ATAN2 Function in Apple Numbers: Coordinate Angles and Quadrants

ATAN2 finds the oriented angle from the positive x-axis to a point (x, y), accounting for both coordinate signs. For a point directly above the origin, enter =DEGREES(ATAN2(0,1)): Apple documents the result as 90°. Apple Numbers requires the x-coordinate FIRST and the y-coordinate SECOND, written ATAN2(x, y). That order is especially important when copying formulas from other programming languages. Official Apple ATAN2.

ATAN(y/x) uses a quotient. For example, both the point (1,1) and the point (−1,−1) give y/x = 1, so ATAN(y/x) returns the same principal 45° angle even though the second point points southwest. ATAN2(x,y) uses both signs to place the result into the appropriate quadrant.

Apple specifies the result relative to the positive x-axis, in radians within −π to +π (−180° to +180°). =DEGREES(ATAN2(-1,-1)) is expected to give −135°, not +45°. The same formula for (1,1) gives +45°. ATAN2 is therefore useful for vector bearings, position changes and screen-coordinate geometry when axes are defined correctly.

Unlike Python’s math.atan2(y, x), Apple’s documented spreadsheet syntax is x, y. The independently checked evidence uses Python with reversed input placement solely to calculate equivalent mathematics, e.g. to test Numbers ATAN2(3,4) it evaluates math.atan2(4,3). The argument-order rule and Apple’s 90° example are explicit in Apple’s reference.

=ATAN2(x, y)

Argument: x

Required
Yes, first

Apple-documented type
Number value

Meaning
Horizontal x-coordinate of the point.

Argument: y

Required
Yes, second

Apple-documented type
Number value

Meaning
Vertical y-coordinate of the point.

Neither argument is optional. No default values, angle unit selector, or distance normalization are documented. The result is radians; wrap the expression in DEGREES if you need degrees. The documented angular interval is −π to +π. The special point (0,0) lacks a mathematically unique direction; the official page does not establish a specific Numbers error or output for that point, so this guide does not invent one. Apple ATAN2; Number argument types.

Formula punctuation, decimals, and references

Apple’s Functions overview uses an English-language formula and a comma to separate distinct arguments. If a regional setting uses the comma as the decimal separator, Apple’s guidance specifies a semicolon argument separator instead. The examples on this page use English function identifiers and a period for decimal values. A display rounded to six places is not a change to the underlying number.

In the same Numbers table, B2 refers to column B, row 2. For a reference in another table, Numbers can use Table 2::B5; for another sheet, a fully qualified reference can use Sheet 2::Table 2::B5. See Apple’s cell-reference guide. When copying down a formula, ordinary references like B2 change to B3; use the Numbers formula editor to select other tables rather than typing unverified names.

1. Make a table named Vector Angles with at least ten rows. Use row 1 as a header and put X in B1, Y in C1, and Angle ° in D1.
2. Enter the real numeric coordinate pairs in columns B and C below. Negative signs belong in the numeric cells, not in adjacent labels.
3. Type =DEGREES(ATAN2(B2,C2)) in D2, then fill down through D10. Change , to ; in comma-decimal locales.
4. Format the result cells to six decimal places and compare with the independently calculated expected values. Do not place the degree symbol inside the formula arguments.

Row: 2

B: X
1

C: Y
0

D: formula
=DEGREES(ATAN2(B2,C2))

Expected degrees (6 d.p.)
0.000000

Row: 3

B: X
1

C: Y
1

D: formula
=DEGREES(ATAN2(B3,C3))

Expected degrees (6 d.p.)
45.000000

Row: 4

B: X
0

C: Y
1

D: formula
=DEGREES(ATAN2(B4,C4))

Expected degrees (6 d.p.)
90.000000

Row: 5

B: X
-1

C: Y
1

D: formula
=DEGREES(ATAN2(B5,C5))

Expected degrees (6 d.p.)
135.000000

Row: 6

B: X
-1

C: Y
-1

D: formula
=DEGREES(ATAN2(B6,C6))

Expected degrees (6 d.p.)
-135.000000

Row: 7

B: X
0

C: Y
-1

D: formula
=DEGREES(ATAN2(B7,C7))

Expected degrees (6 d.p.)
-90.000000

Row: 8

B: X
1

C: Y
-1

D: formula
=DEGREES(ATAN2(B8,C8))

Expected degrees (6 d.p.)
-45.000000

Row: 9

B: X
3

C: Y
4

D: formula
=DEGREES(ATAN2(B9,C9))

Expected degrees (6 d.p.)
53.130102

Row: 10

B: X
-3

C: Y
4

D: formula
=DEGREES(ATAN2(B10,C10))

Expected degrees (6 d.p.)
126.869898

The coordinates (0,0) are not part of this dataset because they provide no direction. Notice the four distinct quadrants: northeast (45°), northwest (135°), southwest (−135°), and southeast (−45°). Apple’s own check is =ATAN2(0,1) → approximately 1.5707963267949 radians, or =DEGREES(ATAN2(0,1)) → 90°. These values are expected based on documentation and independent calculation; they are not Numbers runtime observations.

