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Math calculator

Ratio Calculator

Simplify ratios and scale quantities that stay in proportion. Runs locally in your browser. Free online tool — no sign-up. No account needed.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes
Input interpretation
Enter values to calculate.
Result
—
Verified scope
all published modes
Assurance
Core
Declared partition coverage
PASS · 8/8 declared partitions (simplify, proportion, scale, split, compare, convert, three-term, invalid-domain) · Matrix
Numerical scope
All six published Ratio modes (simplify, proportion, scale, split, compare, convert), including A:B:C where those modes support it. Independent O2 expected values; exact rational BigInt; Node is runtime host only.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Simplify, scale, and compare ratios; solve proportions; split a total; convert to fraction/decimal/percent.
Scope
Finite rationals: integers, terminating decimals, or simple fractions a/b.
Verification
Engine tested · Source checked · v1.0.2 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.2 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision
2026-09-16.sources-no-wolfram · 7/7 property · digest e32c91d652f9
Legacy regression
26/26 tests · Production surface contract 8/8
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
13/13 golden · 7/7 CVP boundary · 7/7 invalid · 7/7 property · 2/2 metamorphic · 2/2 round-trip · 3/3 cross-interface · 8/8 CVP contract · Manifest
Sources
Sources
Evidence
11 legacy golden · 7 legacy boundary · legacy regression suite · 13/13 oracle-backed golden · 7/7 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Simplifyr₁:⋯:rₙ → exact rationals; L=LCM(d₁,…,dₙ); rᵢ′=L·rᵢ; g=GCF(|r₁′|,…,|rₙ′|); (r₁′÷g):⋯:(rₙ′÷g)
ProportionA/B = C/D → A·D = B·C
Scaler₁:⋯:rₙ → (k·r₁):⋯:(k·rₙ)
Split totalpartᵢ = total × (termᵢ / Σ terms) with every term ≥ 0 and Σ terms > 0
iEach term is an exact rational. L = LCM of all denominators, rᵢ′ = L·rᵢ, then divide by g = GCF(|rᵢ′|). Same n-term definition for A:B and A:B:C. Integer inputs skip the clearing step (L=1). Zero in a denominator of a proportion (B or D when solving) is undefined. Simplify, proportion, and compare allow negative terms. Split requires every term ≥ 0 and a positive sum.

How to use

1

Choose a mode

Simplify, proportion, scale, split, compare, or convert.

2

Enter the known values

Leave the unknown blank in proportion mode, or enter a scale factor / total when needed.

3

Read the result and steps

See the reduced ratio, missing term, shares, or conversions.

Example calculations

Common configurations with formula and result.

ϟ

Simplify

12:18

÷ GCF 6
2:3
ϟ

Proportion

4:7 = x:21

x = 4×21/7
12
ϟ

Scale

1:2.5:6.5 × 3

multiply each term
3:7.5:19.5
ϟ

Split total

25 by 3:2

25×3/5, 25×2/5
15 and 10
ϟ

Concrete mix

1:2:3 with sand = 7

scale so B→7
3.5:7:10.5

Quick checks

Common values at a glance.

ProblemResult
Simplify 12:182:3
4:7 = x:21x = 12
2:5 × 48:20
Split 25 by 3:215 and 10
4:6 vs 10:15equivalent
3:5 as fractions of whole3/8 and 5/8
i Part-to-part 1:2 means of a whole of 3, the parts are 1/3 and 2/3.

Ratio calculator specification

Version 1.0.2 · Engine tested

Calculation status

Review policy · Evidence

Definition
A ratio compares relative sizes of two or more quantities (part-to-part), written A:B or A:B:C. Equivalent ratios keep the same relationship when every term is multiplied or divided by the same nonzero factor. Proportions equate two ratios: A:B = C:D.
What it calculates
Simplify, scale, and compare ratios; solve proportions; split a total; convert to fraction/decimal/percent.
Inputs
  • Ratio terms (2 or 3), optional missing term for proportions
  • Scale factor or total amount depending on mode
Outputs
  • Simplified or scaled ratio
  • Missing proportion term
  • Shares of a total
  • Equivalence check
  • Fraction, decimal, and percent forms
Formula
A:B = C:D ↔ A/B = C/D; simplify n terms via exact rationals, L=LCM(dᵢ), rᵢ′=L·rᵢ, g=GCF(|rᵢ′|); scale rᵢ → k·rᵢ; share = total × term/Σ for nonnegative terms
Assumptions
  • Finite rationals: integers, terminating decimals, or simple fractions a/b.
  • Proportion denominators in A/B or C/D must be nonzero when used.
  • Simplify / proportion / compare allow negative terms. Split does not.
Units
  • Dimensionless (or consistent units across terms)
Boundary conditions
  • Cannot simplify an all-zero ratio → ALL_ZERO
  • Proportion needs exactly one blank among A,B,C,D → PROPORTION_ONE_BLANK
  • Split requires every ratio term ≥ 0 → SPLIT_NEGATIVE_TERM
  • Split requires Σ terms > 0 → SPLIT_ZERO_SUM
  • Scale divide-by-zero → DIVISION_BY_ZERO
Numerical precision
  • Terms are exact rationals. Simplify multiplies by L = LCM of all denominators, then divides by GCF of the resulting integers — the same n-term definition for A:B and A:B:C.
  • Integer inputs have L = 1, so denominator clearing is skipped and the terms are divided directly by their GCF. Decimal or fraction inputs show the LCM clearing step.
  • Shareable URLs (?aInput=12&bInput=18&mode=simplify) restore inputs and are server-rendered with the same deterministic engine. Query `v` is ignored — it is not a calculation_version pin. Pin a version with REST/MCP `CalculatorX-Spec-Version`.
  • REST and SSR return { value, mode, formula, steps, … } plus mode-specific fields (terms, solved, shares, equivalent).
Example
12:18 → 2:3; 1.5:2.25 → 2:3; 3/4:5/6 → 9:10; 4:7 = x:21 → x=12
Validation cases

