Ratio Calculator

Calculate ratios, solve proportions, scale dimensions, simplify ratios, convert ratios into percentages, and visualize relationships with interactive charts.

Solve A : B = C : D

Enter any three values — leave the fourth blank and we'll solve it using cross multiplication.

Common Ratios Reference

Ratios that come up everywhere — from photography sensors to TV screens to the golden ratio of design.

Ratio	Meaning
1 : 1	Equal parts — every part is the same size.
1 : 2	One half — first part is 50% of the second.
2 : 3	Two parts to three — 40% : 60% of the total.
3 : 4	Three parts to four — 42.86% : 57.14% (≈ Standard SD).
4 : 5	Four parts to five — 44.44% : 55.56%.
16 : 9	Widescreen HD/4K display — most TVs and YouTube.
4 : 3	Traditional display — old TVs, iPads, presentations.
21 : 9	Ultrawide cinema — flagship monitors and films.
3 : 2	Classic 35mm photography aspect — DSLR sensors.
1 : 1.618	Golden ratio φ — design, architecture, nature.

Screen Resolutions

Tap any preset to load it into the Scale tab.

Common Ratios as Percentages

Each bar shows the split between Part A (blue) and Part B (green) for popular ratios.

Golden Ratio φ Explorer

The golden ratio φ ≈ 1.6180339887 is the unique ratio where the whole is to the larger part as the larger part is to the smaller — 1 : φ = φ : (1 + φ). It appears in design, architecture, the Parthenon, the spirals of pinecones, and the proportions of the human face.

1.61803399

(1 + √5) ÷ 2

1 ÷ φ

0.61803399

φ − 1

φ²

2.61803399

φ + 1

What Is a Ratio?

A ratio is a comparison of two or more quantities expressed in the same units. Writing 3 : 4 says that for every three parts of the first quantity there are four parts of the second — the same relationship as the fraction 3⁄7, the decimal 0.75, or the percentage 42.86% : 57.14%. Ratios let you compare two recipes, two screens, two budgets, or two financial statements on equal footing, without worrying about the absolute sizes of the quantities involved.

This calculator combines four tools on one page: a Ratio Calculator that solves the missing value in any A:B = C:D proportion via cross multiplication, a Ratio Scaling Calculator for enlarging or shrinking dimensions, a Ratio Simplifier that reduces any ratio to lowest terms using the GCD, and a Ratio ↔ Percentage Converter. It pairs naturally with the percentage calculator, the scientific calculator, and the unit converter.

How a Ratio Calculator Works

Set up the proportion

A proportion is the claim that two ratios are equal — A:B = C:D. As soon as three of the four values are known, the fourth is fixed. The calculator accepts your three values, identifies which slot is missing, and applies cross multiplication.

Apply cross multiplication

Two ratios are equal if and only if A × D = B × C. This is the fundamental property of every proportion. Multiply across the equals sign, then solve algebraically for the unknown — the calculator does this automatically.

Simplify to lowest terms

Every ratio has a canonical form where no further reduction is possible. Dividing both terms by their greatest common divisor (GCD) produces this form — 150 : 300 reduces to 1 : 2, and 1920 : 1080 reduces to 16 : 9. The calculator uses the Euclidean algorithm for the GCD.

Express in every useful form

The calculator returns the solved ratio, its simplified form, the decimal quotient A÷B, the normalised 1:k and k:1 forms, the part-percentage breakdown, and the unit value C÷A. Each form is right for different applications — design, finance, science, recipes.

6 Ways to Use This Ratio Calculator

Find the missing fourth value

Drop in any three of A, B, C, D and the calculator returns the fourth via cross multiplication — the classical proportion problem.

Scale a design or photo

Enter the original width and height and a scale factor; the calculator preserves the aspect ratio and reports the new dimensions and area change.

Reduce a ratio to lowest terms

Use the simplifier to convert clunky ratios like 1000 : 2500 or 1920 : 1080 into clean canonical forms like 2 : 5 or 16 : 9, with the GCD shown.

Convert ratio ↔ percentage

Translate any 2- to 8-part ratio into percentages, or recover the simplified ratio behind a set of percentages — perfect for budget allocations, surveys, and pie charts.