1. Direction from one coordinate to another

Let your starting location be (2,3) and endpoint (5,7) in a standard mathematical coordinate system with y increasing upward. The displacement is (5−2,7−3)=(3,4). Enter =DEGREES(ATAN2(5-2,7-3)) for the expected direction 53.130102° counterclockwise from the positive x-axis. In a worksheet with start X/Y in B12/C12 and end X/Y in D12/E12, use =DEGREES(ATAN2(D12-B12,E12-C12)). This uses x-difference first, y-difference second.

2. Recognize screen coordinates versus mathematical coordinates

A screen display may increase Y downward, whereas the table above assumes +Y upward. For a positive-x rightward move and a positive-y downward screen move, ATAN2(x,y) returns the angle below or above the x-axis according to the numbers given, not necessarily the on-screen compass direction expected by your application. If your Y axis is inverted relative to mathematical coordinates, a suitable transform in your model may be =DEGREES(ATAN2(B15,-C15)). Verify the coordinate convention before treating the result as a compass bearing.

3. Convert mathematical angle to a clockwise compass-like bearing

For a standard Cartesian vector with +x east and +y north, calculate the math angle using =DEGREES(ATAN2(B18,C18)) and then convert it to clockwise degrees from north using =MOD(90-DEGREES(ATAN2(B18,C18)),360). A vector (1,1) is expected to yield 45° in either convention; a vector (1,0) (east) yields 90° on the compass-like scale even though the mathematical angle is 0°. This is a derived trigonometric identity, not a claim that this composite formula was run in Numbers or behaves identically in every regional edition.

4. Check quadrant ambiguity caused by division

For (−3,4), =DEGREES(ATAN(4/-3)) produces a principal angle around -53.130102°, which loses the original leftward orientation. Using =DEGREES(ATAN2(-3,4)) produces the expected 126.869898°. Use ATAN2 whenever the direction rather than a simple slope magnitude matters.

• Swapped arguments: ATAN2(y,x) is not Apple’s documented order. For the point (0,1), ATAN2(0,1) gives 90°, whereas swapping them makes a different angle.
• Copied from Python: Python calls math.atan2(y,x); Numbers uses ATAN2(x,y). Reversing inputs is necessary when independently checking examples with Python.
• Origin (0,0): No unique angle exists mathematically. Apple’s help does not state exact runtime behavior for this input, and this guide does not assume an error type or number.
• Negative x-axis boundary: Both −π and +π describe the same geometric ray. Apple’s documented interval does not establish the precise sign convention for every signed-zero or boundary case; avoid strict equality checks there without native testing.
• Degree conversion omitted: ATAN2 returns radians. A result around 1.5707963 is π/2, or 90° after DEGREES.
• Wrong coordinate axes: Check whether x/y axes have been switched or Y increases downward; fix the input convention before adding normalization.
• Text rather than numeric values: Apple expects Number values. This review did not test coercion of strings, empty cells, arrays, or non-finite values in the application.
• Floating-point precision: Compare angles with a reasonable tolerance, especially around a branch cut where an almost-identical direction can move between +180° and −180°.

Troubleshooting routine: Start with =DEGREES(ATAN2(0,1)) and check for an expected 90°. Next enter two numeric columns in the same table, then test cross-table references inserted by Numbers. If your result differs, first verify x/y order, units, signs, locale separator and formatting; only then examine numerical precision.

For ordinary scalar numeric coordinate pairs, Excel and Google Sheets document ATAN2(x,y) and the same fundamental quadrant-aware mathematical purpose. Their routine mathematical answers are comparable, not evidence of identical error strings or coercion rules. Microsoft’s current ATAN2 documentation describes its own behavior at (0,0), but that Excel behavior cannot be attributed to Apple Numbers without a native Numbers test. Google’s function reference list includes ATAN2(x,y); Apple’s ATAN2 page supplies this guide’s authoritative Numbers order.

Apple’s Help 15.4 documents the function now; it does not prove first supported release, cross-platform implementation parity, or exact handling of edge cases in historical Mac, mobile or browser versions. Preserve the official formula’s argument order during migrations and verify critical worksheets in the target software.

• Apple ATAN2 — definition, exact x-then-y syntax, range and documented example; accessed 2026-10-11.
• Apple ATAN — ratio-based inverse tangent and principal interval; accessed 2026-10-11.
• Apple TAN — tangent from radian input; accessed 2026-10-11.
• Apple Functions overview — required arguments and regional separators; accessed 2026-10-11.
• Apple Refer to cells in formulas — same-table and other-table references; accessed 2026-10-11.
• Apple Types of arguments and values — Number values; accessed 2026-10-11.
• Google Sheets function list — ATAN2 availability and x/y signature; accessed 2026-10-11.

• ACOS — continue with a related Apple Numbers calculation.
• ASIN — continue with a related Apple Numbers calculation.
• ATAN — continue with a related Apple Numbers calculation.
• TAN — continue with a related Apple Numbers calculation.
• SIN — continue with a related Apple Numbers calculation.

For a software-specific comparison: LibreOffice Calc ATAN2, Apache OpenOffice Calc ATAN2, Gnumeric ATAN2. 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.