Answer: Enter your values and the Ratio Calculator returns the exact result instantly — formula, worked example, and a plain-English explanation are included below the tool.
Simplify, scale, and solve ratios.
A ratio compares two quantities by division, showing how many times one value contains another. This calculator simplifies ratios to their lowest terms, scales them up or down, and solves for a missing value in a proportion — the workhorse equation a/b = c/d where any three values determine the fourth.
Ratios appear everywhere: recipes (2 parts flour to 1 part water), mixing fuel (50:1 two-stroke oil), screen dimensions (16:9), map scales, and financial metrics like the debt-to-income ratio lenders use. Written with a colon (3:4), a slash (3/4), or the word 'to' (3 to 4), they all mean the same fraction.
To simplify a ratio, divide every term by their greatest common divisor. The ratio 48:64 simplifies to 3:4 because both terms share the factor 16. Simplified form makes comparison easy: is 24:36 a better value than 30:42? Simplified, they are 2:3 and 5:7 — not equal, as cross-multiplication confirms (24 × 42 = 1008 and 36 × 30 = 1080 differ; simplified forms 2:3 ≈ 0.667 and 5:7 ≈ 0.714 make the difference visible at a glance).
Scaling a ratio preserves it: 3:4, 6:8, 30:40, and 300:400 are all the same relationship. This is why recipes scale cleanly — a 2:1 flour-to-water ratio works for one loaf or ten — and why map scales read like 1:25,000, meaning one unit on the map equals 25,000 of the same units on the ground.
A proportion states that two ratios are equal, and it is solved by cross-multiplication: if a/b = c/d then a·d = b·c. If 3 pencils cost $1.50, then 7 pencils cost x, where 3/1.50 = 7/x gives x = $3.50. Every missing-value ratio problem reduces to this one step.
The table below shows famous fixed ratios, including the golden ratio φ ≈ 1.618, which appears when a:b satisfies (a+b)/a = a/b. It surfaces in the geometry of the pentagon, in Fibonacci-number quotients that converge to it, and — somewhat overstated in pop culture — in claims about art and architecture. The aspect ratios are exact by definition; the golden ratio is irrational, so 1.618 is a rounded value.
| Ratio | Value / definition | Where it appears |
|---|---|---|
| 16:9 | 1.778 (width ÷ height) | Widescreen video, most monitors and TVs |
| 4:3 | 1.333 | Classic TV, iPad screens, medium-format photos |
| 1:1 | 1.000 | Square photos, profile images |
| 21:9 | 2.333 | Ultrawide monitors |
| Golden ratio | ≈1.618 | Pentagon geometry, Fibonacci convergence |
| A-series paper | 1:√2 ≈ 1.414 | A4, A3 — halves keep the same proportion |
A ratio compares two quantities of any kind; a percentage is a ratio normalized to 100; a rate is a ratio with different units, like miles per hour or price per ounce. Unit-price shopping is rate comparison: a 12 oz box at $3.00 is $0.25/oz, while 16 oz at $3.84 is $0.24/oz — the bigger box wins on rate even though it costs more in total.
One caution: ratios hide size. A 10:1 win-loss record sounds dominant until you learn it is 10 wins and 1 loss versus 400 wins and 40 losses — the second record's 10:1 came against far more trials. Always ask what the absolute quantities are before comparing ratios alone, since small denominators make ratios volatile.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 48:64, the GCD is 16, so the simplified ratio is 3:4. A quick method: factor both numbers, cancel the shared primes, and multiply what remains — exactly like simplifying a fraction.
How do I solve for a missing value in a proportion?
Cross-multiply. If a/b = c/d, then a·d = b·c. For example, if 5 notebooks cost $7.50, then 8 notebooks cost x where 5/7.50 = 8/x; cross-multiplying gives 5x = 60, so x = $12.00.
Are the ratios 3:4 and 30:40 the same?
Yes. Multiplying both terms of a ratio by the same non-zero number does not change the relationship — 3:4, 30:40, and 300:400 all equal 0.75 when expressed as a fraction. This invariance under scaling is the defining property of ratios.
What is the difference between a ratio and a proportion?
A ratio compares two quantities; a proportion is an equation stating that two ratios are equal. '3:4' is a ratio. '3:4 = 30:40' is a proportion. Proportions are what you solve when a ratio problem contains an unknown.
How do I convert a ratio to a percentage?
Divide the first term by the sum of the terms (for a share of a whole) or by the second term (for a relative comparison), then multiply by 100. A 3:4 split of a whole is 3/7 ≈ 42.9% and 4/7 ≈ 57.1%. A 3:4 advantage is 3/4 = 75%.
Why do lenders care about my debt-to-income ratio?
The DTI ratio measures monthly debt payments against gross monthly income. Under US lending guidelines used for qualified mortgages, a DTI at or below 43% has traditionally been an important threshold, because a higher ratio signals that income is heavily committed to debt service. It is a direct application of ratio comparison to credit risk.