Ratio Calculator
Simplify a ratio to its lowest terms, solve a proportion (A:B = C:x), scale a ratio to hit a target total, or convert between ratio, fraction and percentage. 18:24 simplifies to 3:4 — divide both terms by their greatest common divisor, 6, shown step by step below.
3 : 4
Simplified ratio
GCD(18, 24) = 6 — divide both terms by it.
Show Euclid's algorithm (how the GCD was found)
Simplifying uses the greatest common divisor (Euclid's algorithm); solving a proportion uses cross-multiplication. How we calculate →
Simplifying a ratio with the greatest common divisor (GCD)
A ratio is in its simplest form when both terms share no common factor bigger than 1. To simplify 18:24, find the greatest common divisor of both numbers using Euclid's algorithm (repeated division: divide the larger by the smaller, then repeat with the divisor and the remainder, until the remainder is 0 — the last nonzero remainder is the GCD): 18 = 0 × 24 + 18; 24 = 1 × 18 + 6; 18 = 3 × 6 + 0. That gives GCD = 6.
Divide both terms by the GCD: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18:24 simplifies to 3:4.
Solving a proportion: A:B = C:x
A proportion sets two ratios equal to each other. When three of the four terms are known, cross-multiplication solves for the fourth: A:B = C:x means A × x = B × C, so x = (B × C) ÷ A. For 2:3 = 12:x, that's 2 × x = 3 × 12 → x = (3 × 12) ÷ 2 = 18
This is the same math behind scaling a recipe, converting units, or figuring out how much of an ingredient you need for a different batch size — any time two quantities stay in a fixed proportion to each other.
Scaling a ratio to hit a specific total
Sometimes you know the ratio between two groups and a target grand total, and need the actual amount in each group. For a 2:3 ratio scaled to a total of 25: Step 1 — Total parts in the ratio: 2 + 3 = 5 Step 2 — Scale factor: 25 ÷ 5 = 5 Step 3 — Scaled A: 2 × 5 = 10 Step 4 — Scaled B: 3 × 5 = 15
This pattern shows up constantly — splitting a bill, mixing a solution in a fixed ratio to make a target volume, or dividing a budget between departments according to an agreed ratio.
Converting between ratio, fraction, and percentage
A ratio A:B can be rewritten as the fraction A ÷ (A + B) of the whole, which converts directly to a decimal and then a percentage. For a 3:1 ratio: Step 1 — Total parts: 3 + 1 = 4 Step 2 — Fraction (A of the total): 3/4, simplified to 3/4 Step 3 — Decimal: 3 ÷ 4 = 0.75 Step 4 — Percentage: 0.75 × 100 = 75%
Going the other direction — from a percentage back to a ratio — works in reverse: write the percentage as a fraction over 100, then simplify using the GCD method above to get the smallest whole-number ratio.
Frequently asked questions
How do I simplify a ratio?
Find the greatest common divisor (GCD) of both numbers using Euclid's algorithm, then divide both terms by it. 18:24 has a GCD of 6, so it simplifies to 3:4.
What is the GCD (greatest common divisor) and how is it found?
The GCD is the largest number that divides both terms evenly. Euclid's algorithm finds it by repeated division: divide the larger number by the smaller, then repeat with the divisor and the remainder, until the remainder hits 0 — the last nonzero remainder is the GCD. For 18 and 24, that gives GCD = 6.
How do I solve a proportion like A:B = C:x?
Cross-multiply: A × x = B × C, then solve for x by dividing: x = (B × C) ÷ A. For 2:3 = 12:x, x = (3 × 12) ÷ 2 = 18.
How do I scale a ratio to a target total?
Add the parts of the ratio together to get the total number of "shares," divide your target total by that to get a scale factor, then multiply each term of the ratio by that factor. A 2:3 ratio scaled to 25 becomes 10:15.
How do I convert a ratio to a percentage?
Divide the first term by the sum of both terms to get a decimal, then multiply by 100. A 3:1 ratio is 0.75 as a decimal, or 75% — meaning the first part makes up that share of the whole.
What does a ratio of 1:1 mean?
A 1:1 ratio means both quantities are exactly equal — each makes up half (50%) of the total. It's already in simplest form since the GCD of any number and itself is that number.
Is 4:8 the same ratio as 1:2?
Yes. 4:8 simplifies to 1:2 by dividing both terms by their GCD of 4 — they represent the same proportional relationship, just written with different-sized numbers.
Researched & verified by the Calcuris Data & Research Team. How we build and check our tools →