Ratio Calculator
Two numbers in — the simplest form, the percent split, and every equivalent ratio out.
Simplify any ratio to its lowest terms: the calculator finds the greatest common divisor and divides both terms by it, so 12:18 becomes 2:3. It also shows the ratio as a fraction, a decimal and a percent split. Switch to Standard to find a missing value (12:18 = 9:?) or scale by a factor, Detailed for three-part ratios and splitting a dollar amount in a ratio, or Advanced for the aspect-ratio helper — 1920×1080 is 16:9, and 1280 wide keeps it at 1280×720.
Exact arithmetic — the GCD, percent and split answers are computed, not estimated. Rounding is only applied to display decimals (up to 4 places).
How to simplify a ratio with the GCD
Divide both terms by the greatest common divisor
A ratio is in lowest terms when its terms share no common factor except 1. To get there, find the greatest common divisor (GCD) of the terms and divide every term by it. For 12:18, the divisors of 12 are 1, 2, 3, 4, 6, 12 and the divisors of 18 are 1, 2, 3, 6, 9, 18 — the greatest shared one is 6, so 12:18 = 2:3.
| Ratio | GCD | Lowest terms |
|---|---|---|
| 12 : 18 | 6 | 2 : 3 |
| 45 : 60 | 15 | 3 : 4 |
| 1920 : 1080 | 120 | 16 : 9 |
| 25 : 15 | 5 | 5 : 3 |
| 8 : 12 : 20 | 4 | 2 : 3 : 5 |
Finding the GCD for big numbers: Euclid's algorithm
Listing divisors gets slow, so use Euclid's algorithm: divide the larger term by the smaller, keep the remainder, and repeat with the smaller term and that remainder until the remainder is 0. The last non-zero remainder is the GCD. For 1920 and 1080: 1920 ÷ 1080 leaves 840; 1080 ÷ 840 leaves 240; 840 ÷ 240 leaves 120; 240 ÷ 120 leaves 0 — so the GCD is 120 and 1920:1080 simplifies to 16:9. For a three-part ratio, take the GCD of all three terms: GCD(8, 12, 20) = 4, so 8:12:20 = 2:3:5.
Decimals first, GCD second. If a term has decimals, multiply every term by 10 until they're all whole numbers, then simplify: 2.5:1.5 → ×10 → 25:15 → ÷5 → 5:3. The calculator does this shift automatically.
Ratio to fraction, percent and decimal
One ratio, four faces
The same ratio can be written as a fraction, a percent split or a decimal — the trick is knowing whether you're comparing A with B (divide A by B) or splitting a whole into parts (divide each term by the total of the parts). In 2:3 the parts total 5, so the shares are 2/5 = 40% and 3/5 = 60%, while A ÷ B = 2 ÷ 3 ≈ 0.667.
| Ratio | First part of total | Percent split | A ÷ B |
|---|---|---|---|
| 1 : 1 | 1/2 | 50% : 50% | 1.000 |
| 1 : 2 | 1/3 | 33.3% : 66.7% | 0.500 |
| 2 : 3 | 2/5 | 40% : 60% | 0.667 |
| 3 : 4 | 3/7 | 42.9% : 57.1% | 0.750 |
| 3 : 7 | 3/10 | 30% : 70% | 0.429 |
| 16 : 9 | 16/25 | 64% : 36% | 1.778 |
Going the other way is just as mechanical: the fraction 3/4 is the ratio 3:4, and a "30% : 70%" split is the ratio 30:70, which simplifies (GCD 10) to 3:7. The percent columns always sum to 100% — if yours don't, you divided by one term instead of the total.
Equivalent ratios. Multiply or divide every term by the same number and the relationship is unchanged: 2:3 ≡ 4:6 ≡ 6:9 ≡ 20:30. The quick equivalence test is cross-multiplication — 4:6 and 6:9 match because 4 × 9 = 36 = 6 × 6. The calculator lists the first few multiples of your simplified ratio automatically.
Dividing an amount in a given ratio
Total the parts, price one part, multiply out
To split $500 between two people in the ratio 2:3: the parts total 2 + 3 = 5, so one part is $500 ÷ 5 = $100. The shares are 2 × $100 = $200 and 3 × $100 = $300 — and they add back to $500, which is your check. This is the standard method for splitting bills, profits, commissions or inheritance shares in unequal proportions.
Three-way splits work the same
$1,200 divided in 1:2:3 has 1 + 2 + 3 = 6 parts of $200 each, giving $200, $400 and $600. Enter a third term at the Detailed level and the calculator splits any amount three ways. If the split doesn't land on whole cents, the calculator rounds each share to the cent — for legal or payroll splits, put the rounding difference on an agreed share.
