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ToolBoxGenie

Ratio Calculator

Calculators · Added 15 August 2026

Three ratio jobs in one place: reduce a ratio to its simplest whole-number form, split a total between parties in a given ratio, and solve a proportion for whichever term is missing. Any number of terms is supported, and decimal terms are scaled to whole numbers rather than rounded away.

What do you want to do?
Ratio terms

How to use the ratio calculator

  1. 1Choose what you want to do — simplify, share an amount, or solve a proportion.
  2. 2For simplifying or sharing, enter the ratio terms. Use the buttons to add or remove terms.
  3. 3For sharing, add the total amount to be divided.
  4. 4For a proportion, fill in three of the four boxes and leave exactly one empty.
  5. 5Press Calculate. Percentages and normalised forms appear alongside the simplified ratio.

Examples

Simplifying

Input
8 : 12
Result
2 : 3 — or 40% and 60% of the total

Both terms divide by their greatest common divisor of 4. Note the shares are 40/60, not 25/75 — the terms sum to 5 parts, not 4.

Decimal terms

Input
1.5 : 2
Result
3 : 4

Scaled up to whole numbers before reducing, rather than rounded — 1.5 : 2 is exactly 3 : 4.

Sharing a total

Input
₹12,000 split 2 : 3 : 5
Result
₹2,400 · ₹3,600 · ₹6,000

The terms sum to 10, so each part is that many tenths of the total.

About the ratio calculator

Ratios, fractions and the part-whole trap

A ratio and a fraction look similar and mean different things. 3 : 4 compares two quantities to each other; 3/4 compares one quantity to a whole. The gap between them is where most ratio errors live.

If a business is split 3 : 4 between two partners, the first does not own three quarters. The parts total seven, so the shares are three sevenths and four sevenths — about 43% and 57%. Reading the ratio as a fraction would have given the first partner 75%, which is not a small error.

The reliable habit is to sum the terms first, always. That total is the number of parts, and every share is some number of those parts out of the total. Doing this converts the ratio into fractions with a common denominator, at which point the percentages fall out and the trap closes.

Where proportions do the real work

The proportion a : b = c : d is one of the most reused pieces of arithmetic there is, and it usually appears without being named. Scaling a recipe from four servings to seven is a proportion. Reading a distance off a map at 1 : 50,000 is a proportion. Converting between currencies at a fixed rate, working out a per-kilogram dose, sizing a photograph to fit a frame while keeping its aspect ratio — all the same operation.

What makes it robust is that it does not care about units, provided they are consistent within each ratio. Two centimetres to five centimetres equals eight kilometres to twenty kilometres — the units cancel inside each side, leaving a pure comparison. This is also why the method survives being applied to things that are not lengths at all.

The one thing to watch is what is actually proportional. Doubling a recipe doubles the ingredients but not the baking time, because heat penetration does not scale linearly with volume. Doubling the side of a square quadruples its area rather than doubling it. Proportional reasoning is powerful precisely because it is so easy to apply, which is why it is worth pausing to check that the relationship really is linear before applying it.

Frequently asked questions

Is 1 : 3 the same as one third?
No, and this is the most common ratio mistake. 1 : 3 means one part to three parts, so there are four parts in total and the first share is a quarter — not a third. A ratio compares parts to each other; a fraction compares a part to the whole. Mixing them up when splitting money or mixing a solution produces answers that are wrong by a predictable and embarrassing margin.
How do I share an amount in a ratio?
Add the terms to get the total number of parts, divide the amount by that to get the value of one part, then multiply by each term. For ₹12,000 in 2 : 3 : 5 the parts total 10, so one part is ₹1,200 and the shares are ₹2,400, ₹3,600 and ₹6,000. The calculator does this and shows the percentages alongside.
What is a proportion and how is it solved?
A proportion states that two ratios are equal: a : b = c : d. It is solved by cross-multiplication, because a × d must equal b × c. Rearranging for the missing term gives the answer. This is the arithmetic behind scaling a recipe, converting a map distance, or working out a dose per kilogram — all the same operation.
Can a ratio have more than two terms?
Yes, and this calculator handles as many as you need. Three-term ratios are common in mixing and in profit sharing — concrete at 1 : 2 : 4, partners splitting 2 : 3 : 5. The simplification works the same way: divide every term by the greatest common divisor of all of them together.

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