Compare aspect ratios

Plug in screen, sensor, or print dimensions to see whether your image is 16:9, 4:3, 3:2, 21:9, or something else — handy for video, photography, and UI design.

Adjust a recipe or mix

Use proportion math to scale a recipe up or down — if 2 cups flour : 1 cup sugar feeds 4, the same ratio feeds 12 with 6 cups : 3 cups. The calculator handles every step.

Best Practices for Working With Ratios

Keep units consistent. A ratio of 2 metres : 50 centimetres is meaningless until both sides share the same unit; rewrite as 200 cm : 50 cm = 4 : 1. The calculator assumes both terms of any ratio are in the same unit — if they're not, convert first.

Always simplify your result. A reader cannot quickly compare 1920 : 1080 to 2560 : 1440, but the simplified forms 16 : 9 and 16 : 9 reveal at a glance that the two screens share the same aspect ratio. Use the Simplify tab — or just glance at the "Simplified" stat card in the Solver — every time you report a ratio publicly.

Choose the right form for the audience. Designers want simplified ratios (16:9). Engineers often want decimals (1.7778). Marketers usually want percentages (64.3% : 35.7%). Statisticians prefer fractions (16⁄25). The calculator gives all four; copy the one that fits the document you're writing.

Why Ratios Matter

Design and visual media

Every screen, photo, and video frame has an aspect ratio. 16:9 powers TVs and YouTube; 4:3 lives on in iPads and slide decks; 3:2 is the classic 35mm photo; 21:9 is the cinema ultrawide standard. The golden ratio φ ≈ 1.618 shows up in posters, logos, the Parthenon, and the spiral of pinecones.

Architecture and construction

Scale drawings, mixing ratios for concrete, slope ratios for roofs and ramps, and golden-section facades all rely on proportion math. A 1 : 50 architectural plan means every centimetre on paper equals 50 cm on site — the same calculation the scale tab here performs.

Cooking and brewing

Recipes are ratios in disguise: 2 cups flour to 1 cup sugar; 1 part rice to 1.5 parts water; 1:1:1 simple syrup. Doubling a recipe means scaling every ingredient by the same factor while keeping ratios intact — exactly what the Solver does.

Finance and business

Debt-to-income, price-to-earnings, current-ratio, and cost-to-sales are all ratios. They strip out absolute size and let you compare two companies, two households, or two quarters on a level field. Ratio analysis is one of the foundations of accounting.

Where Ratios Get Tricky

Three or more parts

A 1 : 2 : 3 ratio splits the whole into six parts (1+2+3) — the first quantity is 1⁄6, the second 2⁄6 = 1⁄3, the third 3⁄6 = 1⁄2. The Percentage tab handles up to 8 parts and shows the breakdown of each.

Zero in a denominator

If a known value sits opposite the unknown and is zero, the proportion is unsolvable: 0 : 1 = ? : 5 has no finite answer. The calculator detects this and reports it rather than dividing by zero silently.

Decimal terms

Ratios don't have to be whole numbers. 0.5 : 1 is just 1 : 2 in disguise. The calculator simplifies decimal ratios by scaling to integers first (×10⁶), running the integer GCD, then dividing back — so you get a clean result either way.

Comparing apples to oranges

A ratio is only meaningful when both terms measure the same kind of thing. 100 km : 50 hours is a rate (speed), not a ratio in the pure sense. For mixed-unit comparisons, use the dedicated speed, density, or rate calculators instead.

Core Ratio Formulas

Proportion

A : B = C : D

Two ratios are equal.

Cross multiplication

A × D = B × C

The defining property of every proportion.

Solve for A

A = (B × C) ÷ D

Rearrange cross-multiplication for the missing first term.

Solve for B

B = (A × D) ÷ C

Rearrange for the missing second term.

Solve for C

C = (A × D) ÷ B

Rearrange for the missing third term.

Solve for D

D = (B × C) ÷ A

Rearrange for the missing fourth term.

Simplify (GCD)

a:b ÷ gcd(a, b)

Reduce both terms by their greatest common divisor.

Scale (enlarge)

W' = W × f, H' = H × f

Multiply both dimensions by the same factor.

Scale (shrink)

W' = W ÷ f, H' = H ÷ f

Divide both dimensions by the same factor.

Area change

A' ÷ A = f²

Area scales with the square of the linear factor.

