What is the difference between a ratio and a proportion?

A ratio compares two quantities. A proportion states that two ratios are equal, which is what lets you solve for a missing term.

Math & Statisticsratio

Ratio Calculator

Simplify a ratio, express it as a decimal and as percentages of the whole, and scale it to any figure. Whole-number inputs simplify exactly; decimals are handled by scaling first.

Also called: simplify ratio, ratio to percentage.

Simplified ratio

2 : 5

16 to 40 simplifies to 2 : 5. As a decimal that is 0.4, and the first part is 28.57% of the whole.

As a decimal

0.4

First part of the total

28.57%

Second part of the total

71.43%

Scaled to your figure

not scaled

Greatest common divisor used

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

How this is calculated

Two numbers form a ratio, and simplifying means dividing both by their greatest common divisor. Expressing the parts as percentages of the total answers a different and often more useful question, since 16 to 40 is easier to act on as 28.6% and 71.4%. Scaling keeps the proportion while fixing one side to a number you actually have.

divide both sides by their greatest common divisor

g: Greatest common divisor

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

sixteen to forty

First value: 16
Second value: 40
Scale the first value to: 0

Simplified ratio2 : 5

Greatest common divisor of 8, worked by hand

Open this example

scaling keeps the proportion

First value: 16
Second value: 40
Scale the first value to: 100

Simplified ratio2 : 5

boundary: the proportion holds at any scale

Open this example

Method and limits

What it assumes

Simplification is exact for whole numbers and approximate for decimals.

What it deliberately does not model

Ratios of three or more parts are not handled here.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

What is the difference between a ratio and a proportion?: A ratio compares two quantities. A proportion states that two ratios are equal, which is what lets you solve for a missing term.