About the Ratio Calculator
A ratio compares two quantities of the same kind. Two parts cement to three parts sand. Sixteen students to one teacher. A screen 16 units wide for every 9 units tall. It says nothing about absolute size — only about the relationship — which is exactly what makes it portable: the same 2:3 mix works for a bucket or a lorryload.
The thing ratios are most often confused with is fractions, and the confusion matters. A ratio compares part to part. A fraction compares part to whole. If a drink is mixed 1:4 squash to water, the squash is one part in five, not a quarter. That single slip is behind a great many wrong dilutions.
This calculator does the three things people actually need from ratios: simplifying one to its clearest form, scaling one up or down when only one new value is known, and splitting a total amount in a given ratio.
How to Use the Ratio Calculator
Pick a mode.
Simplify a ratio takes two terms and reduces them. Decimals are fine — 1.5:2 comes back as 3:4, because the calculator scales the decimals away first.
Find the missing term is for scaling. Enter the original ratio, the one new value you already have, and say which side it belongs to. A 2:3 mix scaled so that the first part is 40 gives a second part of 60.
Split a total in a ratio divides an amount. Enter the ratio and the total, and you get both shares. 600 split 2:3 is 240 and 360.
Press Calculate. Along with the answer you get the ratio expressed as 1:n, which is often the most readable form, and as a single decimal, which is the first term divided by the second.
Order matters throughout. 2:3 and 3:2 describe different mixtures.
How Ratios Are Calculated
Simplifying is the same operation as reducing a fraction. Find the greatest common divisor of the two terms and divide both by it. 16:24 share a factor of 8, so they reduce to 2:3.
Decimals need one extra step, because a greatest common divisor is only defined for whole numbers. Multiply both terms by whatever power of ten clears the decimal places — for 1.5:2 that is 10, giving 15:20 — and then reduce as normal to 3:4. Multiplying both sides by the same number never changes a ratio, which is what makes this safe.
Scaling uses the fact that equivalent ratios cross-multiply. If 2:3 is the same relationship as 40:x, then 2x = 3 × 40, so x = 60. It is the same technique as solving a proportion, because that is exactly what it is.
Splitting works by counting shares. A 2:3 ratio means 5 shares in total: two for the first party and three for the second. Divide the amount by 5 to find what one share is worth, then multiply by each term. The two results always add back to the original total, which is the check worth running.
Ratio Formula
Simplifying:
a : b = (a / gcd(a, b)) : (b / gcd(a, b))
Scaling (a : b = c : d):
d = c x b / a when c is known
c = d x a / b when d is known
Splitting a total T in the ratio a : b:
first share = T x a / (a + b)
second share = T x b / (a + b)The a + b denominator in the split formula is the part people leave out. It is the number of shares, and it is what converts a part-to-part comparison into a part-to-whole one.
Step-by-Step Example
A concrete mix is specified as 1:2:3 cement to sand to gravel, but you only need the cement-to-sand relationship: 1:2. You have 1.5 bags of cement. How much sand?
Step 1 — set up the equal ratios. 1:2 = 1.5:x
Step 2 — cross-multiply. 1 × x = 2 × 1.5, so x = 3. You need 3 parts of sand.
Now a split. Two people invest in a venture, one putting in 2 units and the other 3, and the venture returns 600. How is it divided?
Step 1 — count the shares. 2 + 3 = 5 shares in total.
Step 2 — find what one share is worth. 600 ÷ 5 = 120.
Step 3 — multiply out.
First: 120 x 2 = 240
Second: 120 x 3 = 360Step 4 — check. 240 + 360 = 600. It reconciles.
Notice what would have happened with the fraction confusion: treating "2:3" as "two thirds and three thirds" gives 400 and 600, which sums to 1,000 rather than
- The shares have to add up, and that is the fastest way to catch the mistake.
Understanding Your Result
The headline is the ratio, in the form the mode produced: simplified, scaled or split.
The detail line gives the 1:n form, which is usually the most readable way to grasp a proportion. 5:8 as 1:1.6 tells you immediately that the second quantity is a little over half again as large as the first. Design and photography use this form almost exclusively, which is why aspect ratios are quoted as 1:1.85 rather than 37:20.
As a single number is the first term divided by the second. This is the form to use in a spreadsheet or a further calculation, and it is what people mean by "the ratio" when they treat it as one value — a gear ratio of 3.5, for instance.
For a split, the two shares always sum to the total. If they do not, the inputs were wrong.
One thing the result cannot tell you is whether the order is right. 16:9 and 9:16 are both valid ratios and only one of them is a landscape screen.
When Should You Use This Calculator?
Mixing and dilution. Concrete, fertiliser, cleaning solution, cocktails, photographic chemicals — all are specified as ratios, and all need scaling to the quantity you actually have.
Splitting money. Dividing profit between partners, sharing a bill unevenly, allocating a budget across departments in agreed proportions.
Recipes. Baker's percentages and hydration ratios are the same arithmetic. A 3:2:1 shortcrust is flour to fat to water by weight.
Screens and images. Aspect ratios are ratios reduced to lowest terms. A 1920×1080 image is 16:9 once you divide both by 120.
Maps and models. A scale of 1:25,000 means one unit on the map is 25,000 in the world.
Comparing two figures where the relationship matters more than the absolute sizes — staff to students, debt to income, wins to losses.
Common Mistakes
Reading a ratio as a fraction of the whole. A 1:4 mix is one part in five, not one in four. This is the most consequential ratio error there is, and it turns up constantly in dilutions and dosing.
Reversing the order. A ratio is not symmetric. 16:9 is a widescreen display; 9:16 is a phone held upright. Write down which quantity is which before calculating.
Adding ratios. You cannot add 1:2 and 1:3 to get 2:5. Ratios combine by scaling to a common term, not by adding the parts.
Forgetting to sum the terms when splitting. Multiplying the total by each term without dividing by their sum inflates both shares. The check is that they must add back to the total.
Mixing units. A ratio compares like with like. Two kilograms to three litres is not a ratio unless you know the density and convert one of them first.
Simplifying when the original numbers carried information. 24:36 reduces to 2:3, but if those were actual counts of something, reducing them discards the scale. Reduce for comparison; keep the originals for the record.