Scaling recipes and mixes
Scaling is the same move in reverse: multiply every term by the factor. A mortar mix of cement to sand at 1:3 scaled ×5 becomes 5:15 — still 1:3 in character, just bigger. A recipe ratio of 5:3 flour to water scaled ×4 is 20:12. Use the Scale mode at the Standard level, and note the scaled ratio always simplifies straight back to where you started — that's what makes it equivalent.
Aspect ratios: 16:9, 4:3 and resizing without distortion
An aspect ratio is just a simplified pixel ratio
Divide a screen's width and height by their GCD and you have its aspect ratio: 1920 and 1080 share a GCD of 120, so 1920×1080 is exactly 16:9. That's why 1280×720 and 3840×2160 look the same shape — they're the same ratio at different scales.
| Aspect ratio | Shape | Common resolutions |
|---|---|---|
| 16 : 9 (≈1.78:1) | Widescreen TV, laptops, YouTube | 1280×720 · 1920×1080 · 3840×2160 |
| 4 : 3 (≈1.33:1) | Older monitors, iPads, classic TV | 800×600 · 1024×768 |
| 3 : 2 (1.5:1) | Most photo sensors, some laptops | 1080×720 · 6000×4000 |
| 1 : 1 | Square — social posts | 1080×1080 |
| 9 : 16 | Vertical video — Shorts, Reels | 1080×1920 |
| 64 : 27 ("21:9") | Ultrawide monitors | 2560×1080 · 5120×2160 |
Resizing while preserving the ratio
Scale both dimensions by the same factor. To shrink 1920×1080 to 1280 wide: 1280 ÷ 16 = 80, so the height is 9 × 80 = 720 — equivalently, height = 1280 × (1080 ÷ 1920). If the preserved height comes out fractional (say resizing to 1000 wide gives 562.5), round to the nearest even pixel and expect a hairline crop rather than stretching the image.
Marketing vs math. "21:9" ultrawides are really 64:27 (2560 and 1080 have GCD 40 → 64:27 ≈ 2.37:1, while a true 21:9 would be ≈2.33:1). And the golden ratio φ ≈ 1.618:1 sits between 3:2 and 16:9 — prized in design, though no mainstream screen actually uses it.
❓ Frequently asked Frequently asked questions
How do you simplify a ratio?
Divide both terms by their greatest common divisor (GCD). For 12:18, the biggest number that divides both is 6, so 12:18 simplifies to 2:3. For larger numbers, find the GCD with Euclid's algorithm: divide the larger term by the smaller and keep the remainder, then repeat with the smaller term and that remainder until the remainder is 0 — the last non-zero remainder is the GCD. For 1920:1080 the steps give remainders 840, 240, 120, 0, so the GCD is 120 and 1920:1080 simplifies to 16:9. A ratio is fully simplified when its terms share no common factor except 1.
How do I convert a ratio to a fraction?
There are two correct readings, and it pays to be explicit about which one you mean. Read as a comparison, the ratio a:b is the fraction a/b — so 12:18 = 12/18 = 2/3 ≈ 0.667, meaning the first quantity is two-thirds of the second. Read as parts of a whole, each term is divided by the total number of parts: in 2:3 there are 5 parts, so the shares are 2/5 and 3/5. Use the comparison form to compare two quantities directly, and the parts-of-a-whole form when the two terms together make up one total you are splitting.
How do I convert a ratio to a percentage?
Add the terms to get the total number of parts, then divide each term by that total and multiply by 100. For 2:3 the total is 5 parts, so the split is 2 ÷ 5 = 40% and 3 ÷ 5 = 60%. It works for three-part ratios too: 1:2:3 has 6 parts, giving 16.7%, 33.3% and 50%. The percentages always sum to 100% (up to rounding) — that's a quick check that you divided by the total of the parts rather than by one of the terms.
How do I divide an amount of money in a given ratio?
Add the ratio's parts, divide the amount by that total to get the value of one part, then multiply by each term. To split $500 in the ratio 2:3: the parts total 2 + 3 = 5, one part is $500 ÷ 5 = $100, so the shares are 2 × $100 = $200 and 3 × $100 = $300. A three-way example: $1,200 in 1:2:3 has 6 parts of $200 each, giving $200, $400 and $600. The Detailed level of this calculator does the whole split for any amount, including three-part ratios.
What are equivalent ratios?
Equivalent ratios are ratios that express the same relationship — you get one from another by multiplying or dividing both terms by the same non-zero number. So 2:3, 4:6, 6:9 and 20:30 are all equivalent, and all simplify to 2:3. To test whether two ratios are equivalent, cross-multiply: 4:6 and 6:9 are equivalent because 4 × 9 = 36 and 6 × 6 = 36. Equivalent ratios are what you use to scale a recipe, a map distance or a mix without changing its character.
What is the golden ratio?
