Proportion Calculator

Enter three known terms and one unknown, then use ratio tools for scaling, comparison, or part-to-part interpretation.

Stable numericsSubstitute / reconstructIndependent checkLocal calculation

Enter any three values and leave exactly one field blank.

x = 203/5 = 12/20

60 = 60Cross products

0.6Common ratio

4×Left → right scale

0Cross-product difference

a·d = b·c

Algebra round-trip cluster

Solve once, then verify the same object through another representation

Independent round trips and invariants expose sign, scaling, reconstruction and degeneracy mistakes that a single formatted answer can hide.

Quadratics Matrices Systems

All 28 algebra tools

Matrix InverseA↔A⁻¹ identity round trips MidpointEndpoint reflection round trip Linear EquationScale invariance + degeneracy classes DeterminantTranspose/row-operation invariants Quadratic VertexStandard ↔ vertex coefficient round trip Slope InterceptPoints ↔ line-form equivalence Polynomial DivisionQuotient/remainder reconstruction Standard FormSlope-intercept ↔ standard round trip

Transform, then verify

Equivalent forms should agree. Use discriminants, roots, factoring, vertex form, substitution, matrix checks, or the Remainder Theorem where appropriate to verify the result rather than relying on a single opaque output.

How to use the Proportion Calculator

Enter any three values in a/b = c/d and leave exactly one blank. The blank may be in any of the four positions.

Cross multiplication

The completed proportion is verified with a·d = b·c. The result also shows a left-to-right scale factor when it is finite.

Limits

A proportion that requires division by zero does not have a finite solution in this calculator. Use the displayed cross products to inspect the relationship.

Independent algebra verification

The primary calculation is paired with a substitution, invariant, inverse operation, reconstruction, or equivalent-form check so the displayed answer is easier to audit.

Scope and precision

These are bounded browser calculators, not a universal computer algebra system. WebToolArc keeps exact algebraic identities visible where practical, uses stable floating-point algorithms for numeric work, distinguishes undefined/no-solution/infinite-solution cases, and shows an independent check after the main Calculate action.

Practical guide and verification

Use the tool first, then apply these checks to verify inputs, interpret the result, and hand it off without displacing the primary workflow.

Check which term is actually unknown

A proportion such as a/b = c/d can solve one missing value, but the arrangement of quantities still matters. Put like units or comparable quantities in corresponding positions and verify that only the intended term is unknown. A correct cross-multiplication on a badly arranged ratio gives a confidently wrong interpretation.

Reject zero denominators before solving

A ratio with a zero denominator is undefined even when cross-multiplication appears to produce an algebraic expression. Check both denominators and any candidate solution that would make one zero. Domain restrictions belong to the problem, not merely to the final arithmetic step.

Preserve units through the ratio

Percent, scale drawing, recipe, rate, map, dosage-style classroom exercise, and similar proportions can use different units on each side. Convert units before comparing corresponding terms and write the unit beside the solved value. Dimensional consistency is a powerful verification step when the raw numbers alone look plausible.

Substitute the answer back into both sides

After solving, calculate both ratios again with the candidate value and compare them within appropriate rounding tolerance. This simple round-trip catches swapped terms, transcription errors, and premature rounding. For exact fractions, keep the fraction through the algebra and convert to a decimal only for presentation if needed.