Proportion Calculator

What does this proportion calculator compute?

A proportion equates two ratios: A:B = C:D, so A·D = B·C.

The published formula or method is A·D = B·C. 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 4:7 = x:21 with C = A·D / B. 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.ratio v1.0.3 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 a proportion?

A proportion says two ratios are equal: A:B = C:D, which is the same as A/B = C/D. Cross-multiply to get A · D = B · C.

This page only solves that equation. Simplify, scale, split, compare, and convert stay on Ratio. Percent change stays on percentage change.

Input precision, limits and data paths

Use at most48 digits per integer/decimal, or per numerator and denominator of a fraction; signs do not count, leading zeros count, and each token is limited to128 characters. Two or three terms are supported in simplify, scale and split; other modes use A/B and, when needed, C/D. Matching aliases must name the same rational value; conflicting aliases, unknown fields and nonempty inactive fields are rejected.

Decimal and fraction strings preserve the accepted rational exactly. JSON numbers have already passed through binary64 parsing; unsafe integer numbers are rejected, and decimals use their shortest normalized decimal text. Send exact source values as strings. Exponents, mixed numbers and zero fraction denominators are rejected. Exactness applies to accepted tokens, not information rounded before the request.

A proportion requires exactly one blank and a unique solution with both B and D nonzero, including a solved denominator. Degenerate cross-product equations do not establish a valid quotient. Scale factors must be nonzero; split terms and totals must be nonnegative, with a positive sum of terms. Convert leaves undefined A/B or part-of-whole percentages as null and explains the condition. Bars show approximate part-of-whole shares; tiny parts may be invisible, so exact values remain in the text legend. Negative ratios have no part-of-whole bar.

Calculations run locally in the browser. Shared URLs send parameters to the server; REST/MCP also send inputs. Browser history may retain the most recent20 local snapshots; Clear inputs does not delete that history. Optional analytics depends on site configuration; a retention period, deletion guarantee or processing region is not established by this review. Share version labels identify the current-engine calculation and do not replay a historical engine; use REST/MCP version pins for strict version matching.