Ratio Calculator
Simplify, solve, scale and compare ratios with full step-by-step workings
Enter any ratio to reduce it to its simplest form.
What Is a Ratio?
A ratio expresses the relative size of two or more quantities. A ratio of 3:4 means "for every 3 of A, there are 4 of B". Ratios are used everywhere — cooking recipes, maps, financial statements, mixing concentrations, and probability.
Formulas
Real-World Examples
Recipes: A recipe serves 4 in ratio 3:5 (flour to sugar). To serve 10, scale by 10/4 = 2.5× → new ratio 7.5:12.5.
Maps: A 1:50,000 scale map means 1 cm = 50,000 cm = 500 m in reality.
Finance: Profit split in ratio 3:7 means one partner gets 30% and the other 70% of total profit.
Ratios and Proportions: The Math of Scaling Anything
Built and verified by Andrius R. · Updated June 2026
Ratios are how quantities relate; proportions are how those relationships survive scaling. Between them they run kitchens, screens, maps, paint shops and gearboxes. The rules are few; the applications are everywhere.
Simplifying: same idea as fractions
A ratio simplifies by dividing all parts by their greatest common divisor: 48:36 → 4:3 (divide by 12). Ratios with more parts work identically — 12:18:30 → 2:3:5 (divide by 6). Our LCM & GCD calculator finds the divisor instantly. A ratio can also be read as a fraction of the whole: in a 4:3 mixture there are 7 parts total, so the components are 4/7 and 3/7 of everything.
Solving proportions: cross-multiplication
A recipe serving 4 uses 300 g of flour. For 10 servings: set up 300/4 = x/10, cross-multiply: 4x = 3,000 → x = 750 g. Equivalent (often easier) route: find the unit rate first — 75 g per serving — then multiply. Cross-multiplication works because both sides describe the same flour-per-serving relationship; you're just rearranging it.
Dividing an amount by a ratio
To split $1,400 between partners in a 4:3 ratio: total parts = 7, each part = $200, shares = $800 and $600. The same three steps (sum the parts → size one part → multiply out) handle inheritance splits, paint mixes, alloy compositions and group expenses with any number of parties.
Ratios hiding in plain sight
- Screens: 16:9 is the aspect ratio of nearly every TV — which is why 1920 pixels wide pairs with 1920 × 9/16 = 1080 tall. Photography's 3:2 and the older 4:3 explain why pictures get cropped moving between devices.
- Maps: a 1:50,000 scale means 1 cm on paper = 50,000 cm = 500 m of terrain.
- Mixing: 2-stroke fuel at 50:1, concrete at roughly 1:2:3 (cement:sand:aggregate), cordial at 1:4 — get the ratio backwards and the consequences range from bad drinks to seized engines.
- Gears: a 3:1 gear ratio trades speed for force — the output turns once for every three input turns, with triple the torque.
- Finance: debt-to-income, price-to-earnings, loan-to-value — much of financial analysis is ratio literacy wearing a suit.
The mistakes that actually happen
- Order matters. Flour-to-sugar 2:3 is not 3:2; "the ratio of A to B" fixes the sequence. Half of all real-world ratio errors are reversals.
- Ratios scale by multiplying, never adding. To go from 2:3 to "one more of each" (3:4) is a different ratio — scaling 2:3 up means 4:6, 6:9, 20:30.
- Mismatched units. A ratio of 500 g to 2 kg is 1:4, not 500:2 — convert to common units before comparing.
- Ratios aren't percentages. A 1:4 ratio of squash to water means 1 part in 5 total — 20%, not 25%. When precision matters, convert to parts-of-the-whole first.
// Cross Multiply
To solve A:B = C:D for D, cross-multiply: D = B×C÷A. Always check your answer by verifying both ratios simplify to the same fraction.
// Ratio vs Fraction
A ratio 3:4 is not the same as the fraction 3/4. The fraction 3/4 means 3 out of 4 total parts (75%). The ratio 3:4 means 3 parts to 4 parts (7 total).
// Unit Rates
A unit rate is a ratio with 1 in the denominator. £12 for 3 items = £4 per item = a ratio of 4:1 (£:item).
// Scaling
To scale a ratio, multiply both parts by the same number. 3:4 × 5 = 15:20, which simplifies back to 3:4.