Ratio → percentage

p_i = a_i ÷ Σa × 100%

Each part is its share of the total.

Golden ratio

φ = (1 + √5) ÷ 2 ≈ 1.618

1 : φ = φ : (1 + φ) — found in design, art, and nature.

Common Ratio Mistakes

1
Forgetting to convert units before comparing
Writing 1 m : 50 cm and treating it as 1:50 is wrong — convert first, then form the ratio. The clean version is 100 cm : 50 cm = 2:1.
2
Adding instead of multiplying when scaling
If a 4×6 photo is enlarged 2×, the result is 8×12 — every dimension multiplies. Adding 2 to each dimension gives 6×8, a different aspect ratio entirely. Linear scaling multiplies; it never adds.
3
Ignoring the square law on area
Doubling every linear dimension quadruples the area, not doubles it. Pizza shops know this — a 16-inch pizza has four times the area of an 8-inch, despite the diameter only doubling.
4
Adding percentages back to a ratio carelessly
If 25% : 75% maps to 1:3 and 33%:67% maps to roughly 1:2, you cannot average those to get 1:2.5 — you must average the underlying parts, not the ratio strings. Always go back through the integers.
5
Treating ratios as commutative
3 : 4 is not the same proportion as 4 : 3 — the order matters. Always read the labels of A and B (or width and height) carefully before comparing.
6
Confusing ratio with fraction
The ratio 3 : 4 corresponds to the fraction 3⁄7 (part over whole), not 3⁄4 (part over part). The fraction 3⁄4 is the decimal A ÷ B, which is a useful but different number.

Real-Life Uses of Ratios

Map scales

Every map prints a scale ratio — 1 : 25 000 on UK Ordnance Survey sheets, 1 : 24 000 on US Geological Survey quads. One unit on paper equals N units on the ground; the ratio scaling tab converts straight away between paper distance and real-world distance.

Cooking ratios

Baker's percentages, sourdough hydration (1 : 0.75 flour : water), simple-syrup (1 : 1 sugar : water), espresso brew (1 : 2 grams in : grams out) are all proportions. Adjusting batch sizes is pure ratio math.

Financial analysis

Debt-to-equity, current ratio, quick ratio, gross margin, price-to-earnings — fundamental analysis is essentially the art of comparing ratios across companies and over time. Each one strips out absolute size and isolates a quality of the business.

Chemistry mixing

Mole ratios determine stoichiometry; mixing ratios determine concentration. A 1 : 9 dilution makes a 10% solution; a 1 : 99 dilution makes a 1% solution. The simplifier tab cleans up odd-looking ratios from a lab notebook.

Common Ratios at a Glance

Ratio	Meaning
1 : 1	Equal parts — both quantities the same size.
1 : 2	One half — first is 50% of the second.
2 : 3	Two out of five parts — 40% : 60%.
3 : 4	Three out of seven parts — 42.86% : 57.14% (Standard SD screen).
4 : 5	Four out of nine parts — 44.44% : 55.56%.
16 : 9	Widescreen HD/4K display — TVs, YouTube, modern monitors.
4 : 3	Traditional display — older TVs, iPads, slide decks.
21 : 9	Ultrawide cinema and gaming monitors.
3 : 2	Classic 35mm photo aspect — most DSLRs and many printed photo formats.
1 : 1.618	Golden ratio φ — design, architecture, and natural patterns.

Methodology you can verify

Every result is computed live in your browser using the Euclidean algorithm for the GCD, classical cross multiplication for missing values, and straight proportional scaling for dimensions. Float-valued ratios are scaled to integers (×10⁶) before reduction to avoid rounding loss. No numbers are hard-coded. Read more on the methodology and editorial policy pages.

Frequently Asked Questions

A ratio is a comparison of two or more quantities expressed in the same units, written with a colon — for example 3 : 4. It says the first quantity is three parts for every four parts of the second. Ratios let you compare two screens, two recipes, two budgets, or two companies on equal footing, regardless of their absolute size. A ratio of 3 : 4 means exactly the same thing as the fraction 3⁄7 (part-over-whole), the decimal 0.75 (part-over-part), or the percentage split 42.86% : 57.14%.

