How do you simplify a ratio?

Divide every term by the greatest common divisor (GCD) of all the terms. For example, 16:9 shares no common factor, so it stays 16:9, while 8:12 has a GCD of 4 and simplifies to 2:3. This calculator finds the GCD across two or three terms automatically and shows the division step.

How does it handle decimal ratios like 1.5 to 2?

It first multiplies every term by a power of ten large enough to clear the decimals (so 1.5 and 2 become 15 and 20), then divides by the GCD (5) to get 3:4. The working shows both the multiply-up and the divide-down steps so you can follow it.

How do I solve a proportion a:b = c:x?

A proportion is solved by cross-multiplication. Because a:b = c:x means a·x = b·c, the missing term X equals (b·c) divided by a. Leave any single field blank — A, B, C or X — and the calculator rearranges that same identity to solve for whichever one is missing.

What does scaling a ratio mean?

Scaling keeps the proportion the same while changing the actual size. If a recipe is 3:4 flour to water and you fix flour at 15, the scaling factor is 15 divided by 3, which is 5, so water becomes 4 times 5, which is 20, giving 15:20. Pick which term to anchor and enter its target value.

Can a ratio have three terms?

Yes. A three-part ratio such as 2:4:6 is simplified by dividing all three terms by their common GCD (2 here), giving 1:2:3. Leave the third term blank to work with a normal two-term ratio instead.

Is my data sent anywhere?

No. Every calculation runs locally in your browser using plain arithmetic — no numbers are uploaded, logged or stored. You can use the tool offline once the page has loaded.

Ratio Calculator — Gera Tools

A ratio calculator that does three jobs in one place: it simplifies a ratio to its lowest whole-number terms, solves a proportion of the form a : b = c : x for any missing value, and scales a ratio so a chosen term hits a target — and for each it shows the working step by step, not just the answer. It is built for students checking homework, cooks scaling recipes, designers matching proportions, and anyone who needs the maths to be transparent rather than a black box.

How it works

A ratio compares quantities by division, so two ratios are equivalent whenever one is a constant multiple of the other: 2 : 3 is the same relationship as 4 : 6 or 10 : 15. Three operations follow from that single idea.

Simplify. To reduce a ratio you divide every term by the greatest common divisor (GCD) of all the terms. The tool first clears any decimals by multiplying each term by a power of ten, then computes the GCD with the Euclidean algorithm and divides through. So 1.5 : 2 becomes 15 : 20, then 3 : 4.

Solve a proportion. The statement a : b = c : x is equivalent to the equation a · x = b · c (cross-multiplication). Rearranging gives the missing term — for example x = (b · c) / a. Leave any one of the four boxes blank and the calculator solves for exactly that one, guarding against division by zero.

Scale. To resize a ratio while keeping its shape, you multiply both terms by the same factor. Anchor one term, give it a target value, and the scaling factor is target / anchored term; the other term is multiplied by that factor.

Worked example

Take the ratio 3 : 4 of flour to water in a recipe, and suppose you want to use 15 units of flour. Anchor term A (flour) and set the target to 15. The scaling factor is 15 / 3 = 5, so water becomes 4 × 5 = 20, giving the scaled recipe 15 : 20. Feed 15 : 20 into Simplify mode and it returns to 3 : 4, confirming the proportion was preserved. In proportion mode, entering A = 3, B = 4, C = 15 and leaving X blank solves x = (4 · 15) / 3 = 20 — the same answer by cross-multiplication.

Key identities: simplify by dividing by gcd(a, b); solve a : b = c : x with x = (b · c) / a; scale by the factor target / anchored term.

Input	Mode	Result
16 : 9	Simplify	16 : 9 (already lowest terms)
8 : 12	Simplify	2 : 3
1.5 : 2	Simplify	3 : 4
2 : 4 : 6	Simplify	1 : 2 : 3
3 : 4 = 9 : ?	Proportion	X = 12

Every figure is calculated in your browser — no numbers are uploaded or stored.