Ratio Calculator

Two modes, two different jobs

Simplify ratio takes a list of two or more terms — separated by colons, commas, or spaces, like 12:18:24 — and reduces every term to lowest whole-number form. It only accepts positive whole numbers; a zero, a decimal, or a negative term in the list is rejected, because a ratio term represents a count or quantity, and those don't come in fractional or negative amounts here.

Solve equivalent ratio works differently: you fill in three of the four boxes (a, b for the first ratio, c, d for the second) and leave exactly one blank, and the tool solves for it using cross multiplication. This side accepts decimals and negative numbers freely, since it's just solving an algebraic equation rather than reducing a physical quantity. The two denominator positions, b and d, can't be zero if you've filled them in, since a ratio with a zero term on that side is undefined.

Simplifying with the greatest common factor

Every term in the ratio is divided by the same number — the greatest common factor of all of them — so the proportion between terms stays identical. For 15:20:25, the GCF is 5 (5 divides 15, 20, and 25, and nothing larger does), so the simplified ratio is 15÷5 : 20÷5 : 25÷5 = 3:4:5.

This extends past two terms by working pairwise: the calculator finds the GCF of the first two terms, then finds the GCF of that result with the third term, and so on. For 15, 20, and 25, that's GCF(15, 20) = 5, then GCF(5, 25) = 5 — the same answer as computing the GCF of all three directly.

Solving with cross multiplication

To find a missing term, cross multiply the two known diagonal values and divide by the remaining known value. For 3:7 = 9:d, d is missing, so d = (7 × 9) ÷ 3 = 63 ÷ 3 = 21. Checking the result: 3 ÷ 7 ≈ 0.4286 and 9 ÷ 21 ≈ 0.4286, so the two ratios are equal.

A frequent slip here is dividing by the wrong known value — with a missing after 3/7 = 9/d, dividing by 9 or 7 instead of 3 gives a nonsense answer. The rule is always: multiply the two values diagonally across from the blank, then divide by whichever known value sits directly across from it.

What a ratio can't tell you on its own

Simplifying only works if the same divisor is applied to every term at once — dividing just one term of 12:18 by 6 to get 2:18 breaks the ratio entirely, since 2:18 (which reduces to 1:9) is not equivalent to 12:18 (which reduces to 2:3). A ratio also carries no information about actual size: 2:3 could mean 2 cups to 3 cups or 2,000 liters to 3,000 liters, so units always have to be tracked separately.

Decimal ratio terms aren't accepted directly in Simplify mode. To simplify 2.5:5, scale both terms up first — multiply each by 2 to get 5:10 — then simplify normally to reach 1:2.

Everyday ratio problems

Ratios describe how two or more quantities relate, which comes up constantly outside the classroom:

• Recipes – scaling a 2:3 flour-to-sugar ratio up for a larger batch keeps the taste and texture consistent
• Screen dimensions – a 16:9 aspect ratio simplifies from pixel counts like 1920:1080
• Concrete and mortar mixes – a 1:2:3 cement-to-sand-to-gravel ratio needs every part scaled together
• Map scales – a 1:24,000 map ratio means 1 inch on paper equals 24,000 inches (about 0.38 miles) in reality
• Financial ratios – a 3:1 debt-to-equity ratio simplifies from figures like $150,000 debt to $50,000 equity
• Classroom staffing – a 24:1 student-to-teacher ratio simplifies from a school reporting 480 students and 20 teachers

Frequently asked questions

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