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Ratio Calculator

Ratio
:

Simplified

16:9

Decimal
1.7778
GCD used
120
Original
1920:1080

Estimates for educational purposes — not financial, medical, or legal advice. See terms.

A ratio compares two numbers. An aspect ratio of 16:9 says that for every 16 units of width, there are 9 units of height. A debt-to-income ratio of 1:3 says your debt payments are one-third of your gross income. The underlying math is simple, but two operations come up often enough to deserve their own tool: simplifying a ratio to its lowest terms, and solving a proportion for a missing value.

Simplifying a ratio

To simplify $a:b$, divide both sides by their greatest common divisor (GCD):

a:b  =  agcd⁡(a,b):bgcd⁡(a,b)a : b \;=\; \frac{a}{\gcd(a,b)} : \frac{b}{\gcd(a,b)}

For screen dimensions $1920 : 1080$, $\gcd(1920, 1080) = 120$, so the simplified ratio is $16:9$. The simplified form has no common factors — that’s what “lowest terms” means.

Solving a proportion

A proportion is an equation that says two ratios are equal:

ab  =  cd\frac{a}{b} \;=\; \frac{c}{d}

If you know three of the four values, you can solve for the fourth by cross-multiplication. Rearranging gives you:

a⋅d  =  b⋅ca \cdot d \;=\; b \cdot c

From this, each unknown follows:

a=b⋅cd,b=a⋅dc,c=a⋅db,d=b⋅caa = \frac{b \cdot c}{d}, \quad b = \frac{a \cdot d}{c}, \quad c = \frac{a \cdot d}{b}, \quad d = \frac{b \cdot c}{a}

The tool accepts any three values and solves for the one you leave blank.

Example: scaling a photo

You have a photo that’s 1920 × 1080 pixels and you want to resize it to fit a 500-pixel-wide layout slot. You need the corresponding height that preserves the aspect ratio.

In proportion form: $1920 : 1080 ;=; 500 : h$

The tool solves: $h = \dfrac{1080 \times 500}{1920} = 281.25$

Round to 281 pixels tall and the photo fits the slot without distorting.

When to use which mode

  • Simplify when you have two raw numbers and want to see them in lowest terms. Examples: reducing a recipe ratio (4 cups flour : 2 cups milk → 2:1), computing a gear ratio, simplifying odds (4:2 → 2:1). The simplification uses the same logic as the GCD / LCM calculator.
  • Solve proportion when you know two pairs and one value is missing. Examples: scaling a recipe (2 eggs : 4 cups flour = ? eggs : 12 cups flour), converting between units via a fixed ratio, computing equivalent fractions. For pure fraction arithmetic on the resulting ratios, the fraction calculator handles the same-base work.

What this tool does not do

It does not handle three-way ratios like $a:b:c$ (e.g., a recipe ratio of flour:water:salt). For those, simplify each pair independently — or use a dedicated recipe scaling tool. It also does not convert between ratios and percentages automatically — for that, use the percentage calculator in the same category.

Frequently asked questions

What's the difference between a ratio and a fraction?

Mathematically, very little — both compare two quantities. Ratios are usually written with a colon (16 to 9) and fractions with a slash (16/9), and the distinction is often just convention. Ratios are used when comparing two things (aspect ratios, mix ratios, debt-to-income), fractions when describing parts of a whole.

How do you simplify a ratio?

Find the greatest common divisor (GCD) of the two numbers and divide both by it. For 1920 to 1080, the GCD is 120, so 1920/120 to 1080/120 gives 16 to 9. The simplified form has no common factors other than 1 — that's the definition of a ratio in lowest terms.

What does solving a proportion mean?

A proportion is an equation where two ratios are equal — for example, 1 to 2 equals 3 to 6. If you know three of the four values, you can find the fourth by cross-multiplication. The tool accepts any three values and solves for the missing one.

Can ratios be negative?

Yes. The sign carries through — a negative 4 to 6 simplifies to negative 2 to 3. The tool handles negative inputs correctly, preserving the sign on the first term.