Ratio Calculator
One ratio, three readings: simplified to lowest terms, scaled to any equivalent, and split into the shares a total implies.
Ratio Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Two-term ratios only (a:b:c chains are a different beast).
- Fractional terms accepted but the GCD needs whole terms.
- No inverse-ratio doctrine (1/a : 1/b).
In short: 12:18 simplifies by their GCD of 6 to 2:3; times five, that is 10:15. Give it a total of 30 and the 2:3 shares are 12 and 18 — five 6-unit parts, two and three of them. As fractions of the whole: 2/5 and 3/5.
Formula
simplify: a:b = (a÷G) : (b÷G), G = GCD(a, b)
split: total ÷ (p+q) parts, shares = terms × unit
part/whole: a/(a+b) and b/(a+b)
[('GCD', 'the one reduction to lowest terms'), ('parts', '2:3 has five parts, not three'), ('2/5, 3/5', 'part-to-whole, not part-to-part'), ('cross-solve', 'a missing term lives on Proportion')]
Worked Example
- Enter both terms; read the lowest-terms pair.
- Scale by any multiple — all equivalents agree.
- Enter a total to split it into shares.
- Distinguish part-to-part from part-to-whole.
- A missing term across two ratios? Proportion page.
12:18 → 2:3 (GCD 6); ×5 → 10:15; total 30 → 12 & 18 (five 6-unit parts); as fractions of the whole 2/5 & 3/5.
Strengths & Limits Of This Model
Where this engine is strong
- Simplify, scale and split from one input row
- Parts-vs-whole confusion named on the card
- Boundary to Proportion stated in the note
Where it stops
- No three-term ratios
- No unit-rate framing
Practical Use Cases
Recipe scaling
Ratios survive doubling.
Team splits
Prize money by contribution.
Mixing
Fuel, concrete, cordial.
Map scales
1:50,000 reading.
Screen sizes
Aspect ratios, simplified.
Methodology & Editorial Standards
Simplification divides both terms by Euclid's GCD; equivalents scale the lowest pair; a total splits into sum-of-terms parts with the unit printed and the shares crossed back to percentages of the whole. Negative terms and the 0:0 pair refused; blank totals skip the split card. Missing-term solving is deliberately out of scope — that is the Proportion page's cross-multiplication.
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.
Ratio Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. 12 and 18 share 6, so 12:18 simplifies to 2:3 — the same comparison in the smallest whole terms.
How do I split an amount by a ratio?
Count the PARTS: 2:3 is five parts. Divide the total by five, then give each term its share — 30 split in 2:3 makes each part 6, so 12 and 18.
What is the difference between 2:3 and 2/5?
Everything — 2:3 compares one part to the other (part-to-part); 2/5 measures one part against the whole (part-to-whole). Both live inside the same split, and mixing them is the classic error.
Are 12:18 and 2:3 the same ratio?
Yes — multiply 2:3 by six and you have 12:18. Ratios are relationships, and scaling both terms preserves the relationship exactly.
What about a ratio like 1:1.5?
Whole terms keep the arithmetic exact: scale to 2:3 and simplify there. The page takes any non-negative terms and reduces by the GCD when both are whole.
Does zero belong in a ratio?
One zero is honest — 3:0 says the second quantity is absent. Both zero compares nothing to nothing, and the page refuses it.
What is a unit rate?
A ratio scaled so one term is 1: 60 miles in 2 hours is 30 miles per hour. It is the ratio law in its most comparable clothing — this page simplifies to smallest whole terms; divide through for the unit form.
How do I solve 3/4 = 12/x?
That is not simplification — it is a proportion with a missing term, solved by cross-multiplication: x = 4×12÷3 = 16. The Proportion page owns that question.