Ratio Calculator
Result Summary
No results yet
Enter your details and hit “Calculate” to see your results.
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.