Ratio Calculator

Simplify a ratio and solve proportions like a:b = c:x for the missing value.

Ratio Calculator

Simplify a ratio and solve proportions like a:b = c:x for the missing value.

A (first term)

B (second term)

Scale A to…

Enter values above and click Calculate — results will appear here with the formula explained.

a : b = c : x ⟹ x = (c × b) ÷ a

How does this work?

A ratio compares two quantities. Simplifying divides both terms by their greatest common divisor, producing the smallest whole-number pair with the same relationship — 16:10 simplifies to 8:5.

Ratios are also used to scale quantities. If you know a:b, scaling a up to some new value c requires scaling b by the same factor: x = c × b ÷ a. This cross-multiplication trick is the basis for recipes, map scales, aspect ratios and mixing instructions.

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What is Ratio?

A ratio compares two quantities. Simplifying divides both terms by their greatest common divisor, producing the smallest whole-number pair with the same relationship — 16:10 simplifies to 8:5. Formula: a : b = c : x ⟹ x = (c × b) ÷ a

Quick Answer

Ratio Calculator computes simplify a ratio and solve proportions like a:b = c:x for the missing value. Formula: a : b = c : x ⟹ x = (c × b) ÷ a. Example: A recipe uses sugar and flour in a 16:10 ratio, simplifying to 8:5.

What it does: Simplify a ratio and solve proportions like a:b = c:x for the missing value.
Formula: a : b = c : x ⟹ x = (c × b) ÷ a
Inputs: A (first term) · B (second term) · Scale A to…
Example: A recipe uses sugar and flour in a 16:10 ratio, simplifying to 8:5.

Calculator Inputs at a Glance

Field	What to enter
A (first term)	e.g. 16
B (second term)	e.g. 10
Scale A to…	Leave blank to just simplify.

All fields use the exact formulas shown below — results include step-by-step breakdowns you can verify by hand.

How to Use This Calculator

1Enter the two terms of your ratio in fields A and B.
2See the simplified form and decimal equivalent immediately.
3Optionally enter a new value for A to solve for the matching B in the scaled ratio.

Formula Used

a : b = c : x ⟹ x = (c × b) ÷ a

A ratio compares two quantities. Simplifying divides both terms by their greatest common divisor, producing the smallest whole-number pair with the same relationship — 16:10 simplifies to 8:5.

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Worked Example

A recipe uses sugar and flour in a 16:10 ratio, simplifying to 8:5. If you use 24 cups of sugar, the flour needed is 24 × 10 ÷ 16 = 15 cups.

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Frequently Asked Questions

QHow do I simplify a ratio?

Divide both terms by their greatest common divisor. For 16:10, the GCD is 2, giving 8:5.

QWhat is the difference between a ratio and a fraction?

A ratio compares two separate quantities (parts to parts); a fraction expresses a part of one whole. 3:2 could become 3/(3+2) = 3/5 when converted into shares of a total.

QCan ratios involve decimals or three terms?

Yes in principle, though this calculator focuses on the classic two-term integer form. Decimal ratios are usually multiplied through until both sides are whole numbers.

Quick Answer

What it does: Simplify a ratio and solve proportions like a:b = c:x for the missing value.

Formula: a : b = c : x ⟹ x = (c × b) ÷ a

Inputs: A (first term) · B (second term) · Scale A to…

Example: A recipe uses sugar and flour in a 16:10 ratio, simplifying to 8:5.

Field

What to enter

A (first term)

e.g. 16

B (second term)

e.g. 10

Scale A to…

Leave blank to just simplify.

Formula Used

a : b = c : x ⟹ x = (c × b) ÷ a

A ratio compares two quantities. Simplifying divides both terms by their greatest common divisor, producing the smallest whole-number pair with the same relationship — 16:10 simplifies to 8:5.

Frequently Asked Questions

QHow do I simplify a ratio?

Divide both terms by their greatest common divisor. For 16:10, the GCD is 2, giving 8:5.

QWhat is the difference between a ratio and a fraction?

A ratio compares two separate quantities (parts to parts); a fraction expresses a part of one whole. 3:2 could become 3/(3+2) = 3/5 when converted into shares of a total.

QCan ratios involve decimals or three terms?

Yes in principle, though this calculator focuses on the classic two-term integer form. Decimal ratios are usually multiplied through until both sides are whole numbers.