Ratio Calculator

Ratio tools

Solve or scale a ratio

Fill any three values in A : B = C : D and leave one blank, or scale both terms of a ratio by the same factor.

Proportion solver

Enter three known values

The blank field is the unknown. All three known values must be positive.

Completed proportion

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A is the missing value. The highlighted answer makes both ratios equal.

Cross multiplicationA × D = B × CA = (B × C) ÷ D = (10 × 3) ÷ 5 = 6

Simplified A : B: 3 : 5
Unit forms: 1 : 1.66666666667or0.6 : 1
Equality check: 0.6 = 0.6

A : B as shares of A + BPart-to-whole view of the left-hand ratio

A · 37.5%B · 62.5%

Ratio and proportion guide

Solve, scale, and interpret ratios with confidence

A ratio compares two quantities in a stated order; a proportion says that two ratios are equal. Enter any three terms of A:B = C:D to solve the fourth, then use the checks below to confirm that the result matches the intended scale and meaning.

Step-by-step guide · Ratio and proportion guide

Solve 3:4 = 600:D by cross multiplication

Ratio: A:B means A/B
Proportion: A:B = C:D means A/B = C/D
Cross-product check: A×D = B×C, with B and D nonzero

Preserve the correspondence
Write 3:4 = 600:D as 3/4 = 600/D. The first terms, 3 and 600, correspond; the second terms, 4 and D, correspond. Leaving D in the fourth position preserves what each number represents.
Set the cross products equal
Cross multiply to obtain 3×D = 4×600, so 3D = 2,400. This is valid because both denominators are nonzero.
Isolate and verify the missing term
Divide both sides by 3: D = 800. Substitution gives 3/4 = 600/800 = 0.75, and the scale factor from 3 to 600 is 200 while 4×200 = 800. Both checks confirm 3:4 = 600:800.

Solve, scale, and interpret ratios with confidence: A ratio compares two quantities in a stated order; a proportion says that two ratios are equal. Enter any three terms of A:B = C:D to solve the fourth, then use the checks below to confirm that the result matches the intended scale and meaning.

A ratio compares quantities; a proportion equates two comparisons

The ratio A:B compares A with B in that order and can also be written A/B or ‘A to B.’ Labels matter: a ratio of 3 red markers to 4 blue markers is red:blue = 3:4, while blue:red = 4:3. When the quantities use the same dimension, convert them to a common unit before comparing; 1 meter:25 centimeters becomes 100:25 = 4:1.

A proportion is an equation asserting that two ratios represent the same comparison: A:B = C:D is equivalent to A/B = C/D, provided B and D are not zero. Equal fractions have equal cross products, so A×D = B×C. That rule lets this ratio calculator solve whichever one of A, B, C, or D is missing; there is no need to move a basic unknown-ratio problem to a different page.

Solve 3:4 = 600:D by cross multiplication

Preserve the correspondence
Write 3:4 = 600:D as 3/4 = 600/D. The first terms, 3 and 600, correspond; the second terms, 4 and D, correspond. Leaving D in the fourth position preserves what each number represents.
Set the cross products equal
Cross multiply to obtain 3×D = 4×600, so 3D = 2,400. This is valid because both denominators are nonzero.
Isolate and verify the missing term
Divide both sides by 3: D = 800. Substitution gives 3/4 = 600/800 = 0.75, and the scale factor from 3 to 600 is 200 while 4×200 = 800. Both checks confirm 3:4 = 600:800.

Equivalent scaling and simplest form answer different questions

Apply the same positive scale factor to both terms
Multiplying or dividing both terms by the same positive number preserves the ratio. To shrink 250:280 by 2.5, divide both terms: 250÷2.5 = 100 and 280÷2.5 = 112, giving 100:112. The reverse check multiplies both new terms by 2.5 to recover 250:280.
Reduce further only when simplest integers are wanted
The scaled result 100:112 is correct for the requested 2.5-times shrink, but it is not in simplest whole-number form. Divide both terms by their greatest common factor, 4, to obtain 25:28. The greatest common factor calculator can identify that shared factor for larger integers.
Keep the requested scale separate from reduction
The ratios 250:280, 100:112, and 25:28 are all equivalent because each equals 25/28. Use 100:112 when dimensions must be exactly 2.5 times smaller; use 25:28 when the task asks only for the simplest ratio.

