Ratio Calculator

About this Ratio Calculator

The Ratio Calculator reduces two values to the smallest whole-number ratio when possible. Ratios are useful for recipes, maps, screen dimensions, mixtures, comparisons and many everyday proportional relationships.

Simplifying a ratio to its smallest whole-number form makes it far easier to compare against other ratios at a glance, which is why recipe scaling, aspect ratios in photography and video, and mixing proportions in construction or chemistry are all commonly expressed in simplified ratio form.

For related tasks, try Fraction Calculator, Proportion Calculator or Percentage Change Calculator.

How the calculation works

For whole-number inputs, both sides are divided by their greatest common divisor. Decimal inputs are scaled before reduction so common practical ratios can still be simplified.

How to use it

1. Enter the first value in the ratio.
2. Enter the second value.
3. Calculate to see the simplified ratio and first-to-second decimal.

Practical example

A ratio of 20 to 30 simplifies to 2:3 after both values are divided by 10.

A ratio of 16:9, the standard widescreen aspect ratio, is already in simplest form since 16 and 9 share no common factors other than 1, whereas a ratio of 20:15 simplifies down to that same relationship pattern at 4:3.

Things to double-check

A ratio and a fraction represent related but distinct ideas: a ratio of 3:4 compares two separate quantities to each other, while the fraction 3/4 usually represents a part relative to a whole; converting between the two requires knowing whether the ratio's two numbers together make up the whole or are being compared independently.

Simplifying a ratio

To simplify a ratio, divide both numbers by their greatest common divisor. The ratio 24 to 36 has a GCD of 12, so it simplifies to 2 to 3. As a decimal, 24 divided by 36 is about 0.667, which tells you the first quantity is two thirds of the second. Simplified ratios are easier to compare and to remember, which is why recipes, maps and design specifications use them.

Sharing in a ratio

Ratios are also used to split amounts. To share 900 in the ratio 2 to 3 to 4, add the parts to get 9, divide 900 by 9 to get 100 per part, and the shares are 200, 300 and 400. The method works for any number of parts, such as dividing profit between partners in proportion to what each invested. Check your answer by adding the shares to confirm they match the total.

Common ratios in daily life

Screens use 16 to 9 and 4 to 3 aspect ratios, coffee is often brewed at about 1 part coffee to 15 or 16 parts water by weight, and paint tints, cement mixes and cleaning solutions are specified in ratios. When you follow a mix ratio, make sure the parts use the same unit, such as weight or volume, otherwise the mixture will be off. Photographers and designers check the ratio before cropping so the image keeps its shape.

Ratios, fractions and percentages

A ratio of 2 to 3 is the same as saying the first part is 2/5 of the total and the second part is 3/5. As percentages, that is 40 percent and 60 percent. Converting between these forms is useful when a problem is stated one way and you need the other. Remember that a ratio compares two parts, while a fraction compares one part with the whole.

Resizing screens and images

Aspect ratios keep a picture from stretching. A 16 to 9 image that is 1,920 pixels wide is 1,080 tall, and scaled to 1,280 wide it should be 720 tall. A 4 to 3 image at 1,024 wide is 768 tall. To find the missing side, multiply the known side by the other half of the ratio and divide by the first half. Photographers, video editors and web designers use this to crop and resize without distortion, and it also works for scaling drawings, maps and models.

Worked example: a mixing ratio

A mix for concrete is given as 1 part cement, 2 parts sand and 4 parts gravel by volume. The total is 7 parts. To make 0.7 cubic metres of mix, one part is 0.1 cubic metres, so you need 0.1 of cement, 0.2 of sand and 0.4 of gravel. In practice, the dry materials take up more space than the finished concrete, so builders often allow about 50 percent more dry volume. The ratio itself, though, tells you the relative amounts, and the calculator helps you simplify a mix such as 150 to 300 to 600 to the simple form 1 to 2 to 4.

Ratios in finance and business

Business uses ratios to judge health. A company with 120,000 of debt and 80,000 of equity has a debt-to-equity ratio of 3 to 2, or 1.5. The current ratio compares what a company owns in the short term with what it owes soon, and a figure above 1 suggests it can cover its bills. Price-to-earnings compares a share price with profit per share. Ratios are useful because they make companies of different sizes comparable, but they depend on how the inputs are measured, so compare firms in the same industry and over the same period.

Special ratios in nature and paper

Some ratios appear in design and in nature. The golden ratio, about 1.618 to 1, is often described in art and architecture, though claims about its appeal are often exaggerated. The A series of paper sizes uses the ratio 1 to the square root of 2, about 1 to 1.414, so that folding a sheet in half gives a smaller sheet of the same shape. An A4 sheet is 210 by 297 millimetres. Screens use 16 to 9, cameras often use 3 to 2, and old televisions used 4 to 3. Knowing the ratio lets you crop and resize without distortion.

Comparing ratios

To compare two ratios, turn them into fractions or decimals. The ratio 3 to 5 is 0.6 and 4 to 7 is about 0.571, so the first is larger. You can also cross multiply: 3 times 7 is 21 and 4 times 5 is 20, so 3 to 5 is larger. For sharing, remember to add the parts: a ratio of 3 to 5 means the first share is 3/8 of the total and the second 5/8. When a problem mixes ratios with percentages, convert everything to the same form first. Writing the ratio with labels, such as boys to girls, keeps the order clear.

Key terms explained

A ratio compares quantities, and its terms are the numbers in it. Equivalent ratios have the same relationship, like 1 to 2 and 3 to 6, and the simplest form has no common factor. A part-to-part ratio compares groups with each other, while a part-to-whole ratio compares a group with the total. A rate is a ratio with different units, such as kilometres per hour. A proportion states that two ratios are equal, the aspect ratio gives width to height, and the scale factor links a model with the original.

Rules of thumb and quick checks

To simplify a ratio, divide each term by the greatest common divisor. To convert a part-to-part ratio into shares, add the parts to find the total: a ratio of 3 to 2 means 3/5, or 60 percent, and 2/5, or 40 percent. To scale a recipe or mix, multiply every term by the same factor. Always keep the order of the terms consistent with their labels, and check that the shares add up to the total.

Frequently asked questions