A proportion is the statement that two ratios are equal — A : B = C : D. As soon as three of the four values are known, the fourth is determined by cross multiplication: A × D = B × C. Rearranging gives D = (B × C) ÷ A, C = (A × D) ÷ B, B = (A × D) ÷ C, or A = (B × C) ÷ D depending on which slot is empty. Enter your three known values into the Solver tab, leave the unknown blank, and the calculator picks the right formula automatically and returns the answer along with a full step-by-step trail.

A proportion is an equation between two ratios — A : B = C : D. It says that the relationship between A and B is exactly the same as the relationship between C and D. Proportions are the engine behind scale models, map distances, recipe adjustments, and currency conversions. The defining property of every proportion is cross multiplication: A × D = B × C, which the calculator uses to solve for any missing term in a single step.

Divide both terms by their greatest common divisor (GCD). The GCD is the largest integer that divides both numbers exactly — the calculator finds it using the Euclidean algorithm. For example, 150 : 300 has GCD 150, so dividing both terms gives 1 : 2. For 1920 : 1080 the GCD is 120, so the simplified form is 16 : 9 — the canonical aspect ratio of HD video. The Simplify tab shows the original ratio, the simplified form, the GCD it used, and a table of equivalent ratios up to ×6.

Cross multiplication is the algebraic fact that A : B = C : D if and only if A × D = B × C. Visually, multiply across the equals sign — the outer pair (A and D) equals the inner pair (B and C). It works because both ratios can be rewritten as the equal fractions A⁄B = C⁄D; multiplying both sides by B × D removes the denominators. Every missing-value proportion problem is solved by rearranging this single identity for the unknown.

To scale a width × height while preserving its ratio, multiply (to enlarge) or divide (to shrink) both dimensions by the same factor. A 250 × 280 image shrunk by 2.5 becomes (250 ÷ 2.5) × (280 ÷ 2.5) = 100 × 112. The aspect ratio 25 : 28 is preserved exactly. Area, in contrast, scales with the square of the linear factor — that same 2.5× shrink reduces the area by a factor of 2.5² = 6.25. The Scale tab handles both calculations and shows a side-by-side rectangle visualisation.

A ratio's percentage form is each part divided by the sum of all parts, multiplied by 100. For 3 : 4, the total is 7, so the percentages are 3⁄7 × 100% ≈ 42.857% and 4⁄7 × 100% ≈ 57.143%. The Percentage tab handles up to eight parts and shows fractions, decimals, and percentages side by side. To go the other way — from percentages back to a simplified ratio — the calculator scales each percentage to an integer (×100), then divides by the GCD. So 25% : 75% recovers the clean ratio 1 : 3.

An aspect ratio is the ratio of a rectangle's width to its height — written as W : H. Common aspect ratios include 16 : 9 (modern TVs, 1080p / 4K video, YouTube), 4 : 3 (older TVs, iPads, presentations), 3 : 2 (35mm photography, most DSLRs), 21 : 9 (ultrawide cinema and gaming monitors), and 1 : 1 (Instagram squares). The Scale tab returns the aspect ratio of any width × height pair in both simplified form and as a decimal. The reference table on this page lists every popular aspect ratio with examples.

Equivalent ratios are ratios that simplify to the same lowest-terms form. To generate them, multiply (or divide) both terms by the same number — 3 : 4 is equivalent to 6 : 8, 9 : 12, 12 : 16, 15 : 20, 30 : 40, and so on, all of which simplify back to 3 : 4 via the GCD. The Simplify tab's Equivalent Ratios table lists multiples up to ×6 automatically. Two ratios are equivalent if and only if their cross products are equal — a quick check is A × D = B × C.

Ratios are used everywhere — design (16 : 9 video, 3 : 2 photos, golden-ratio layouts), construction (1 : 50 scale drawings, slope ratios for roofs and ramps), cooking (sourdough hydration, simple syrup, espresso brew ratios), chemistry (mole ratios for stoichiometry, dilution ratios), finance (debt-to-income, P/E ratio, current ratio), cartography (map scales like 1 : 25 000), photography (sensor aspect ratios), and statistics (odds, hazard ratios, relative risk). Anywhere two like quantities need to be compared without their absolute size getting in the way, ratios do the job.

Related Calculators

Pair the ratio calculator with other math tools for percentages, conversions, and proportional analysis.