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Ratio Calculator

Simplify ratios and solve missing proportion values

About Ratio Calculator

Ratios and proportions are the mathematical backbone of scaling recipes, converting aspect ratios, mixing paint or chemicals, dividing investments, and solving geometry problems. This calculator handles all three standard ratio tasks in one tool. Proportion solver: enter three of the four values in A:B = C:D and the missing term is calculated using cross-multiplication. Simplifier: enter any ratio — such as 144:192 — and the tool reduces it to lowest terms using the Greatest Common Divisor, for example 3:4. Aspect ratio mode: enter a reference ratio (16:9, 4:3, 21:9, or any custom ratio) with one known dimension and the calculator returns the other. Results are displayed simultaneously as A:B notation, as a decimal fraction, and as a percentage, giving you the format most useful for your context. The tool handles integers and decimals in all input fields, and the simplification.

Why use Ratio Calculator

Solve for the Missing Term

Enter three of the four values in a proportion and the calculator finds the fourth using exact cross-multiplication arithmetic. No rearranging formulas manually — just leave the unknown blank and read the answer.

Auto-simplify to Lowest Terms

Any ratio is reduced to its simplest irreducible form using the Greatest Common Divisor algorithm. Enter 144:192 and get 3:4 instantly, with the GCD shown for transparency and learning.

Three Output Formats

Results are shown simultaneously as A:B colon notation, as a decimal (0.75), and as a percentage (75%), so you can use whichever format your spreadsheet, design tool, or document requires.

Recipe and Ingredient Scaling

Scale any multi-ingredient recipe up or down by changing the serving count. The calculator proportionally adjusts every ingredient value, handling decimals correctly so you do not end up with fractionally wrong measurements.

Aspect Ratio and Screen Dimensions

Preset screen ratios — 16:9, 4:3, 21:9 — plus custom input. Enter a width to get the matching height for video export, image cropping, or responsive design breakpoints.

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 in any database.

How to use Ratio Calculator

Choose a mode: Proportion Solver, Simplify Ratio, or Aspect Ratio
For Proportion Solver, enter three of the four values A, B, C, D and leave one blank
For Simplify, enter the two numbers in the ratio field (such as 144 and 192)
For Aspect Ratio, choose a preset (16:9, 4:3, 21:9) or enter a custom ratio, then enter one known dimension
Click Calculate or watch the live result update as you type
Copy the result in ratio, decimal, or percentage format using the copy buttons

When to use Ratio Calculator

When scaling a recipe from four servings to six and needing all ingredient amounts proportionally adjusted
When exporting a video at a non-standard resolution and needing to maintain 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 a paint mixing formula specifies a 3:1:2 ratio and you need to scale it to a larger batch
When comparing two fractions or ratios to see if they are equivalent after reducing to lowest terms
When diluting a chemical solution from a concentrate at a specified concentration ratio to a target volume

Examples

Proportion — solve for D

Input: A:B = C:D where A=3, B=4, C=12, D=?

Output: D = 16 (effective ratio 0.75)

Simplify a ratio

Input: 144 : 192

Output: Simplified: 3 : 4 (GCD = 48)

Aspect ratio width to height

Input: Ratio 16:9, Width = 1920 px

Output: Height = 1080 px

Tips

Always simplify before comparing two ratios — 12:16 and 3:4 look different but are equal, so reducing first avoids wrong conclusions
Use percentage view to compare ratios with very different scales at a glance without doing mental division
When scaling recipes, start with the largest ingredient first to establish the scale factor, then apply it to smaller amounts to minimise rounding cascade
Aspect ratio mismatches cause letterboxing or cropping in video export — verify width-to-height ratio before rendering or exporting
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

What is the difference between ratio and proportion?▾

A ratio compares two quantities: for example, 3:4 means three parts of A for every four parts of B. A proportion is a statement that two ratios are equal: 3:4 = 6:8. Proportions are used to find missing values when one ratio is known and part of the equivalent ratio is unknown.

How do I simplify a ratio to lowest terms?▾

Divide both terms by their Greatest Common Divisor (GCD). For 144:192, the GCD is 48, so 144÷48 = 3 and 192÷48 = 4, giving 3:4. If the GCD is 1, the ratio is already in its simplest form.

How do I find a missing term in A:B = C:D?▾

Use cross-multiplication: A × D = B × C. If D is unknown, D = (B × C) ÷ A. For example, 3:4 = 12:?, D = (4 × 12) ÷ 3 = 16. This works for any single unknown in the four positions of a proportion.

What is GCD and why does it matter?▾

The Greatest Common Divisor is the largest integer that divides both terms of a ratio without remainder. Dividing by the GCD reduces a ratio to its simplest form, making it easier to compare with other ratios and to spot equivalent proportions.

Can I have decimal ratios like 1.5:2?▾

Yes — the calculator accepts decimal inputs in all fields. A ratio like 1.5:2 is equivalent to 3:4 after multiplying both terms by 2. The simplifier will reduce decimal ratios to integer form where possible.

How do aspect ratios apply to screens and images?▾

An aspect ratio like 16:9 means the width is 16 units for every 9 units of height. For a 1920-pixel-wide display, the matching height is 1920 × 9 ÷ 16 = 1080 pixels. Any width can be used as input — the calculator solves the missing dimension.

How do I scale a recipe from 4 servings to 6?▾

The scale factor is 6 ÷ 4 = 1.5. Multiply every ingredient amount by 1.5. In the proportion solver, set A:B = 4:6 and enter each ingredient quantity as C to find the scaled D value. Alternatively use the recipe-scaler mode with serving count fields.

What is the golden ratio?▾

The golden ratio — approximately 1:1.618 or φ ≈ 1.61803398875 — is a proportion found throughout art, architecture, and nature. It is the ratio where the whole is to the larger part as the larger part is to the smaller. Enter 1:1.618 in the simplifier to confirm it cannot be reduced further to integers.

Explore the category

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.