), shows you the corrected formula, and explains the degrees-vs-radians mismatch in plain terms. Tell it "calculate the rise of a 15-degree ramp over 20 feet" and it wires up =20*TAN(RADIANS(15)) with the conversion already in place — no silent factor-of-a-radian error.

Frequently asked questions

Why does =SIN(30) give -0.988 instead of 0.5 in Excel?

Because Excel's trig functions measure angles in radians, not degrees. 30 is read as 30 radians (about 279° once you unwind the full circles), whose sine is -0.988. To get the sine of 30 degrees, convert first: =SIN(RADIANS(30)), which returns 0.5.

How do I use degrees with SIN, COS and TAN in Excel?

Wrap the angle in RADIANS(): =SIN(RADIANS(30)), =COS(RADIANS(60)), =TAN(RADIANS(45)). RADIANS() converts degrees to the radians the function expects. If your angle is already in radians, pass it directly without the wrapper.

Why doesn't TAN(90°) give an error in Excel?

Tangent is undefined at 90° because cosine is zero there, but RADIANS(90) is only a floating-point approximation of π/2, so the cosine underneath is a tiny non-zero number rather than exactly zero. Dividing by it yields a huge finite value (around 1.6×10¹⁶) instead of #DIV/0!. Treat quadrillion-scale trig output as an asymptote flag.

What's the difference between SIN and ASIN in Excel?

SIN takes an angle and returns a ratio; ASIN (arcsine) takes a ratio and returns the angle. SIN expects radians in; ASIN gives radians out (wrap it in DEGREES() for a human angle). See the inverse-trig guide.

Can I avoid RADIANS by using PI()?

Yes — =SIN(30*PI()/180) is the same as =SIN(RADIANS(30)). But RADIANS() is the function built for the job, reads more clearly, and doesn't tempt you to hardcode a truncated 3.14159. Prefer it, and reach for PI() when you actually need the constant itself.

Tested in

Tested in: Excel 365 (Windows 11) — last verified 2026-07-24.