Find a missing value
3:4 = 600:x. Cross multiply: 3x = 4 × 600 = 2,400, so x = 2,400 ÷ 3 = 800.
Ratio Calculator — Simplify, Scale and Solve Ratios
Choose a ratio task
Accepted formats: integers, decimals, scientific notation (2e3), and fractions (3/4). Keep units consistent. Negative values are allowed where algebraically meaningful.
Enter both terms of A:B. Decimal and fraction terms are normalized before the ratio is reduced.
Enter three values in A:B = C:D and leave exactly one field blank for x.
Optional: choose the unknown manually
Multiply both terms by the same scale factor to produce an equivalent ratio.
For example, use 2.5 to make a recipe 2½ times as large.
Compare A:B with C:D using simplified forms and exact cross products.
Split a total, including a signed algebraic total, using two or three nonnegative ratio weights.
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Result
Step-by-step working
Optional visual view for the first two positive terms
Use with care: the pie and parts bar are meaningful only when the two values are parts of the same whole. They may mislead for dimensions, rates, negative values, or quantities with different units. The rectangle is an aspect-ratio preview.
Term ATerm B
Parts-of-whole pie
Term A and term B
Aspect preview
Width = B, height = A
Calculate a ratio with two positive terms to update this text alternative.
Worked ratio examples
Simplify 12:18
The greatest common factor is 6. Divide both terms by 6: 12 ÷ 6 : 18 ÷ 6 = 2:3.
Scale a recipe
A 2:3 flour-to-liquid recipe scaled by 2.5 becomes 2 × 2.5 : 3 × 2.5 = 5:7.5.
Divide an amount
Split 120 in 2:3. There are 5 shares; each is 120 ÷ 5 = 24. The amounts are 48 and 72.
Preserve image dimensions
For 16:9 at a width of 1,920 px, 16:9 = 1,920:x. Then x = 9 × 1,920 ÷ 16 = 1,080 px.
Ratio concepts that prevent common mistakes
Part-to-part vs part-to-whole
In 2 red to 3 blue, 2:3 is part-to-part. Red is 2 out of 5 total, so its part-to-whole ratio is 2:5 and its share is 40%.
Proportions and equivalent ratios
A proportion states that two ordered ratios are equal. Multiplying every term of 2:3 by 5 produces the equivalent ratio 10:15.
Rates and matching units
A rate compares quantities with different units, such as miles per hour. Match corresponding units and their order when setting up a proportion.
Scale factor
The scale factor is the common multiplier between equivalent ratios. From 3:4 to 600:800, it is 600 ÷ 3 = 800 ÷ 4 = 200.
Order matters
A:B is generally not the same as B:A. Label terms, preserve their order, and do not compare measurements until their units are compatible.
When a pie chart applies
Use a pie only when positive A and B are parts of one whole. Dimensions, rates, unrelated units, and signed values need algebra or a labeled comparison instead.
Missing-value formulas
For A:B = C:D, where ratio denominators are nonzero: A = BC/D, B = AD/C, C = AD/B, and D = BC/A.
Method and review
Maintained by:
Starlight Tools Editorial Team
Calculation review:
Starlight Tools Mathematics Review
Last reviewed:
Calculation method: input strings are parsed as rational values. Simplification uses integer normalization and greatest common divisors, so terminating decimals and common fractions reduce reliably. Other answers are calculated from the displayed formulas and rounded only for presentation at the precision you choose.
References: OpenStax, Ratios and Rate and Solve Proportions and Their Applications. These references describe decimal ratio normalization, equivalent ratios, and cross-product verification.
Everything runs locally in your browser; calculation inputs are not uploaded.
Ratio calculator FAQs
How do I simplify a ratio?
Divide every term by the greatest common factor. For decimals, first multiply all terms by the same power of 10 to make integers; for example, 1.5:2.5 becomes 15:25, then 3:5.
How do I solve a missing value in a proportion?
Write the equality as A:B = C:D, or A/B = C/D, then use A × D = B × C. Isolate the blank term with A = BC/D, B = AD/C, C = AD/B, or D = BC/A.
Does ratio order matter?
Yes. A ratio of 2 red to 3 blue is 2:3; reversing it gives 3:2, which answers a different comparison. Keep the term order and units consistent on both sides of a proportion.
How can I tell whether two ratios are equivalent?
For A:B and C:D, with B and D nonzero, compare the cross products A × D and B × C. The ratios are equivalent exactly when those products are equal.
How do I convert a ratio to fractions or percentages?
For a two-part ratio A:B, the fractions of the combined whole are A/(A+B) and B/(A+B). Multiply each fraction by 100 for its percentage, provided the terms represent parts of the same whole and their sum is not zero.
How do I divide a total by a ratio?
Add the ratio parts, divide the total by that sum to find one share, then multiply that share by each ratio term. To divide 120 in 2:3, one share is 120/5 = 24, so the parts are 48 and 72.
Can I enter decimals, fractions or scientific notation?
Yes. The calculator accepts integers, decimals such as 1.5, scientific notation such as 2e3, and common fractions such as 3/4. A fraction denominator cannot be zero.
What happens with zero or negative values?
Negative and zero terms can be algebraically valid, but B and D cannot be zero in A/B = C/D. Division weights must be nonnegative and not all zero. Pie and parts visuals appear only for two positive parts because dimensions and parts of a whole are normally positive.