Excel RADIANS, DEGREES & PI — Converting Angle Units (and Why PI() Is a Function)

TL;DR — Excel's trig functions work in radians; humans work in degrees. RADIANS() and DEGREES() are the two-way bridge between them. The rule is directional: RADIANS() goes on the way in to SIN/COS/TAN, DEGREES() goes on the way out of ASIN/ACOS/ATAN. PI() is a function, not a stored constant — it needs the empty parentheses, and it's more accurate than any 3.14159 you'd type by hand.

=RADIANS(180)        ' degrees -> radians -> 3.14159265358979
=DEGREES(PI())       ' radians -> degrees -> 180
=PI()                ' the constant pi to full precision -> 3.14159265358979
=DEGREES(2*PI())     ' a full circle in degrees -> 360

These three functions look trivial — and their syntax is. But they're the reason trig works at all in Excel, because they resolve the one mismatch that silently breaks it: the angle unit. Get the direction of the conversion right and SIN, COS, TAN and their inverses all behave. Get it wrong — or skip it — and every answer is quietly off.

What you'll learn

The mental model: two units, one native to Excel, one native to you
Which converter goes where — the directional rule that never changes
Why PI() is a function with parentheses, not a bare constant
Why you should never hardcode 3.14159
The × π/180 shortcut, and why the named function beats it

The mental model: a translation layer between two worlds

There are two ways to measure an angle. Degrees split a circle into 360 parts — the human convention, the one on protractors and compass bearings. Radians measure the angle by arc length, so a full circle is 2π (about 6.283) — the convention mathematics uses because it makes the calculus of trigonometry clean. Neither is "more correct"; they're two languages for the same thing.

Excel's engine speaks radians exclusively. Your data almost always arrives in degrees. RADIANS() and DEGREES() are the translators sitting on the border between those two worlds. Every trig headache in a spreadsheet comes down to a missing or backwards translation — so the whole skill is knowing which direction you're crossing.

The directional rule: RADIANS in, DEGREES out

This is the entire game, and it never changes:

Going into a forward trig function (SIN, COS, TAN) you have a degree angle and Excel wants radians → wrap it in RADIANS().
Coming out of an inverse trig function (ASIN, ACOS, ATAN, ATAN2) you get radians back and want a human degree → wrap it in DEGREES().

=SIN(RADIANS(30))        ' degrees in: convert first -> 0.5
=DEGREES(ATAN(1))        ' radians out: convert after -> 45
=DEGREES(ASIN(0.5))      ' the angle whose sine is 0.5 -> 30
=RADIANS(90)             ' 90 degrees as radians -> 1.5707963267949

A useful mnemonic: RADIANS feeds the machine, DEGREES reads the result. Forward functions consume angles (feed them radians); inverse functions produce angles (read them as degrees). If you ever see a trig answer that's off by a factor of about 57 (that's 180/π), you've almost certainly applied the converter in the wrong direction or skipped it.

PI() is a function, not a constant

Unlike some languages, Excel has no bare PI keyword. PI is a function that takes no arguments and returns π — which means it always needs its empty parentheses:

=PI()      ' -> 3.14159265358979   (correct)
=PI        ' -> #NAME?             (Excel thinks PI is a named range)
=2*PI()    ' two pi, a full circle in radians -> 6.28318530717959

Leave off the () and Excel reads PI as the name of a range or defined name, finds nothing, and returns #NAME?. The empty parentheses are how Excel knows you mean the function. Every zero-argument function works this way — TODAY(), NOW(), RAND() — and PI() is the one people forget most.

Never hardcode 3.14159

It's tempting to type 3.14159 and move on. Don't. PI() carries π to about 15 significant digits — 3.14159265358979 — while any value you type by hand is truncated, and that truncation compounds:

=DEGREES(PI())       ' full-precision pi -> 180   (exactly)
=DEGREES(3.14159)    ' truncated by hand -> 179.999522...   (off already)

For a compass bearing the error is invisible; for a machined part, an orbital calculation, or anything that multiplies up, it isn't. Use PI() every time you need π — it costs nothing and removes an entire category of rounding error. The same logic is why you use RADIANS() instead of writing the conversion out longhand.

The × π/180 shortcut (and why RADIANS beats it)

Before these functions existed, people converted by hand: multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees. It still works, and you'll see it in older workbooks:

=30*PI()/180         ' manual degrees -> radians -> 0.523598775598299
=RADIANS(30)         ' the same thing, named -> 0.523598775598299
=1.5708*180/PI()     ' manual radians -> degrees -> ~90

The results are identical, so this isn't about accuracy — it's about readability and safety. RADIANS(30) says exactly what it does; 30*PI()/180 makes the next person decode it, and invites the mistake of flipping the fraction to 180/π in the wrong place. Reach for the named converter. Keep the manual form for when you're reading someone else's sheet and need to recognise it.

How ExcelMaster helps

Angle-unit bugs are the kind you can stare at for ten minutes — the formula looks right, the number is just wrong. Ask ExcelMaster "convert this column of degrees to radians" and it drops in =RADIANS(A2) down the range. Paste a trig formula that's off by a factor of 57 and it recognises the signature of a missing or reversed converter, and tells you whether you need RADIANS() on the input or DEGREES() on the output. It also swaps any stray 3.14159 for PI() so precision stops leaking.

Frequently asked questions

How do I convert degrees to radians in Excel?

Use RADIANS(): =RADIANS(180) returns 3.14159265358979. Wrap it around any degree value before passing it to SIN, COS or TAN — for example =SIN(RADIANS(30)). To go the other way, use DEGREES().

How do I convert radians to degrees in Excel?

Use DEGREES(): =DEGREES(PI()) returns 180. It's the exact inverse of RADIANS(), and you typically apply it to the output of an inverse trig function, like =DEGREES(ATAN(1)) which gives 45.

Why does PI return #NAME? in Excel?

Because PI is a function and needs its empty parentheses: write =PI(), not =PI. Without the (), Excel interprets PI as an undefined named range and returns #NAME?.

Should I use PI() or type 3.14159?

Always PI(). It carries π to about 15 significant digits, whereas any typed value is truncated and introduces rounding error that compounds through a calculation. =DEGREES(PI()) is exactly 180; =DEGREES(3.14159) is already 179.9995.

What's the difference between RADIANS and DEGREES?

They convert in opposite directions. RADIANS() turns degrees into radians (used before forward trig functions); DEGREES() turns radians into degrees (used after inverse trig functions). A full circle is RADIANS(360) = 2π radians = DEGREES(2*PI()) = 360.

Tested in

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