# Equivalent Ratio Calculator

Created by Anna Szczepanek, PhD
Reviewed by Davide Borchia
Last updated: Jan 18, 2024

Omni's equivalent ratio calculator will help you solve various problems related to ratios of two or three numbers. In particular, our tool can solve for a missing value in equivalent ratios, i.e., it can solve the equation of the form A : B = x : D or A : x = C : D.
However, before dealing with this type of problems, we shall recall what the equivalent ratios are, go together through an example, and then discuss how to find the equivalent ratio.

Let's dive straight into the definition of equivalent ratios!

## What are equivalent ratios?

Equivalent ratios are two (or more) ratios that express the same proportion. That is, given the numbers A, B, C, D, the ratios A : B and C : D are equivalent if:

A : B = C : D.

In other words, the fractions A/B and C/D must be equal.

To better understand the definition of equivalent ratios, let's discuss an example. Imagine we need 30 sausages and 8 bottles of soda to throw up a barbecue party for 10 friends. In other words, the desired ratio of sausages to soda bottles is

30 sausages : 8 bottles.

If we want to invite as many as 20 people (that would be quite a party, wouldn't it?), we need to double the number of sausages and bottles:

60 sausages : 16 bottles.

On the other hand, if we wanted to invite only the 5 closest friends (half the initial number), we need to divide the initial number of sausages and bottles by 2:

15 sausages : 4 bottles.

We have here three equivalent ratios: they all correspond to the same relationship, but use different quantities (different scale). As you can see, we've obtained them by dividing/multiplying the initial 30 : 8 ratio by 2.

Easy, right? And the good news is that once you've understood this example, learning how to find equivalent ratios is a piece of cake. Here comes the equivalent ratio formula!

## How do I find equivalent ratios?

It follows directly from the definition of equivalent ratios that to find ratios equivalent to a given ratio A : B, you need to multiply or divide both A and B by some non-zero factor. That is, the equivalent ratio formula reads:
A : B = (k × A) : (k × B),
where k is any non-zero real number.

## How do I solve for a missing value in equivalent ratios?

• To solve for x in A : B = C : x, you need to rewrite this problem as fractions: A/B = C/x and solve for x. In an analogous manner solve for other missing values in equivalent ratios.

• To solve for x in A : B : C = D : E : x, you can ignore one pair of non-missing corresponding values. For instance, we can ignore A and D. The problem reduces to the previous case: B : C = E: x, and solve for x as explained above.

As you can see, using the equivalent ratio formula or solving for a missing value in equivalent ratios is not that hard; however, doing it by hand may be time-consuming. Using Omni's calculator is a better idea!

## How to use this equivalent ratio calculator?

Our tool is indispensable if you want to check if two ratios are equivalent or if you need to solve for a missing value in equivalent ratios. Here are the steps to follow:

1. Pick the size of the ratios: do we deal with ratios of 2 numbers or 3 numbers?
2. Input the values that you are given.
3. All the missing values will be immediately determined by our equivalent ratio calculator!

Satisfied with the equivalent ratio calculator? Here are related tools featured by Omni:

## FAQ

### Are 7 : 25 and 3 : 10 equivalent ratios?

No. To see why, multiply the first ratio by 4 and the second ratio by 10. We obtain 28 : 100 and 30 : 100, respectively. Clearly, these ratios are not equal, because their numerators are equal and denominators differ.

### How many equivalent ratios are there for a given ratio?

There are infinitely many ratios equivalent to a given ratio. This is because multiplying the given ratio by any non-zero number yields an equivalent ratio, and there are infinitely many potential multipliers.

Anna Szczepanek, PhD
Ratio of...
two numbers (A : B)
A : B = C : D
A
B
C
D
For other ratio calculations, hit the Advanced mode button below.
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