Ratio Calculator

About this tool

Ratios and proportions are the mathematical backbone of scaling recipes, resizing images, mixing paint or chemicals, and solving geometry problems. This calculator handles the two standard ratio tasks in one page. The simplifier takes any two-term ratio — such as 144:192 — and reduces it to lowest terms using the Greatest Common Divisor, giving 3:4. Decimal terms are scaled to whole numbers first, so 1.5:2 becomes 3:4. The proportion solver takes x:y = x2:y2: fill in any three of the four fields, leave exactly one blank, and click Solve to get the missing value by cross-multiplication, shown to four decimal places. That covers aspect-ratio questions too — enter 16 and 9 with a width of 1920 and the solver returns a height of 1,080. Clear error messages appear for zero terms, more than one blank, or a zero divisor, and all maths runs in your browser.

Why use it

• Solve for the Missing Term: Enter three of the four values in a proportion and the calculator finds the fourth using cross-multiplication. No rearranging formulas manually — just leave the unknown blank.

• Auto-simplify to Lowest Terms: Any two-term ratio is reduced to its simplest form using the Greatest Common Divisor. Enter 144:192 and get 3:4 instantly.

• Decimal-friendly: Decimal inputs work in every field. The simplifier scales decimals to whole numbers before reducing, so 1.5:2 becomes 3:4 and 0.25:0.75 becomes 1:3.

• Aspect Ratios and Scaling: Use the solver for screen and image sizes — 16:9 with a 1920 px width gives a 1080 px height — or to scale a recipe quantity to a new serving count.

• Complete Privacy: All ratio and proportion calculations run entirely in JavaScript in your browser. No values you enter are sent to a server or stored.

How to use

1. To simplify, enter the two terms in Ratio A and Ratio B and click Simplify ratio
2. Read the lowest-terms result in the Simplified ratio box
3. To solve a proportion, fill three of the four fields x, y, x2 and y2 and leave one empty
4. Click Solve missing proportional value
5. Read the missing value, shown to four decimal places, in the Result box

When it helps

• When scaling a recipe from four servings to six and needing an ingredient amount proportionally adjusted
• When exporting a video at a non-standard resolution and needing to keep the original 16:9 or 21:9 aspect ratio
• When a maths or science problem gives you three terms of a proportion and asks for the fourth
• When comparing two fractions or ratios to see if they are equivalent after reducing to lowest terms
• When diluting a concentrate and you know the ratio and one of the volumes

Examples

Tips

• Always simplify before comparing two ratios — 12:16 and 3:4 look different but are equal, so reducing first avoids wrong conclusions
• Leave exactly one proportion field empty — the solver refuses to run with zero or two blanks
• When scaling recipes, keep the servings in x and x2 and change only the ingredient amount in y for each run
• Aspect ratio mismatches cause letterboxing or cropping in video export — verify width-to-height ratio before rendering
• Any ratio A:B remains equivalent if you multiply both terms by the same constant k: A:B = (kA):(kB). Use this to check equivalence quickly

Frequently Asked Questions

Glossary

Ratio

A comparison of two quantities expressed as A:B, indicating how many times one value contains the other. Ratios can be simplified, converted to fractions, or expressed as decimals.

Proportion

An equation stating that two ratios are equal: A:B = C:D. Proportions are used to solve for an unknown fourth term when three values are known, using cross-multiplication.

Greatest Common Divisor (GCD)

The largest positive integer that divides two numbers without a remainder. Dividing both terms of a ratio by their GCD reduces it to its simplest irreducible form.

Aspect Ratio

The ratio of width to height in a rectangular image, screen, or frame — for example, 16:9 for widescreen video or 4:3 for traditional monitors. Maintaining the aspect ratio prevents distortion when resizing.

Scale Factor

The multiplier applied to both terms of a ratio to produce an equivalent but larger or smaller ratio. A scale factor of 1.5 converts a 4-serving recipe to a 6-serving recipe by multiplying every ingredient by 1.5.

Equivalent Ratios

Two ratios that reduce to the same simplest form: 3:4, 6:8, and 12:16 are all equivalent ratios. They represent the same relative comparison, just at different scales.