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Ratio calculator

Make a ratio smaller or find the one missing number in two equal ratios.

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Formula and steps included

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Optional learning Learn how this math works See the formula, definitions, and step-by-step method.

Formula

Ratio and proportion formulas

Equivalent ratios: a:b = c:d when a × d = b × c; Simplified ratio = (a ÷ g):(b ÷ g), where g = GCF(a, b)

A ratio compares two quantities in a fixed order. Dividing both terms by the same nonzero factor changes their size but not the relationship between them.

A proportion means two ratios have the same value. To find one missing number, multiply the two known numbers across from each other and divide by the remaining known number.

How to use the formula

  1. Keep the numbers in order

    Make sure the first and second numbers mean the same thing on both sides.

  2. Simplify with the GCF

    For a single ratio, divide both whole-number terms by their greatest common factor.

  3. Find and check a missing number

    Multiply the two known numbers across from each other, divide by the remaining known number, and check that both ratios now match.

Worked examples

Ratio calculator examples

Simplify a ratio

The biggest shared factor of 18 and 24 is 6, so 18:24 simplifies to 3:4.

Find one number in matching ratios

For 5:8 = x:40, use 5 × 40 = 8x. Then 200 = 8x, so x = 25.

Common questions

Ratio calculator FAQ

What is the difference between a ratio and a proportion?

A ratio compares two quantities. A proportion is an equation stating that two ratios have the same value.

Do ratio terms need the same units?

Convert comparable quantities to the same units before simplifying. A part-to-part ratio can compare different categories, but its labels and order must remain clear.

Can a ratio contain zero?

A ratio can have zero as its first number. Its second number cannot be zero because that would mean dividing by zero. A matching-ratio question must also avoid division by zero.

Does the ratio calculator store my values?

Your values stay in your browser and are not saved by default or uploaded. Use Save on this device to keep them here, or download a backup file.