Proportion Calculator
Two ratios, one unknown — the cross-multiplication law that solves maps, recipes and scale models, with the cross-check printed beside the answer.
Proportion Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Direct proportion only.
- Three knowns, one unknown, two-term ratios.
- No unit conversion inside the law — convert first.
In short: 3:4 = 12:x solves by cross-multiplication: x = 4×12÷3 = 16, and the cross products agree — 3×16 = 48 = 4×12. The same law reads a map: 4 cm on a 1:50,000 map is 200,000 cm of ground — 2 km. Scale a recipe from 3 servings to 5 and 2 cups becomes 10/3 ≈ 3.33.
Formula
a:b = c:d ⇒ ad = bc
x = (diagonal product) ÷ (term across)
check: the two cross products must agree
[('ad = bc', 'the whole law in four letters'), ('2 km', '4 cm on a 1:50,000 map'), ('10/3', '2 cups for 3 → 5 people'), ('inverse ≠ direct', 'more workers, fewer days — different law')]
Worked Example
- Write the proportion as a:b = c:d.
- Mark which term is the unknown.
- Multiply the diagonal, divide by the term across.
- Verify with the printed cross products.
- Confirm the problem is DIRECT before trusting it.
3:4 = 12:x → x = 16 (3×16 = 48 = 4×12). Map: 4 cm at 1:50,000 → 2 km. Recipe: 2 cups / 3 people → 3.33 cups / 5 people.
Strengths & Limits Of This Model
Where this engine is strong
- The cross-check is printed as proof, not claimed
- Map-scale and recipe canons in the answer
- The inverse-proportion trap named explicitly
Where it stops
- No joint variation
- No inverse mode
Practical Use Cases
Map & model scales
Centimetres to kilometres.
Recipe scaling
Servings up and down.
Unit pricing
Price per amount, solved.
Mixing
Concentrate to water.
Classroom
The cross-product proof, shown.
Methodology & Editorial Standards
One unknown by mode term: x = (product of the diagonal terms) ÷ (the term across), with the surviving denominators refused at zero. The cross-check card prints both diagonal products and verifies agreement to double precision. Only direct proportion is modeled; inverse proportion is named as a different law in the note.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Proportion Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I solve a proportion with an unknown?
Cross-multiply and divide: a:b = c:x gives x = b×c ÷ a. For 3:4 = 12:x that is 4×12÷3 = 16. The check is automatic — the cross products must agree.
Why does cross-multiplication work?
Because a:b = c:d is the equation a/b = c/d, and multiplying both sides by b×d clears the fractions to ad = bc. The diagonals of a proportion are always equal products.
How does map scale work as a proportion?
A 1:50,000 map promises 1 cm of paper per 50,000 cm of ground. Four centimetres therefore solve 1:50,000 = 4:x to x = 200,000 cm — 2 km. Change units carefully and only once.
How do I scale a recipe from 3 servings to 5?
Every ingredient is proportional to servings: 2 cups at 3 servings solves 2:x = 3:5 to x = 10/3 ≈ 3.33 cups. Seasonings scale too — taste still rules.
What if the problem is inverse proportion?
Then cross-multiplying lies to you. More workers means fewer days — the product stays constant, x = ac/b — and no proportion of equals describes it. Confirm the direction before you solve.
Can all four terms be negative?
Ratios of quantities are taken positive here — the page refuses zero denominators and keeps signs out of the scale story.
What are the extremes and the means of a proportion?
In a:b = c:d the outer terms a and d are the extremes, the inner terms b and c the means — and the law says product of extremes equals product of means: ad = bc. Same fact, older vocabulary.
Proportion page or Ratio page?
The Ratio page simplifies and splits ONE ratio. This page solves for a MISSING term across TWO ratios — the cross-multiplication law with its proof printed.