Part-to-part and part-to-whole percentages use different denominators

Paint ratio: compare blue directly with white

For blue:white = 5:2, every five measures of blue correspond to two measures of white. Blue is 5/2 = 2.5 times as much as white, or 250% of the white amount. Reversing the question gives white:blue = 2:5.

Blue share: compare blue with the whole blend

The whole contains 5+2 = 7 parts. Blue therefore represents 5/7 of the blend, about 71.43%—not 5/2 and not 250% of the total. The fraction calculator keeps that part-to-whole share exact when a decimal is unnecessary.

White share: use the same seven-part whole

White represents 2/7 of the blend, about 28.57%. The two part-to-whole shares add to 100%, while the original 5:2 notation remains a part-to-part comparison.

Common ratio applications keep the same structure in different settings

Recipes and mixtures

A cement, paint, or food ratio preserves composition when every ingredient is scaled by the same factor. Add the terms only when converting recipe parts into shares of a known total.

Maps, models, and drawings

A scale of 1:50 means one unit on the drawing represents 50 of the same units in reality. Convert units first, then multiply or divide using the stated direction of the scale.

Screen and video aspect ratios

An aspect ratio compares width with height. Both 1920:1080 and 1280:720 reduce to 16:9, so they have the same rectangular shape even though their pixel counts and resolutions differ.

Check the setup before trusting a ratio result

Label all four positions before entering numbers. A:B = C:D requires A to correspond with C and B to correspond with D; swapping only one pair changes the proportion.
Leave exactly one term unknown, keep B and D nonzero, and reject quantities that the context makes impossible, such as negative paint volume or a zero-width screen.
Convert like quantities to a common unit before simplifying. A ratio of 1 liter to 250 milliliters is 1000:250 = 4:1, not 1:250.
For scaling, multiply or divide every term by the same factor. For a proportion, substitute the result and confirm that A×D and B×C agree; unequal cross products expose an order or arithmetic error.
Keep full precision until the final display, then round for the context. Rounding an intermediate scale factor can make ratios that should be equivalent fail the cross-product check.
Name the percentage denominator explicitly: another part for a part-to-part comparison, or the sum of all parts for a part-to-whole share. If the final repeating decimal needs a declared display precision, use the rounding calculator; the same numerator can otherwise produce very different percentages.

Important limitations

Inputs must be positive finite numbers. A zero denominator is undefined, negative terms and multi-part ratios are outside this tool, and rounded real-world measurements can make mathematically equivalent ratios look slightly different.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

Ratio and proportion guide

Solve, scale, and interpret ratios with confidence

Step-by-step guide · Ratio and proportion guide

Solve 3:4 = 600:D by cross multiplication

Ratio: A:B means A/B
Proportion: A:B = C:D means A/B = C/D
Cross-product check: A×D = B×C, with B and D nonzero

Preserve the correspondence
Write 3:4 = 600:D as 3/4 = 600/D. The first terms, 3 and 600, correspond; the second terms, 4 and D, correspond. Leaving D in the fourth position preserves what each number represents.
Set the cross products equal
Cross multiply to obtain 3×D = 4×600, so 3D = 2,400. This is valid because both denominators are nonzero.
Isolate and verify the missing term
Divide both sides by 3: D = 800. Substitution gives 3/4 = 600/800 = 0.75, and the scale factor from 3 to 600 is 200 while 4×200 = 800. Both checks confirm 3:4 = 600:800.

A ratio compares quantities; a proportion equates two comparisons

Solve 3:4 = 600:D by cross multiplication

Preserve the correspondence
Write 3:4 = 600:D as 3/4 = 600/D. The first terms, 3 and 600, correspond; the second terms, 4 and D, correspond. Leaving D in the fourth position preserves what each number represents.
Set the cross products equal
Cross multiply to obtain 3×D = 4×600, so 3D = 2,400. This is valid because both denominators are nonzero.
Isolate and verify the missing term
Divide both sides by 3: D = 800. Substitution gives 3/4 = 600/800 = 0.75, and the scale factor from 3 to 600 is 200 while 4×200 = 800. Both checks confirm 3:4 = 600:800.