The golden ratio φ (phi) is the special ratio where the whole relates to the larger part exactly as the larger part relates to the smaller: (a + b) : a = a : b. Solving that gives φ = (1 + √5) ÷ 2 ≈ 1.6180339887, so the golden ratio is about 1.618:1. Ratios of consecutive Fibonacci numbers approach it — 21/13 ≈ 1.615 and 34/21 ≈ 1.619 — which is why it shows up in spiral patterns. It's celebrated in art and design, though claims about its use in famous works are often overstated.
Is 1920×1080 a 16:9 aspect ratio, and how is it different from 4:3?
Yes — the GCD of 1920 and 1080 is 120, and 1920 ÷ 120 = 16 while 1080 ÷ 120 = 9, so 1920×1080 is exactly 16:9 (about 1.78:1), the standard widescreen shape shared by 1280×720 and 3840×2160 (4K). The older 4:3 shape (about 1.33:1) is squarer — 1024×768 and 800×600 are 4:3. To resize while preserving the ratio, scale both dimensions by the same factor: 1920×1080 reduced to 1280 wide is 1280×720, because 1280 ÷ 16 = 80 and 9 × 80 = 720. One trap: 2560×1080 monitors are marketed as 21:9, but the exact ratio is 64:27.
Can a ratio include decimals or fractions?
Yes — ratios are usually written with whole numbers, but you can simplify a decimal ratio by first multiplying both terms by a power of 10 until they're whole. For 2.5:1.5, multiply both by 10 to get 25:15, then divide by the GCD 5 to get 5:3. For fractions, multiply both terms by a common denominator: 1/2 : 3/4 multiplied by 4 becomes 2:3. This calculator clears decimals automatically, so you can type 2.5 and 1.5 straight in.
What is the difference between a ratio and a proportion?
A ratio compares two or more quantities — 2:3 says there are 2 of one thing for every 3 of another. A proportion is an equation stating that two ratios are equal, such as 2:3 = 8:12, and solving a proportion means finding the value that makes the equation true. This page is built for working on a single ratio — simplifying, scaling, converting and dividing amounts. If you need to solve a/b = c/d for a missing value with cross-multiplication, our Proportion Calculator is built exactly for that.
Where these figures come from
Ratio arithmetic is standard mathematics, not a matter of published rates — every result on this page follows from the definition of a ratio and the greatest common divisor. The conventions and named constants referenced above come from these references:
- Definition and notation of a ratio — Wolfram MathWorld — Ratio.
- Greatest common divisor and Euclid's algorithm — Wikipedia — Euclidean algorithm.
- The golden ratio φ = (1 + √5)/2 ≈ 1.6180339887 — Wolfram MathWorld — Golden Ratio.
- Display and image aspect-ratio conventions (16:9, 4:3, 64:27) — Wikipedia — Aspect ratio (image).
Last checked: July 2026. Mathematical definitions don't change, but naming conventions (like marketing "21:9" for 64:27 panels) do drift — the resolutions table reflects usage as of this check.
Select the question that matches what you're working on.
The headline is your ratio in lowest terms — the same relationship as what you typed, expressed with the smallest possible whole numbers.
12:18 and 2:3 describe the identical relationship — simplifying changes nothing but readability. If your two terms come out as 1:1.5 or 0.67:1 in decimal form, those are the same ratio wearing different clothes.
2:3 flour to water is not 3:2. The calculator never reorders your terms, so make sure the first number matches the first-named quantity before you act on a split.
For most practical decisions the 40% : 60% reading is the one you want — it tells you each side's share of the whole directly, no further division needed.
Three habits cover almost every ratio problem: know your total parts, keep units consistent, and scale both sides together.
In 2:3 there are 5 parts, not 2 or 3 — that 5 is the denominator for every share, percent and split. Most ratio mistakes are dividing by a term instead of the total.
A ratio only means something when both terms are in the same unit. 30 minutes to 2 hours isn't 30:2 — convert first: 30:120, which simplifies to 1:4.
Multiplying or dividing both terms by the same number preserves the ratio; adding or subtracting does not. 2:3 doubled is 4:6 — still equivalent. But 2:3 with 1 added to each term is 3:4, a genuinely different ratio. That asymmetry is the source of most wrong answers on ratio test questions.
The everyday jobs this tool is built for, and the fastest route to each.
Detailed level: enter the ratio and the dollar amount. $500 in 2:3 → $200 and $300; add a third term for three-way splits.
Standard level, Scale mode: a factor of 4 turns 2:3 into 8:12 — same character, four times the quantity. Works on three-part ratios too.
Advanced level: 1920×1080 at a target width of 1280 gives 1280×720 — the height is recomputed so nothing stretches.
Ratios sit next to proportions, percentages and volumes — these tools pick up where this one stops.
Cross-multiplication, missing values and word problems — the full proportion toolkit.
Proportion →