Ratio Scaling Calculator

Scale A:B to a target first term, second term, multiplier, or new total. Get the exact equivalent ratio, scale factor, simplified form, percentage shares, cross-product proof, and optional batch targets.

Exact ratio scaling workbench

Scale a ratio by one side, a multiplier, or a new total — without rounding away the proof.

Enter the source ratio, choose what you know about the target, and get the equivalent ratio, exact scale factor, simplified form, shares, and cross-product verification. Fractions and mixed numbers stay exact.

4 solve modesExact fractionsMixed numbersEquivalence proofBatch targetsRuns locally

Source APositive integer, decimal, fraction, or mixed number.Source BExample: 7, 2.5, 3/4, or 1 1/2.Scale byChoose the new B value; A is solved proportionally.Target BThe target can also be a fraction or mixed number.

Scaled ratio20 : 35

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5×Scale factor

4 : 7Simplified ratio

55Scaled total

Exact ✓Cross-product check

Ready.

Exact calculation & equivalence proof

Batch-scale many targets

Use the same source ratio and solve mode for many targets. Paste up to 250 values separated by commas or new lines. Results stay in this browser.

Target values

Target	Scaled A	Scaled B	Factor	Total
Add targets to build a batch.

Recent calculations & privacy

Saved calculations are optional and stay in local browser storage. Portable links put only the current ratio, mode and target into the URL hash; no ratio data is uploaded.

Scope: this page verifies mathematical ratio equivalence. In real recipes, maps, drawings, mixtures or manufacturing work, make sure the compared quantities use compatible units and that any rounding tolerance is appropriate. Scaling both terms by the same factor preserves the ratio; it does not by itself validate the real-world inputs.

Four ways to describe the same scaling job

Set one side

If 4:7 must become ?:35, the scale factor is 35 ÷ 7 = 5, so the matching first term is 4 × 5 = 20.

Set the total

For 2:3 with a new total of 25, the five ratio parts are worth 5 each. The result is 10:15, still exactly 2:3.

Prove equivalence

Two ratios A:B and C:D are equivalent when A×D = B×C. WebToolArc checks that identity with exact rational arithmetic instead of a rounded decimal comparison.

How to use this Ratio Scaling Calculator

Enter a source ratio and one desired target term to calculate the matching equivalent ratio and scale factor.

What it calculates

Scale a ratio to a target first or second term.

Ratio model

These pages treat ratios as mathematical proportional relationships. A real-world application can still require compatible units and context before two quantities should be compared directly.