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Ratio Calculator

Simplify ratios to lowest terms, solve for a missing value in a proportion, scale a ratio to a given total, or compare multiple ratios. Enter any ratio or proportion problem and get the answer with full working shown.

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Ratios can be whole numbers or decimals. For recipe scaling, enter the original ratio and the desired total to get each ingredient amount.

Ratio Calculator

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    Step-by-Step Working

    Scaled Ratios Table

    "The golden ratio (1:1.618…) appears in the proportions of the Parthenon, the spiral of a nautilus shell, and the arrangement of seeds in a sunflower. It is the most studied ratio in mathematics."

    — Mathematics in Nature

    How ratios work

    A ratio compares two or more quantities. 3:4 means for every 3 of one thing, there are 4 of another. Ratios are simplified by dividing all parts by their greatest common factor, exactly like simplifying fractions. 6:8 simplifies to 3:4 (divide both by 2).

    A proportion says two ratios are equal: 3:4 = 9:12. To solve for a missing value, use cross-multiplication: if 3:4 = x:12, then 3×12 = 4×x, so x = 36/4 = 9.

    Scaling a ratio to a total is common in cooking and mixing. If the ratio is 2:3 (total 5 parts) and you want to make 500g total, each part is 100g, so you need 200g and 300g.

    Ratio FAQs

    What is the golden ratio?

    The golden ratio φ = (1+√5)/2 ≈ 1.61803… is the ratio where a:b = (a+b):a. It appears throughout nature, art, and architecture. A rectangle whose sides are in the golden ratio is considered aesthetically optimal by many designers and artists.

    How do you solve a proportion?

    Given a:b = c:d, cross-multiply to solve for any missing value. If a:b = c:?, then ? = b×c/a. This works because equal ratios have equal cross-products: a×d = b×c. Example: 2:5 = 8:?, so ? = 5×8/2 = 20. Check: 2:5 = 8:20 = 0.4 ✓.

    What is the difference between a ratio and a fraction?

    A fraction represents a part of a whole (3/4 means 3 out of 4 equal parts). A ratio compares two separate quantities (3:4 means 3 of one thing vs. 4 of another). Every fraction can be written as a ratio (3/4 = 3:4) but ratios don’t always represent parts of a whole.

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