SQRTPI Function in Apple Numbers: Square Root of a Number Times Pi

=SQRTPI(non-neg-number)

Parameter: non-neg-number

Required?
Yes

Expected type
Number

Meaning
The value to multiply by π before taking its square root; must be ≥ 0.

Apple’s official SQRTPI reference names the argument non-neg-number, specifies its domain, and shows its single-argument signature. No optional/default argument is documented. SQRTPI() with no argument is not valid under that signature. Do not confuse this function with SQRT(non-neg-number) or with PI() multiplied after a square root.

Mathematically:

SQRTPI(x) = √(π × x)      for x ≥ 0

You can check the relationship using =SQRT(B2*PI()), since SQRT computes a square root and PI supplies an approximation of π. Both formulas describe the same real-number quantity; formatting/rounding can affect the visible decimal digits.

Regional settings: The English documentation shows comma-separated function arguments, but Apple instructs users whose decimal separator is a comma to use a semicolon between multiple arguments. SQRTPI takes only one argument, so there is no separator inside its own parentheses; nested functions or other formulas may require different separators. A decimal such as 0.25 may be entered with the locale’s appropriate decimal mark. See Apple’s function syntax overview.

Version and platform scope: This tutorial cites the 15.4 edition of Apple’s Formulas and Functions Help. That is the help-document edition, not an assertion that Numbers itself is version 15.4 or that SQRTPI first appeared in that app version. Apple describes an in-app Functions Browser for Numbers on Mac, iPhone and iPad and iWork on iCloud.com (official welcome). No historical first-supported app versions or cross-device numerical equivalence were established; native tests remain outstanding.

Make one Numbers table called Pi Inputs with a single header row. Enter the following in columns A and B and put results in C:

Row: 2

A: Test case
Zero

B: x
0

C: Expected SQRTPI(x) (9 decimals)
0.000000000

Row: 3

A: Test case
Quarter

B: x
0.25

C: Expected SQRTPI(x) (9 decimals)
0.886226925

Row: 4

A: Test case
One

B: x
1

C: Expected SQRTPI(x) (9 decimals)
1.772453851

Row: 5

A: Test case
Two

B: x
2

C: Expected SQRTPI(x) (9 decimals)
2.506628275

Row: 6

A: Test case
Five

B: x
5

C: Expected SQRTPI(x) (9 decimals)
3.963327298

Row: 7

A: Test case
Eight

B: x
8

C: Expected SQRTPI(x) (9 decimals)
5.013256549

Type in C2:

=SQRTPI(B2)

Copy C2 down to C7. The expected display values above assume you format column C to nine decimal places. The independent calculation for row 6 is sqrt(5 × π) ≈ 3.96332729760601; Apple’s official example also identifies the 5-input value (SQRTPI). This is a genuine mathematical computation, not simply the square root of B6 and not a rounding-to-integer operation.

For an independent worksheet cross-check, put in D2:

=SQRT(B2*PI())

Copy D2:D7. Values should agree with column C at the displayed precision. PI() already supplies π: do not calculate SQRTPI(B2*PI()), which would multiply by π twice. In Numbers a same-table reference such as B2 needs no table qualifier; a different table may require Pi Inputs::B2 or Sheet Name::Pi Inputs::B2 (Apple cell-reference rules).

An illustrative use for SQRTPI(2) is the constant √(2π) in the denominator of the standard normal probability density function. This is a mathematical application; SQRTPI alone does not calculate a probability or an entire normal distribution.

Create a separate Numbers table named Normal Curve, with a header row and x values in B2:B5:

Row: 2

A: Point
Centre

B: x
0

C: Expected density (9 decimals)
0.398942280

Row: 3

A: Point
+1 standard deviation

B: x
1

C: Expected density (9 decimals)
0.241970725

Row: 4

A: Point
−1 standard deviation

B: x
−1

C: Expected density (9 decimals)
0.241970725

Row: 5

A: Point
+2 standard deviations

B: x
2

C: Expected density (9 decimals)
0.053990967

In C2, enter:

=EXP(-(B2^2)/2)/SQRTPI(2)

Copy C2 through C5. The values are expected independent mathematical calculations, using the formula exp(−x²/2)/√(2π). In particular, C2 calculates 1/√(2π) ≈ 0.398942280 when x = 0. The input of SQRTPI in this formula is always 2, so it remains nonnegative even when the x coordinate in B4 is negative. This distinction avoids a common error: writing SQRTPI(B4) when x is negative.

