Free Online Ratio Calculator

This ratio calculator simplifies ratios, solves for a missing value, checks whether two ratios are equivalent, and scales a ratio up or down — all in one tool. It works with both 2-term (A:B) and 3-term (A:B:C) ratios, and shows how each answer was worked out.

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Ratio Calculator

Enter 2 values (A and B, or C and D) to simplify. Enter 3 values to solve the missing one. Enter all 4 to check if the ratios are equivalent.

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Enter a full triple (A,B,C or D,E,F) plus 0 or 1 value from the other triple, or all 6 to check equivalence.

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Which Mode Should I Use?

ModeUse It To
A:B = C:DSimplify a ratio, solve a missing value, or check if 2 ratios match
A:B:C = D:E:FSame, but for 3-term ratios (e.g. cement:sand:gravel)
Scale A:BMultiply or divide a 2-term ratio by a factor
Scale A:B:CMultiply or divide a 3-term ratio by a factor

Result

Choose a mode, fill in your values, and your answer will appear here.

What Is a Ratio?

A ratio compares the size of two or more quantities against each other. If a fruit bowl has 3 apples for every 2 oranges, that's a ratio of 3:2 — it tells you the relationship between the two counts without needing to know the total number of pieces of fruit.

How to Simplify a Ratio

Simplifying a ratio works exactly like simplifying a fraction — divide every term by their greatest common factor (GCF) until nothing but 1 divides evenly into all of them.

12 : 18 → GCF is 6 → 12÷6 : 18÷6 = 2 : 3

If a ratio is already fully simplified (its GCF is 1), there's nothing left to reduce — in that case this calculator shows you an equivalent ratio instead, by multiplying both terms by 2.

How to Solve for a Missing Ratio Value

Two equivalent ratios form a proportion, and every proportion follows one simple rule: cross-multiplying both sides always gives equal results. That rule is what lets you solve for any single missing value once you know the other three.

A : B = C : D   ⇒   A × D = B × C

For example, given 2 : 5 = 6 : D, solve for D:

2 × D = 5 × 6 → D = 30 ÷ 2 = 15

How to Scale a Ratio

Scaling means multiplying (or dividing) every term of a ratio by the same number, which keeps the relationship between the parts exactly the same. This comes up constantly in real life — think paint mixing ratios, concrete mixes, or resizing a recipe.

Say a paint mix uses a 2:5:1 ratio of red, white and blue, and you need triple the amount for a bigger job:

2 × 3 : 5 × 3 : 1 × 3 = 6 : 15 : 3

Checking If Two Ratios Are Equivalent

To check whether A:B equals C:D, cross-multiply both sides. If A×D equals B×C, the ratios are equivalent. If they don't match, whichever side gives the bigger product tells you which ratio represents the larger proportion.

Turning a Ratio Into a Fraction

A part-to-part ratio can be rewritten as fractions of the whole by adding up all the parts to get the denominator. For a ratio of 1:3, the whole is 1+3=4, so the first part is 1/4 of the total and the second part is 3/4.

Frequently Asked Questions (FAQs)

A fraction always compares a part to the whole, while a ratio can compare a part to another part (like 3 apples to 2 oranges) without referring to the total at all. Every ratio can be converted into a fraction of the whole, but not every fraction started life as a ratio.

If your ratio's terms share no common factor other than 1, it's already in its simplest form and can't be reduced any further. In that case, the calculator shows an equivalent ratio (double the original) so you still get a second, matching pair of numbers to work with.

Decimals work fine for solving, evaluating and scaling. Simplifying to lowest whole-number terms works best with whole numbers, since finding a common factor for decimal values isn't mathematically defined the same way.

Enter a complete triple (either A, B, C or D, E, F), then one matching value from the other triple to solve for the remaining two. Enter all 6 values instead if you just want to check whether the two triples are equivalent.

Concrete mixing is a classic one — a common cement:sand:gravel ratio is 1:2:3, and scaling it up or down lets you work out exactly how much of each material you need for any size of batch.

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