Ratio Calculator
Solve a proportion, reduce a ratio to lowest terms, or scale one up or down — pick a tab, enter your numbers, get the answer instantly.
Enter any three values, choose which one to solve for, then calculate.
Solve for
The 1 : n form needs a non-zero first term.
Tap a result to copy it
Three ratio problems, one calculator
Almost every real-world ratio question is one of three shapes: you know three parts of a proportion and need the fourth, you have a messy ratio and want it in its simplest form, or you have a ratio and need it bigger or smaller while keeping the same shape. This calculator gives each shape its own tab so you never have to rearrange the algebra by hand.
Which tab answers your question
- Solve proportion — you know A, B, and C in "A is to B as C is to what," and need the missing fourth value. Recipe scaling, unit conversion, and "if X costs this much, how much do Y cost" questions all reduce to this.
- Simplify ratio — you have a ratio like 24:36 and want the smallest whole-number version (2:3), plus its 1:n form for comparing against map scales or mixing ratios.
- Scale ratio — you have a ratio and a multiplier and want both terms scaled up or down together, like doubling a recipe or blowing up a 16:9 frame to a specific pixel size.
The math behind each tab
Solve proportion: a proportion A:B = C:D is really the equation A ÷ B = C ÷ D. Cross-multiplying clears the fractions: A × D = B × C. Whichever term is unknown, isolate it by dividing: for example, solving for D gives D = (B × C) ÷ A.
Simplify ratio: divide both terms by their greatest common divisor (GCD), found with the Euclidean algorithm (repeatedly replacing the larger number with the remainder of dividing it by the smaller, until the remainder is 0). Decimal terms are first scaled up to whole numbers so the same method still applies.
Scale ratio: multiply both terms by the same factor. Because the two terms grow by an identical amount, the simplified ratio — the shape — never changes, only the size of each part.
Worked examples
Example 1 — recipe scaling (Solve proportion). A recipe for 8 servings needs 12 oz of flour. You want to cook for 6 people. Enter A=8, B=12, C=6, solve for D: D = (12 × 6) ÷ 8 = 9 oz.
Example 2 — reducing a ratio (Simplify ratio). A survey shows 24 people prefer tea to 36 who prefer coffee. Enter 24:36 and the tool reduces it to 2:3 — for every 2 tea drinkers there are 3 coffee drinkers — plus 1 : 1.5 in 1:n form.
Example 3 — a map scale (Simplify ratio, 1:n form). A distance of 4 cm on a map corresponds to 2.1 km (210,000 cm) in reality. Enter 4:210000 and the 1:n result reads 1:52,500 — a scale you can now compare directly against a printed 1:50,000 map.
Example 4 — enlarging an aspect ratio (Scale ratio). A 16:9 screen ratio scaled by a factor of 120 becomes 1920:1080, a standard Full HD frame — the same shape, just bigger.
Quick reference
| You want to find | Formula | Tab to use |
|---|---|---|
| A missing value in A:B = C:D | cross-multiply, then divide | Solve proportion |
| The smallest whole-number form of a ratio | divide both terms by their GCD | Simplify ratio |
| A ratio written as 1:n (e.g. map scales) | divide both terms by the first term | Simplify ratio |
| A bigger or smaller version of the same ratio | multiply both terms by the same factor | Scale ratio |
Equivalent ratios and common mistakes
Two ratios are equivalent when one can be turned into the other by multiplying or dividing both terms by the same nonzero number — 2:3, 4:6, and 24:36 are all the same ratio in different clothes, exactly like 1/2 and 2/4 are the same fraction. The most common mistake is changing only one term of a ratio (turning 2:3 into 2:4 to "make it bigger") — that changes the shape entirely rather than scaling it. The second most common mistake is tipping the cross-multiplication the wrong way when solving a proportion; this tool always applies A × D = B × C so the direction is handled for you.
What this tool does not do
This calculator handles two-term ratios (A:B) and four-term proportions (A:B = C:D). It does not currently handle three-or-more-term ratios (like splitting a total across three shares such as 2:3:5) or automatic unit conversion between the two sides of a ratio — enter both terms in the same unit and convert separately if needed.
Sources & further reading
Frequently asked questions
How do I solve a proportion like 8 is to 12 as 6 is to x?
Enter the three known values in the Solve proportion tab and pick the missing one from the Solve for row. Cross-multiplying gives the rule: A times D equals B times C. For 8:12 = 6:x, solve for D: x = (12 times 6) divided by 8 = 9. This is exactly how recipe scaling works too — if 8 servings need 12 oz of flour, 6 servings need 12 times 6 divided by 8 = 9 oz.
How do I simplify a ratio like 24:36 to its lowest terms?
Divide both terms by their greatest common divisor (GCD). The GCD of 24 and 36 is 12, so 24 divided by 12 is 2 and 36 divided by 12 is 3, giving 2:3. The Simplify ratio tab does this automatically, including for ratios with decimals — it scales both terms to whole numbers first, finds the GCD, then reduces.
What does a map scale like 1:50000 mean, and how do I convert my own ratio to 1:n form?
A map scale of 1:50000 means 1 unit on the map equals 50000 of the same unit in the real world — 1 cm on the map is 500 m on the ground. The Simplify ratio tab's 1:n result divides both terms by the first one, so any ratio you enter — say 4:210000 — comes back as 1:52500, ready to compare against a known map scale.
How do I scale a ratio like an aspect ratio or a recipe up or down?
Enter the original ratio and a scale factor in the Scale ratio tab. A 16:9 screen ratio scaled by 120 becomes 1920:1080 — still the same shape, just bigger. The same math scales a recipe: a 2:3 sugar-to-flour ratio scaled by 1.5 for a bigger batch becomes 3:4.5. Scaling never changes the simplified ratio, only the size of each part.
Is my ratio data sent to a server?
No. This ratio calculator runs entirely in your browser — nothing you type is uploaded, tracked, or stored on a server. There's no sign-up, and your last inputs are saved only in your own browser's local storage so they're there next time you open the page.