Subtraction Calculator

What does this subtraction calculator compute?

Subtraction takes the subtrahend away from the minuend. The result is the difference: Minuend − Subtrahend = Difference. It is the inverse of addition and is neither commutative nor associative.

The published formula or method is Minuend − Subtrahend = Difference. The following references support the stated mathematics or method:

• Margaret Stevens — The Maths Workbook (University of Oxford): Algebraic addition/subtraction, multiplication/division, distributive rules, equivalent fractions, common denominators and reciprocals. Ratios are interpreted as quotients. Equality of ratios with nonzero denominators permits cross multiplication, and solving a proportion uses the chapter’s equation transformations. A zero divisor is excluded; integer quotient/remainder uses the separately cited Euclidean-division reference. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

Which inputs and limits should you check?

Follow the input domain, units, branch or solve direction, and rounding policy in the specification. Preserve exact outputs and any additional candidates or warnings.

The worked example uses 8 − 3 with minuend − subtrahend. Compare it with the Example calculations and the complete result for the same inputs.

How can you verify and cite this result?

CalculatorX is responsible for this page. The mathematical references above explain the model; implementation checks and their scope are documented separately in the math.subtraction v1.0.1 Evidence and capability contract. Read the displayed verification and production state together with the specification's numerical limits.

Use the clean calculator URL to cite the tool. A shared input link identifies a particular calculation. Content updates, numerical verification, and domain reviews have separate dates and scopes.

What is subtraction?

Subtraction is taking one quantity (the subtrahend) away from another (the minuend). The result is the difference:

Minuend − Subtrahend = Difference

It is the inverse of addition: if a + b = c, then c − a = b and c − b = a. Subtracting b is the same as adding −b:

a − b = a + (−b)

Properties

Long subtraction with regrouping

1. Stack the minuend on top and the subtrahend below; align place values and decimal points.
2. Subtract each column right → left.
3. If the top digit is smaller than the bottom, borrow 1 from the left (that digit − 1) and add 10 to the current top digit.
4. Continue until every column is done.
5. If the minuend is smaller than the subtrahend, the result is negative. For the column work, subtract the smaller magnitude from the larger magnitude, then apply the negative sign.

Example: 245 − 147 = 98 (ones and tens both need regrouping). When minuend < subtrahend: 45 − 123 = −(123 − 45) = −78. Display still stacks the original minuend on top.

Precision and machine contract

Difference uses IEEE-754 binary64, including decimal-to-binary conversion. Its shortest round-trip display preserves the computed value; it is not exact decimal arithmetic. All normalized integral operands must lie within ±(2^53−1). Subtracting nearly equal inputs can amplify relative input or conversion error; measurement uncertainty is not modeled. Provide exactly two terms: three filled terms are rejected rather than silently replacing the supplied difference. Nonzero textual underflow is rejected as NUMERIC_UNDERFLOW; nonzero subnormal values are accepted.

Long mode accepts non-negative plain decimals and uses exact digit arithmetic with borrowing. At most 48 aligned columns are allowed, counting the greatest integer width plus the greatest fractional width after redundant zeros are removed. display and exact_value contain the exact decimal result; JSON numeric fields are approximate conveniences. Send large operands as strings. Long mode requires minuend and subtrahend, with difference blank or omitted. For 999999999999999999999999 − 1, the exact result is 999999999999999999999998.

Each token is limited to 512 characters. Grouping commas, hexadecimal text, invalid types/modes, unknown keys and conflicting aliases are rejected. Canonical names are minuend, subtrahend, difference; supported aliases are minInput/a, subInput/b, diffInput/d. Missing mode means Difference; diff and sub alias Difference. Blank fields stay blank when shared, cleared or reloaded. Shared links execute the current engine and do not preserve historical runtimes.

Typing calculates locally. Shared query URLs and REST/MCP calls send inputs to the server; URLs may appear in logs or browser history. Recent calculations may persist in local browser storage and can be cleared using History. CSV and copied JSON include the full output and work. Invalid inputs disable result export.