Equivalent scaling and simplest form answer different questions

Apply the same positive scale factor to both terms
Multiplying or dividing both terms by the same positive number preserves the ratio. To shrink 250:280 by 2.5, divide both terms: 250÷2.5 = 100 and 280÷2.5 = 112, giving 100:112. The reverse check multiplies both new terms by 2.5 to recover 250:280.
Reduce further only when simplest integers are wanted
The scaled result 100:112 is correct for the requested 2.5-times shrink, but it is not in simplest whole-number form. Divide both terms by their greatest common factor, 4, to obtain 25:28. The greatest common factor calculator can identify that shared factor for larger integers.
Keep the requested scale separate from reduction
The ratios 250:280, 100:112, and 25:28 are all equivalent because each equals 25/28. Use 100:112 when dimensions must be exactly 2.5 times smaller; use 25:28 when the task asks only for the simplest ratio.

Part-to-part and part-to-whole percentages use different denominators

Paint ratio: compare blue directly with white

Blue share: compare blue with the whole blend

White share: use the same seven-part whole

White represents 2/7 of the blend, about 28.57%. The two part-to-whole shares add to 100%, while the original 5:2 notation remains a part-to-part comparison.

Common ratio applications keep the same structure in different settings

Recipes and mixtures

A cement, paint, or food ratio preserves composition when every ingredient is scaled by the same factor. Add the terms only when converting recipe parts into shares of a known total.

Maps, models, and drawings

A scale of 1:50 means one unit on the drawing represents 50 of the same units in reality. Convert units first, then multiply or divide using the stated direction of the scale.

Screen and video aspect ratios

An aspect ratio compares width with height. Both 1920:1080 and 1280:720 reduce to 16:9, so they have the same rectangular shape even though their pixel counts and resolutions differ.

Check the setup before trusting a ratio result

Label all four positions before entering numbers. A:B = C:D requires A to correspond with C and B to correspond with D; swapping only one pair changes the proportion.
Leave exactly one term unknown, keep B and D nonzero, and reject quantities that the context makes impossible, such as negative paint volume or a zero-width screen.
Convert like quantities to a common unit before simplifying. A ratio of 1 liter to 250 milliliters is 1000:250 = 4:1, not 1:250.
For scaling, multiply or divide every term by the same factor. For a proportion, substitute the result and confirm that A×D and B×C agree; unequal cross products expose an order or arithmetic error.
Keep full precision until the final display, then round for the context. Rounding an intermediate scale factor can make ratios that should be equivalent fail the cross-product check.
Name the percentage denominator explicitly: another part for a part-to-part comparison, or the sum of all parts for a part-to-whole share. If the final repeating decimal needs a declared display precision, use the rounding calculator; the same numerator can otherwise produce very different percentages.

Enter three known values

Preserve the correspondence

Set the cross products equal

Isolate and verify the missing term

A ratio compares quantities; a proportion equates two comparisons

Solve 3:4 = 600:D by cross multiplication

Equivalent scaling and simplest form answer different questions

Part-to-part and part-to-whole percentages use different denominators

Paint ratio: compare blue directly with white

Blue share: compare blue with the whole blend

White share: use the same seven-part whole

Common ratio applications keep the same structure in different settings

Recipes and mixtures

Maps, models, and drawings

Screen and video aspect ratios

Check the setup before trusting a ratio result

Important limitations

Enter three known values

Preserve the correspondence

Set the cross products equal

Isolate and verify the missing term

A ratio compares quantities; a proportion equates two comparisons

Solve 3:4 = 600:D by cross multiplication

Equivalent scaling and simplest form answer different questions

Part-to-part and part-to-whole percentages use different denominators

Paint ratio: compare blue directly with white

Blue share: compare blue with the whole blend

White share: use the same seven-part whole

Common ratio applications keep the same structure in different settings

Recipes and mixtures

Maps, models, and drawings

Screen and video aspect ratios

Check the setup before trusting a ratio result