Ratio Calculator

What is Ratio?

A ratio is a way of comparing two or more quantities to show how much of one there is compared to another. It tells you the relationship between numbers rather than their actual size.

Ratios are usually written with a colon, like 2:3, but they can also be shown as a fraction (2/3) or with the word "to" (2 to 3). For example, if a class has 10 boys and 15 girls, the ratio of boys to girls is 10:15, which simplifies to 2:3. That means for every 2 boys, there are 3 girls.

The key idea is that ratios compare quantities of the same kind, and the order matters. Writing 2:3 is not the same as 3:2.

Ratio Formula

The basic formula for comparing two quantities is:

Here a is the first quantity and b is the second. Both must be in the same unit.

To simplify: divide both numbers by their greatest common factor.
Example: 12:18 ÷ 6 = 2:3

Proportion: when two ratios are equal → a : b = c : d, meaning a × d = b × c
Example: 3:4 = 9:x → 3x = 36 → x = 12

Ratio to percentage: (a ÷ b) × 100

Splitting a total by ratio: add the parts first, then multiply.
Example: $200 in a 3:2 ratio → 200 × 3/5 = $120 and 200 × 2/5 = $80

How to Use This Calculator

To use this Ratio Calculator, follow 3 steps:

How This Calculator Works

Using the ratio calculator takes just a few seconds.

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  Enter your known values. Type the numbers you already have into the input boxes — for example, 3 and 4 in the first ratio, and 9 in the second.
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  Leave the unknown blank. The field you want solved stays empty. The calculator treats it as the missing value.
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  Click Calculate. Hit the button, and the calculator solves for the missing number right away.
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  Review the step-by-step breakdown. Below the answer, you'll see the cross-multiplication formula written out so you can follow how the result was reached.

The calculator also works for simplifying ratios — just enter two numbers, and it reduces them to their lowest terms using the greatest common factor.

Formula & Equations Used

Behind the calculator are a handful of core mathematical rules. Here are the ones used most often:

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  Ratio definition
  a : b = a / b
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  Simplifying a ratio
  a : b = (a / GCD) : (b / GCD)
  Where GCD is the greatest common divisor of a and b.
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  The proportion formula (cross-multiplication)
  a / b = c / d ⟹ a × d = b × c

  From that single identity, you can find any one variable if you have the other three:

  a = (b × c) ÷ d

  b = (a × d) ÷ c

  c = (a × d) ÷ b

  d = (b × c) ÷ a
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  Ratio to fraction
  Part A as a fraction of the whole = a / (a + b)
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  Ratio to percentage
  Percentage of Part A = [a / (a + b)] × 100
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  Scaling up or down
  To scale a ratio by factor k: a : b ⟹ (a × k) : (b × k)
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  Dividing an amount into a ratio
  Share A = Total × [a / (a + b)], Share B = Total × [b / (a + b)]

Example Problems & Step-by-Step Solutions

Here are 3 example problems with step-by-step solutions using this Ratio Calculator:

Ratio Scaling Calculator

A ratio scaling calculator lets you enlarge or reduce a ratio while keeping the proportion exactly the same. You change the size of the numbers, not the relationship between them.

Aspect Ratio Calculator

An aspect ratio calculator works out the relationship between the width and height of an image, video, or screen — and helps you resize it without stretching or squashing the picture.

Aspect ratio describes the proportional relationship between width and height. It is widely used in photography, videography, monitors, and UI design.

Golden Ratio Calculator

A golden ratio calculator works out proportions based on the number phi (φ), which is approximately 1.618. It's used to divide a length into two parts that feel naturally balanced to the eye.

The golden ratio appears in architecture, art composition, logo design, and natural patterns (shell spirals, flower petals, leaf arrangements).

Percentage to Ratio

Converting a percentage into a ratio shows the same information in a different form. A percentage always compares something to 100, while a ratio compares quantities directly to each other. Both describe the same relationship — you're simply changing how it's expressed.

Evaluate Equivalent Ratios

Equivalent ratios are different pairs of numbers that express the same relationship. Just as 1/2 and 2/4 are the same fraction, 1:2 and 2:4 are the same ratio.

Scale Ratio Calculator

A scale ratio calculator converts between the size of a model or drawing and the size of the real object it represents. It's the tool you need whenever something has to be shrunk down or blown up by a fixed factor.

Scale is written as model : real. A scale of 1:100 means one unit on the drawing equals 100 units in real life — so 1 cm on paper represents 1 metre on site.

Divide by Ratio Calculator

A divide by ratio calculator splits a total amount into parts according to a given ratio. Instead of guessing or working through the fractions by hand, you enter the total and the ratio, and the tool returns each share.

Practical Example: Concrete Mix Ratios

Concrete Mix Ratios define the proportion of cement, sand, and gravel before mixing solutions. A standard concrete mix uses a 1 : 2 : 3 ratio — 1 part cement, 2 parts sand, 3 parts gravel. For 1 cubic meter (35.31 cubic feet) of standard concrete, this mix requires approximately 300 kilograms (661.39 pounds) of cement, 600 kg (1322.77 lbs) of sand, and 900 kg (1984.16 lbs) of gravel.

Practical Example: Scaling a Recipe

Scaling a recipe applies the Ratio Calculator to cooking. A cookie recipe calls for flour, sugar, and butter in a ratio of 3 : 2 : 1. When blending spices or adjusting portion counts, multiply each ingredient by the same scale factor to maintain the correct proportions.

Convert Ratio to Fraction

A ratio and a fraction can express the same relationship, but they aren't always interchangeable. The difference comes down to what each one is comparing.

Converting a ratio to a fraction helps compare individual components against the total sum of all parts.