Ratio Calculator

Simplify any ratio to lowest terms and solve proportions (A : B = C : x) by cross-multiplication — with 1:n form, worked examples, and the recipe/map/mix use cases.

Ratio Calculator

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Ratios compare quantities by division, so they simplify exactly like fractions — divide both sides by the GCD (24:36 → 2:3) — and scale by multiplying both sides by anything. Solving a proportion uses cross-multiplication: if A:B = C:x, then A·x = B·C, so x = B×C ÷ A. The 1:n form the calculator adds (24:36 = 1:1.5) is the comparison-friendly version — it answers 'how many of the second per one of the first', the phrasing recipes, maps, and mixing instructions actually use.

About Ratios

Ratios are recipes' native tongue (2:1 rice to water), maps' legend (1:50,000), engines' lifeblood (50:1 fuel mix), and the classroom bridge between fractions and proportions. Two skills cover nearly every use: reducing a ratio to its simplest honest form, and finding the missing number when two ratios must match.

Simplify mode reduces A:B and re-expresses it as 1:n and as a fraction; solve mode cross-multiplies A:B = C:x for x, with the check shown. Decimals work in solve mode; simplify keeps integers honest via the GCD.

Ratios written vertically are just fractions — arithmetic on those lives in the Fraction Calculator.

Simplifying & Cross-Multiplying

The two moves, formally:

Simplify: A : B = (A ÷ GCD) : (B ÷ GCD) Solve: A : B = C : x → x = B × C ÷ A Check: A·x should equal B·C

Worked examples: 24:36 shares GCD 12 → 2:3 (equivalently 1:1.5). Solving 3:4 = 9:x → x = 4×9÷3 = 12, and the check 3×12 = 36 = 4×9 confirms it. The scale factor (9 is 3× the 3) is often the fastest mental route.

Worked Examples

Both modes on everyday numbers — computed by this calculator:

Problem	Answer	The move
Simplify 24 : 36	2 : 3	÷ GCD 12
Simplify 15 : 25	3 : 5	÷ GCD 5
Simplify 16 : 9	16 : 9 (already lowest)	GCD 1
3 : 4 = 9 : x	x = 12	cross-multiply
2 : 5 = x-solve at C=7	x = 17.5	4 × 9 ÷ 3 pattern
1 : 50,000 map, 3 cm	1.5 km real	scale ratios ARE ratios

The map row is the payoff pattern: a 1:50,000 scale means every map centimeter is 50,000 real ones — proportion solving in disguise.

Ratios in the Wild

Kitchens run on them (rice 1:2, vinaigrette 3:1, coffee brewing's famous 1:16), workshops mix by them (epoxy 1:1, two-stroke fuel 50:1, mortar 1:3), and screens name themselves after them — 16:9 is a ratio wearing a product name. Scaling a recipe or a mix is always the same operation: multiply BOTH sides.

The classic misread: a 1:4 ratio means 1 part to 4 parts — FIVE parts total, so 'dilute 1:4' fills 20% concentrate, not 25%. Cleaning products and lab protocols trip people exactly here. When instructions matter, translate the ratio to fractions-of-total first (1:4 → 1/5 and 4/5), then measure.

Frequently Asked Questions

How do I simplify a ratio?

Divide both sides by their greatest common divisor: 24:36 has GCD 12, giving 2:3. If either side isn't whole, multiply both until they are (2.5:4 → 5:8) — scaling both sides is always legal.

How do I solve A : B = C : x?

Cross-multiply: x = B × C ÷ A. For 3:4 = 9:x, x = 36÷3 = 12. The built-in check (A·x = B·C) catches slips instantly — 3×12 and 4×9 both hit 36.

What does a 1:4 ratio mean in parts?

One part of the first per four of the second — five parts total. As fractions of the whole: 1/5 and 4/5 (20% and 80%). The '25%' misread comes from dividing by 4 instead of 5; the total-parts step prevents it.

Are ratios and fractions the same?

Close cousins: A:B carries the same information as the fraction A/B, and both simplify by the GCD. Fractions usually mean part-of-whole; ratios compare two parts. 3:1 odds and the fraction 3/4-of-total describe the same split from different angles.

How do ratios extend to three terms?

Same machinery: 2:3:5 simplifies by the common GCD and describes a 10-part split (20%, 30%, 50%). To scale, multiply all three. Concrete's classic 1:2:3 (cement:sand:aggregate) is the everyday example.

How do map scales work?

A 1:50,000 map means 1 unit on paper = 50,000 in reality — any unit. So 3 cm measures 150,000 cm = 1.5 km. It's a proportion solve where the ratio is fixed and famous; hiking maps run 1:25k–1:50k, road atlases far larger.

Methodology. This calculator uses standard, peer-reviewed mathematical formulas. It is reviewed and maintained by the Vast Calculators editorial team.

Last updated · July 11, 2026

Results are estimates for general use; verify critical figures independently.

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