12 published on this page · 26/26 tests · Production surface contract 8/8 · View evidence

  • simplify 12:18 → 2:3
  • 4:7 = x:21 → 12
  • 2:5 × 4 → 8:20
  • split 25 by 3:2 → 15, 10
  • 4:6 vs 10:15 → equivalent
  • 1.5:2.25 → 2:3
  • 3/4:5/6 → 9:10
  • split −2:3 of 100 → error SPLIT_NEGATIVE_TERM
  • simplify 6:9:12 → 2:3:4
  • 1:2:3 × 4 → 4:8:12
  • split 30 by 1:2:3 → 5, 10, 15
  • convert 2:3 → A/B = 2/3; 40% | 60% of whole
Sources
  • OpenStax Prealgebra 2e — Ratios and Rates — 5.6 Ratios and rates; writing and simplifying A:B
    Supports: A ratio compares two quantities; equivalent ratios are found by multiplying or dividing all terms by the same nonzero number; simplify by dividing by the GCF
  • OpenStax Prealgebra 2e — Solve Proportions — 6.5 Cross-multiply to solve A/B = C/D
    Supports: A proportion is two equal ratios; missing terms are solved by cross-multiplication
  • Encyclopedia of Mathematics — Greatest common divisor — Pairwise Euclidean GCF used after clearing denominators
    Supports: Computation of the GCF of the integerized ratio terms after clearing denominators; multiple-term GCF is obtained iteratively (GCF(a,b,c)=GCF(GCF(a,b),c))
  • CalculatorX split convention — Nonnegative parts only
    Supports: Split requires every term ≥ 0 and Σ terms > 0, so shares are nonnegative allocations of a total
Calculation version
1.0.2

Background

Interpretation and common distinctions.

What is a ratio?

A ratio compares the relative size of two or more numbers. Common writings:

  • A:B or “A to B”
  • as a fraction A/B (part-to-part)
  • three-term forms such as A:B:C (recipes, mixes)

Part-to-part compares parts to each other (e.g. cucumber:tomato = 5:4). Part-to-whole compares a part to the total (e.g. cucumber:vegetables = 5:50 = 1:10).

Modes in this calculator

Mode Use when
Simplify Reduce A:B or A:B:C to lowest terms
Proportion Solve A:B = C:D for one missing value
Scale Multiply or divide every term by a factor
Split Divide a total using the ratio parts
Compare Check whether two ratios are equivalent
Convert Fraction, decimal, %, and part-of-total %

Other calculators in this family: Fractions, GCF, Percentage, LCM .

a/b Fractions › gcd GCF › % Percentage › lcm LCM ›
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Frequently asked questions

Key distinctions behind the calculation.

What is a ratio?

A comparison of relative sizes of quantities, often written A:B (“A to B”). Part-to-part ratios compare parts to each other; part-to-whole compares a part to the total.

How do you simplify a ratio?

Divide every term by their greatest common factor (GCF). Example: 12:18 ÷ 6 → 2:3.

What is an equivalent ratio?

Two ratios that express the same relationship, such as 2:3 and 4:6. You get them by multiplying or dividing all terms by the same nonzero number.

How do you solve a proportion A:B = C:D?

Write A/B = C/D and cross-multiply: A·D = B·C. Solve for the missing letter. Example: 4:7 = x:21 → x = 4×21/7 = 12.

Can I split a total by a ratio?

Yes, when every ratio term is ≥ 0. Add the parts, then each share is total × (that part / sum). For 3:2 and total 25: shares are 15 and 10. Negative terms are rejected in Split.

How do I convert a ratio to a fraction of the whole?

Add the terms for the whole. Each term becomes a numerator over that sum. For 1:2, whole = 3 → 1/3 and 2/3.

Are three-term ratios supported?

Yes for simplify, scale, and split (A:B:C). Proportion mode solves two-term pairs A:B = C:D.

How are decimals and fractions simplified?

Each term is an exact rational. The calculator multiplies every term by the LCM of all denominators, then divides by the GCF of those integers. Example: 1.5:2.25 → 3/2:9/4 → multiply by 4 → 6:9 → GCF 3 → 2:3. Same n-term rule for 6:9:12 → 2:3:4. Integer inputs skip the clearing step.

Can a split use negative ratio terms?

No. Split requires every term ≥ 0 and a positive sum, so shares are ordinary nonnegative allocations. Simplify, proportion, and compare still allow negatives (for example −12:18 → −2:3).

Is 2:3 the same as 66.67%?

No. 2:3 is part-to-part. Of a whole of 5 parts, the shares are 40% and 60%. 2 as a percent of 3 is a different reading (A of B), shown separately in Convert.