Ratio Calculator

Ratio Calculator: How It Works

A ratio compares quantities; a proportion states that two ratios are equal. Between them they cover scaling recipes, mixing solutions, reading maps, sizing images and dividing money — and one recurring mistake accounts for most errors with them.

Part-to-part and part-to-whole

This is the distinction that causes trouble. A class with 12 boys and 18 girls has:

A part-to-part ratio of boys to girls of 12:18, simplifying to 2:3.
A part-to-whole fraction of boys of 12/30, which is 2/5 or 40%.

Reading 2:3 as 'two-thirds are boys' is wrong, and it is the single most common ratio error. In a 2:3 ratio the total is five parts, not three.

Simplifying

Divide every term by the greatest common divisor. For 1920:1080 the GCD is 120, giving 16:9. For three-term ratios the same applies: 20:30:50 divides by 10 to give 2:3:5.

Solving a proportion

Cross-multiply. If 3:4 = x:20, then 4x = 60, so x = 15.

The critical rule is consistency of order. Writing 'boys:girls = girls:boys' inverts the relationship and produces a plausible-looking wrong answer. Label each side before you calculate.

Dividing an amount by a ratio

Split 8,000 in the ratio 3:5.

Total parts = 3 + 5 = 8
One part = 8,000 ÷ 8 = 1,000
Shares = 3,000 and 5,000

Extends directly to more terms: for 2:3:5, the total is 10 parts.

Scale ratios

Scale	1 cm on the drawing	Typical use
1:1	1 cm	Full-size templates
1:50	50 cm	Room plans
1:100	1 m	Building floor plans
1:1,000	10 m	Site plans
1:50,000	500 m	Topographic maps

Note that area scales as the square of the linear ratio. Doubling every dimension of a room quadruples its floor area, and a 1:100 model has one ten-thousandth of the real area. This catches people out constantly when estimating materials.

Aspect ratios

An aspect ratio is width:height. Common values are 16:9 for video, 4:3 for older displays and many documents, 1:1 for square social posts, and 21:9 for ultrawide. To resize while preserving the ratio, multiply both dimensions by the same factor — changing one alone distorts the image.

Mixing and dilution

Ratios in mixing instructions are usually part-to-part, so a 1:4 concentrate means one part concentrate to four parts water — five parts in total, not four. Getting this backwards produces a solution 25% stronger than intended, which matters for chemicals, medications and anything where the concentration is specified for a reason.

The golden ratio

Approximately 1:1.618, arising when the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. It appears in mathematics and in some natural growth patterns. Claims that it governs classical architecture and produces inherently pleasing proportions are largely retrospective, and the evidence for an aesthetic effect is weak — it is a genuinely interesting number surrounded by a great deal of overstatement.

Frequently Asked Questions

Does a 2:3 ratio mean two-thirds?

No, and this is the commonest ratio error. A 2:3 ratio has five parts in total, so the first quantity is two-fifths, or 40%. Part-to-part ratios and part-to-whole fractions are different things.

How do I divide an amount by a ratio?

Add the parts to get the total, divide the amount by that total to find one part, then multiply by each term. Splitting 8,000 in the ratio 3:5 gives 3,000 and 5,000.

Does a 1:4 dilution mean four parts total?

No — five. One part concentrate plus four parts water. Reading it as four parts total makes the mixture 25% stronger than intended, which matters for chemicals and medication.

How does scale affect area?

Area scales as the square of the linear ratio. A 1:100 model has one ten-thousandth of the real area, and doubling a room's dimensions quadruples its floor space — a frequent source of material-estimating errors.

How do I resize an image without distorting it?

Multiply both width and height by the same factor. To fit a specific width, divide the target width by the original width and apply that factor to the height as well.

Is the golden ratio really used in art and architecture?

Less than commonly claimed. It is a genuine mathematical constant that appears in some natural growth patterns, but most attributions in classical art and architecture are retrospective, and evidence for an inherent aesthetic effect is weak.