Subtraction (-)

What it does

number1 - number2

A - B converts each operand to a number and returns the IEEE-754 binary64 difference, rounded once to nearest with ties to even.

Subtraction is where floating-point arithmetic stops being invisible. Two properties are worth stating precisely, because they generate most of the questions readers arrive with:

1. The subtraction itself is exact when the operands are close. By Sterbenz's lemma, if B/2 ≤ A ≤ 2B then A - B is representable exactly and the operation introduces no error at all. The damage was done earlier: catastrophic cancellation is the revelation of error already present in A and B, not error created by -.
2. A - B is not A + (-B) in every observable respect. They agree on the finite arithmetic, but they are different call shapes with different operand counts, and the sign of a zero result differs: x - x is a positive zero under round-to-nearest, while x + (-x) is too, but 0 - 0 and 0 + -0 are not the same expression. If anything in a workbook can observe the sign of a zero, the rewrite is not neutral.

As with every operator in this family, the operand conversion is the part that varies: - never sees a cell, only values already resolved and coerced by the shared rules of coercion and lifting.

Arguments

Arity is exactly 2; no optional arguments, no defaults. Order is load-bearing — A - B and B - A differ in sign — which distinguishes this row from + and *.

The same - character in prefix position is FUNC.OP_NEGATE, a one-argument operator. Which one a given - is depends on the formula grammar, and formula grammar is explicitly out of this Handbook's scope (CHARTER.md section 4).

Try it

Quirks

Result and edge cases

• Text and logical operands. Governed by the shared to-number rules, exactly as for +. Nothing about - changes them.
• Dates. Date arithmetic is subtraction: a date is a number wearing a format, so date2 - date1 is an ordinary difference of serial numbers and the "number of days" reading is a presentation fact, not a semantic one. The published result carries no date format of its own; how the host formats the difference cell is host-side adaptation, outside the function's semantics (chapter 03).
• Empty and omitted operands. Per-family policy under chapter 02, and unrecorded here.
• Overflow. The recorded real-result policy is non_finite=allow, and data/functions/FUNC.OP_SUBTRACT.json marks that axis default-unexamined. A difference of two large opposite-signed operands can overflow; what Excel publishes there is not settled on this page.

How to implement

Notes for implementers

• Do not "optimize" A - B into A + (-B) or vice versa in a compatibility implementation. The finite results agree, but the call shape, the operand count, and the zero-sign story do not, and a compatibility target should preserve the shape it was given.
• Cancellation is a modelling problem, not an operator problem. If a workbook loses significance in a subtraction, the fix belongs in the expression that produced the operands, not in a "better" subtraction — there is no better subtraction; the IEEE difference is already exact when it matters.
• Broadcast and coercion are shared machinery. Implementing - as a distinct code path from + invites the two to drift; the reference implementation keeps them in one family module for exactly that reason.

Rust code

CatalogueEntry::operator(MINUS, "-", Notation::Infix, NUMBERS, minus)

fn minus(
    arguments: &[CalcValue],
    services: &mut EvalServices<'_>,
) -> Result<CalcValue, FunctionFault> {
    binary(MINUS, arguments, services, Site::subtract)
}

No implementation has been published with a Handbook test suite for this function.

Version differences

No comparison between specific Excel builds is recorded here yet. This does not establish that all builds behave alike.

Alternatives

Relationships

• FUNC.OP_ADD — the additive sibling; same coercion, same broadcast shapes.
• FUNC.OP_NEGATE — prefix -. Same character, one operand.
• IMSUB — complex subtraction over text-encoded complex numbers.
• DAYS, DATEDIF, YEARFRAC — the calendar-aware alternatives to subtracting two date serials. They answer different questions; - answers only "difference of two numbers".

Named variants

No named variants are recorded yet.