Other useful identities and exact checks

• =SQRTPI(0) → 0 (expected). Zero is inside Apple’s allowed domain.
• =SQRTPI(1) → approximately 1.772453851, which is √π.
• =SQRTPI(4) → approximately 3.544907702, which is 2√π.
• =SQRTPI(5)^2 → approximately 15.707963268 (5π) before displayed rounding. Squaring the unrounded result illustrates the identity, but slight floating-point discrepancies are possible.

Negative input: Apple’s documentation explicitly states the input must be nonnegative. Therefore =SQRTPI(-1) is outside the documented real-number domain and should be treated as an invalid example—not as a positive square root or a reliably specified error string. Excel’s official manual specifies #NUM! for its own negative SQRTPI input, but Apple did not establish an identical exact error label in the cited entry (Apple SQRTPI; Microsoft SQRTPI).

Not numeric: If a referenced cell contains imported text that visually resembles a number, verify its cell format before using it as a numeric argument. Apple’s formula-error guidance recommends checking number formatting and references. Do not assume every text or empty-cell coercion behavior matches Excel; those cases need native testing.

Unexpected decimal output: Check whether you accidentally used =SQRT(B2)*PI() instead of =SQRT(B2*PI()). For x=4 the former is approximately 6.283185307, while SQRTPI(4) is approximately 3.544907702. This is a difference in algebra, not a rounding issue.

Wrong table or circular reference: Type the formula in C2, not B2. A formula in B2 referencing B2 can cause a circular reference. Use Apple’s error guide to inspect a displayed warning/error icon and verify references.

Extra separators: SQRTPI takes one required number. Formula =SQRTPI(B2,2) has an extra argument and does not match the official signature. In comma-decimal locales, take care with literal decimals and semicolon argument separators in other functions.

Very large numeric values: The manual does not specify the maximum representable value or exact overflow/underflow error for SQRTPI. Avoid claiming unlimited precision; validate boundary cases in Numbers when they matter.

Microsoft officially documents SQRTPI(number) for Excel and specifies the negative-number error #NUM! there (Microsoft SQRTPI). Apple’s function uses the same algebraic operation and documented nonnegative input domain (Apple SQRTPI). That is not proof of identical error messages, number precision, table references, or regional behavior. This page does not assert support or syntax for Google Sheets, LibreOffice, or historical Numbers releases without separate verification.

• SQRT — Apple Functions Help: square root of an ordinary nonnegative input.
• PI — Apple Functions Help: a numerical approximation of π.
• Functions overview — Apple: requirements and local argument separator rules.

1. Apple SQRTPI reference (Help 15.4) — checked 2026-10-12. Basis for name, exact argument, domain, and the Apple examples SQRTPI(5) and SQRTPI(8).
2. Apple Functions overview (Help 15.4) — checked 2026-10-12. Basis for parameter notation, parentheses and decimal-comma locales.
3. Apple refer to cells (Help 15.4) — checked 2026-10-12. Basis for unqualified and cross-table cell references.
4. Apple formula troubleshooting (Help 15.4) — checked 2026-10-12. Basis for input format and formula error guidance.
5. Apple SQRT and Apple PI — checked 2026-10-12. Related-function identities.
6. Microsoft Excel SQRTPI — checked 2026-10-12. Excel comparison only, not an Apple error-code claim.

• SUMSQ — continue with a related Apple Numbers calculation.
• SQRT — continue with a related Apple Numbers calculation.
• PI — continue with a related Apple Numbers calculation.
• SUMPRODUCT — continue with a related Apple Numbers calculation.

For a software-specific comparison: LibreOffice Calc SQRTPI, Apache OpenOffice Calc SQRTPI, Gnumeric SQRTPI. A shared name does not establish identical argument, error or version behaviour.

The linked official function documentation was reviewed on October 12, 2026. Apple’s Formulas and Functions Help 15.4 identifies the documentation edition, not a minimum Numbers release or a guarantee of historical platform parity. Selected worked examples were checked using independent mathematical or text-processing models; results are expected values, not observations from the spreadsheet application. Native Apple Numbers execution was not performed. Undocumented coercion, exact error messages and platform-specific behaviour remain unverified.

View reproducible example inputs and independent check results. This record is not a native spreadsheet test log.