Subtraction Calculator
Subtract minuend − subtrahend to get the difference. Free online tool — no sign-up. Clear formulas and worked examples. Interactive calculations run locally in your browser.
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Core
- Declared partition coverage
- PASS · 6/6 declared partitions (difference, solve-for-minuend, solve-for-subtrahend, long-normal, long-negative-result, invalid-domain) · Matrix
- Numerical scope
- ≤2 ULP on the numeric value for difference, solve-for-minuend, solve-for-subtrahend, and long-mode difference. Column-work strings and regrouping steps are not an O2 numerical claim.
- Known limitations
- Declared partitions are difference, solve-for-minuend, solve-for-subtrahend, long-normal, long-negative-result, invalid-domain — aligned with published capability modes. O2 checks numeric values and long-mode domain; column-work strings are not an independent numerical claim.
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Difference of two numbers, optional solve-for-missing-term, and long subtraction with regrouping steps.
- Scope
- Difference mode: finite reals; scientific notation allowed.
- Verification
- Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
- Verification revision
- 2026-09-16.sources-no-wolfram · 2/2 property · digest c11ae651671e
- Legacy regression
- 7/7 tests · Production surface contract 1/1
- Trust layers
- Verification VERIFIED · Production CURRENT · overall VERIFIED
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Not performed
- Named expert review
- Not performed
- CVP suite
- 5/5 golden · 1/1 CVP boundary · 3/3 invalid · 2/2 property · 1/1 metamorphic · 2/2 round-trip · 5/5 cross-interface · 1/1 CVP contract · Manifest
- Sources
- OpenStax Prealgebra 2e — Subtract Whole Numbers
- CalculatorX mathematical conventions
- Evidence
- 6 legacy golden · 1 legacy boundary · legacy regression suite · 5/5 oracle-backed golden · 3/3 invalid · Artifact integrity PASS
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Choose Difference or Long subtraction
Difference solves a − b (any two of three fields). Long mode shows borrowing steps.
Enter the numbers
Minuend on top / first; subtrahend second. Decimals and negatives work in Difference mode.
Read the difference
Long mode prints aligned columns and each regrouping step under the form.
Example calculations
Common configurations with formula and result.
Simple
8 − 3
With regrouping
245 − 147
Decimals
2.30 − 1.12
Minus a negative
4 − (−3)
Solve for minuend
? − 6 = 9
Quick checks
Common values at a glance.
| Problem | Difference |
|---|---|
| 8 − 3 | 5 |
| 245 − 147 | 98 |
| 15 − 6 | 9 |
| 2.30 − 1.12 | 1.18 |
| 4 − (−3) | 7 |
| −4 − 3 | −7 |
Subtraction calculator specification
Version 1.0.1 · Engine tested
- Engine tested 7/7 tests · Production surface contract 1/1
- Named expert review Not performed
- Calculation version 1.0.1
- Definition
- 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.
- What it calculates
- Difference of two numbers, optional solve-for-missing-term, and long subtraction with regrouping steps.
- Inputs
- Minuend and subtrahend (or any two of minuend, subtrahend, difference)
- Mode: Difference or Long subtraction
- Outputs
- Difference (and solved missing term when applicable)
- Column work with borrowing (Long subtraction)
- Formula
Minuend − Subtrahend = Difference- Assumptions
- Difference mode: finite reals; scientific notation allowed.
- Long subtraction: non-negative decimal numbers without scientific notation.
- Order is minuend − subtrahend. When minuend < subtrahend the difference is negative; long mode still stacks the minuend on top. Column work subtracts the smaller magnitude from the larger, then applies the sign.
- Units
- Numeric only. If the values represent quantities, use the same unit for both inputs; the difference has that same unit.
- Boundary conditions
- Exactly one blank among three fields when solving for a missing term
- Long mode rejects negatives and scientific notation
- Long mode does not require minuend ≥ subtrahend (45 − 123 = −78)
- Example
- 245 − 147 = 98
- Validation cases
6 published on this page · 7/7 tests · Production surface contract 1/1 · View evidence
- 8 − 3 → 5
- 245 − 147 → 98
- 2.30 − 1.12 → 1.18
- 4 − (−3) → 7
- ? − 6 = 9 → 15
- 45 − 123 (long) → −78
- Sources
- OpenStax Prealgebra 2e — Subtract Whole Numbers — 1.3 Minuend − subtrahend = differenceSupports: Subtraction as taking away; place-value algorithm with regrouping.
- CalculatorX mathematical conventions — Long subtraction with regroupingSupports: Column subtraction with borrowing; negative differences keep the minuend on top.
- OpenStax Prealgebra 2e — Subtract Whole Numbers — 1.3 Minuend − subtrahend = difference
- Calculation version
- 1.0.1
Background
Interpretation and common distinctions.
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
| Property | Subtraction |
|---|---|
| Commutative? | No — a − b ≠ b − a in general |
| Associative? | No — (a − b) − c ≠ a − (b − c) in general |
| Inverse of | Addition |
Long subtraction with regrouping
- Stack the minuend on top and the subtrahend below; align place values and decimal points.
- Subtract each column right → left.
- 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.
- Continue until every column is done.
- 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.
Related tools
Other calculators in this family: Division Calculator, Fractions Calculator, Multiplication Calculator, Scientific Notation Calculator, Sum Calculator . Explore all Basic Arithmetic.
Frequently asked questions
Key distinctions behind the calculation.
What is subtraction?
Taking the subtrahend away from the minuend. The result is called the difference: Minuend − Subtrahend = Difference.
What are minuend and subtrahend?
The minuend is the starting number (first). The subtrahend is the amount taken away (second). In 8 − 3, 8 is the minuend and 3 is the subtrahend.
Is subtraction commutative?
No. Order matters: 10 − 3 = 7, but 3 − 10 = −7.
Is subtraction associative?
No. For example (10 − 3) − 1 = 6, while 10 − (3 − 1) = 8.
How do I subtract a negative number?
Subtracting a negative is the same as adding its opposite: a − (−b) = a + b. Example: 4 − (−3) = 7.
What is regrouping (borrowing)?
When a top digit is smaller than the bottom digit in a column, borrow 1 from the next higher place (that digit decreases by 1) and add 10 to the current top digit, then subtract.
How do I subtract decimals?
Align decimal points, pad with zeros so both have the same number of fractional digits, subtract as integers, then put the decimal back in the same place.