Ratio Calculator — Simplify, Scale and Split Ratios

÷What a ratio is — and how simplifying works

A ratio compares two quantities by division. Simplifying means dividing both parts by their greatest common divisor (GCD) — the largest number that divides both parts exactly. For decimals, both parts are first scaled to whole numbers:

Simplified = (a ÷ GCD) : (b ÷ GCD)

• 12 : 18 — GCD is 6 → divide both → 2 : 3.
• 0.5 : 1.5 — decimals are first scaled ×10 to 5 : 15, GCD is 5 → 1 : 3.
• 7 : 11 — the GCD is 1, so the ratio is already in simplest form.

Two ratios are equivalent exactly when one is the other multiplied by a single factor — which is why the scale tool is always exact, never an approximation. Simplifying a ratio keeps its meaning while shrinking its numbers, so 12:18 and 2:3 describe the identical relationship.

That GCD step is the entire job of a simplify ratio calculator, and it is the mode I reach for first on this page. The tool above doubles as a dedicated ratio simplifier: decimals are scaled to whole numbers, the GCD is divided out, and you get the simplest form back with its decimal value and percentage split. A few I run through it often: 45 : 60 → divide by 15 → 3 : 4; 24 : 36 → divide by 12 → 2 : 3; 0.75 : 1.25 → scale ×100 to 75 : 125, divide by 25 → 3 : 5. Money behaves identically — prices of $45 and $60 stand in the ratio 3 : 4, because 15 divides both.

🔗Equivalent ratios: same relationship, different numbers

Two ratios are equivalent ratios when they describe the same relationship — one is simply the other multiplied (or divided) by a single factor. 3:4, 6:8 and 30:40 all say the same thing: for every 3 of the first quantity, there are 4 of the second. I lean on equivalents constantly, because real life rarely hands me the tidy textbook version of a ratio — it hands me 45:60 and expects me to recognise 3:4 hiding inside it.

The Scale tab above generates equivalent ratios for any factor — including fractions, so × 0.5 halves a recipe without disturbing its balance. And if you are wondering how to picture an equivalent ratio, watch the pie above: 3:4 and 30:40 draw the identical pie, slice for slice. Same shares, same percentages — only the numbers grew.

≔Solving proportions: A : B = C : D

A proportion states that two ratios are equal. Give any three of the four terms and the fourth is forced — this is the “find X” problem behind countless textbook exercises, and the new Proportion tab above solves it instantly.

The engine is cross-multiplication: A : B = C : D means A × D = B × C. To solve for a missing term, isolate it — this proportion calculator does the rearrangement for you:

• Missing D: D = B × C ÷ A
• Missing C: C = A × D ÷ B
• Missing B: B = A × D ÷ C
• Missing A: A = B × C ÷ D

Worked example: 2 : 3 = 10 : D → D = 3 × 10 ÷ 2 = 15. Check: 2/3 ≈ 0.6667 and 10/15 ≈ 0.6667 ✓. Another: 2 : 3 = C : 15 → C = 2 × 15 ÷ 3 = 10. Leave exactly one field empty; the calculator refuses zero denominators and non-positive inputs with a plain-language error.

One more I solve all the time: 3 : 8 = 12 : x — say, 3 scoops of powder for every 8 cups of water, scaled up to 12 scoops. Cross-multiplying gives x = 8 × 12 ÷ 3 = 32 cups. Whenever a problem is phrased “for every”, I read it as a missing-term proportion and let the tab do the rearranging.

🔢Three-part ratios: a : b : c

Recipes and mixtures rarely stop at two ingredients — enter an optional third part and the calculator handles 1 : 2 : 3 style ratios. The GCD is taken across all three numbers, the pie chart gains a third slice, and the split tool divides the amount three ways.

Worked example: split 600 by 1 : 2 : 3. Total parts = 6, so each share is 600 ÷ 6 = 100 → parts get 100 / 200 / 300 (16.7% / 33.3% / 50.0%). A concrete mix of 1:2:4 with 350 kg total gives 50 / 100 / 200 kg. Leave the third field empty any time to return to two-part ratios.

%Ratio vs fraction vs percent

Ratios, fractions and percentages describe the same split, but each shines in a different context:

• Ratios win for recipes and mixtures — “2:3 cement to sand” tells a builder the exact parts to mix, no percentages needed.
• Percentages win for comparison — “40% of students” is easier to compare across schools of different sizes than “2:3”.
• Decimals win for math — 0.6667 plugs straight into formulas and spreadsheets.

They are linked precisely: the ratio 2:3 means part a is 2/5 of the whole (40%), and the decimal form of the ratio (a ÷ b = 0.6667) is the fraction a/b. This calculator shows all three at once, so you can pick whichever form your situation calls for. Share of a = Q × a ÷ (a + b): splitting $500 by 2:3 gives 500 × 2/5 = $200 and 500 × 3/5 = $300.

The conversion that trips people up is not the arithmetic — it is knowing what the whole is. A part-to-part ratio compares the parts to each other: in a fruit bowl holding 3 apples and 5 oranges, apples to oranges is 3 : 5. A part-to-whole ratio compares one part with everything: apples to all the fruit is 3 : 8, because the bowl holds 8 pieces. Same bowl, two different ratios — and they convert to different percentages, which is why my first question is always “part of what?”.

Going from a ratio to fraction form is direct: a : b becomes the fraction a/b, so 3 : 5 is 3/5. Going from a ratio to percentage has two honest answers, depending on the question. “How big is a compared with b?” divides a by b — 3 ÷ 5 = 60%. “What share of the whole is a?” divides a by a + b — 3 ÷ 8 = 37.5%. The calculator’s percentage split always shows the share version; this table keeps both side by side:

Nowhere does the distinction bite harder than dilution labels. A bottle marked 1 : 10 normally means 1 part concentrate to 10 parts water — a part-to-part reading, so concentrate is 1/11 ≈ 9.1% of the finished mix. Read it as “1 part in 10 total” and it would be 10%. At weak dilutions the gap is a rounding error; at strong ones it is not — 1 : 2 read part-to-part makes concentrate 1/3 ≈ 33.3% of the mix, while “1 in 2” would mean 50%. I settle the reading before I mix anything. The Fraction Calculator and Percentage Calculator linked below take each of these forms further.

🖼️Aspect ratios: a quick reference

An aspect ratio is just a ratio applied to width vs height — screens, photos, video and paper all live by them:

Scaling is how resolutions relate: 1920×1080 and 3840×2160 are both 16:9 — the second is the first scaled by 2. Use the Scale tab above to check any width–height pair.

Resolutions are just aspect ratios wearing bigger numbers. A named resolution simplifies to its ratio exactly the way any pair of numbers does — divide width and height by their GCD:

My favourite honesty check: the once-common laptop resolution 1366 × 768 is sold as 16:9, but it simplifies to 683 : 384 — close to 16:9, not exactly it. The “21:9” ultrawide label hides two different true ratios as well (64:27 and 43:18, depending on the panel). I keep this section a reference table rather than a resizing tool on purpose: type any width : height pair into the calculator above and the simplified ratio on the results card tells you the truth of the label.

φThe golden ratio: genuinely special, honestly oversold

The golden ratio, written φ (phi), is the number (1 + √5) ÷ 2 ≈ 1.618. It shows up when a line is split so that the whole relates to the longer part exactly as the longer part relates to the shorter one: split a 10-unit line in golden ratio and you get 6.18 and 3.82 — and 10 ÷ 6.18 ≈ 6.18 ÷ 3.82 ≈ 1.618. The Fibonacci sequence homes in on it too: consecutive terms divide out at 1.667, 1.6, 1.625, 1.615, 1.619…, settling on φ.

Where I part company with the posters is the mythology. The claims that φ secretly structures the Parthenon, the nautilus shell and the human face are mostly not supported by measurement — people who actually checked found the quoted proportions cherry-picked, or simply not there. What is real: designers deliberately use ≈ 1.618 proportions because they look balanced, and a golden rectangle — sides in the ratio 1.618 : 1, like 16.18 × 10 cm — does crop elegantly. You can test the number above: 1618 : 1000 simplifies to 809 : 500, which is φ to three decimal places, produced by an ordinary ratio.

💡Where ratios run the world

• Cooking: double a recipe by scaling every ingredient by 2 — the ratio never changes, only the batch size.
• Maps: a 1:50,000 map means 1 cm on paper = 50,000 cm (500 m) on the ground — pure proportion solving.
• Finance: debt-to-income and price–earnings ratios compress two numbers into one comparable figure.
• Mixing: paint, concrete, fertilizer and medicine dilutions are all stated as ratios — and split with Q × part ÷ total.