CalcaTools

Ratio Calculator | Simplify ratios, convert, and solve proportions

Simplify ratios to lowest terms and convert them to fractions, percentages and decimals in one step. Enter two or three numbers and the tool divides by the greatest common factor and shows the working — essential for recipes, mixing, and comparing proportions.

Last updated: July 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

RatioSimplified
12:182:3
45:303:2
100:254:1
3:7Already simplest

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

Use caseMethod
Recipe scalingMultiply every part by same factor
Maps/modelsKeep proportional units
ComparisonConvert to same denominator or decimal

lightbulb Example — simplifying the ratio 18:24

Divide both sides by their greatest common factor. The GCF of 18 and 24 is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4.

Result: 18:24 simplifies to 3:4.

What this means: Equivalent ratios scale together — 3:4 is the same proportion as 18:24 or 30:40.

Formula & methodology

Formula: a:b simplified by dividing both terms by GCF(a,b)

The Ratio Calculator is built on a well-established calculation method. It uses the formula a:b simplified by dividing both terms by GCF(a,b) to turn your inputs into a reliable result. Enter two or three numbers and this ratio calculator simplifies them to their lowest terms, converts the ratio to a fraction, percentage, and decimal, and can scale it up to find equivalent ratios. It also solves The steps are shown on the page so you can follow the reasoning from input to output.

A ratio compares quantities. Simplifying divides every part by the same greatest common factor so the relationship stays unchanged.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do I use the ratio calculator?
Enter two or three numbers that make up your ratio, such as 18 and 24, and the tool simplifies them to lowest terms by dividing both by their greatest common factor — the GCF of 18 and 24 is 6, giving 3:4. It also converts the ratio to a fraction, a percentage, and a decimal, so you can use whichever form fits your recipe or comparison.
What formula does the ratio calculator use?
The Ratio Calculator uses the standard a:b simplified by dividing both terms by GCF(a,b). You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
Is the ratio calculator accurate?
The Ratio Calculator applies the standard formula: a:b simplified by dividing both terms by GCF(a,b). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.
Why do my results differ from another calculator?
The Ratio Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Enter two or three numbers and this ratio calculator simplifies them to their lowest terms, converts the ratio to a fraction, percentage, and decimal, and can scale it up to find equivalent ratios. It also solves missing-value proportion problems — for There is no limit on usage, and it works on any device.
How do I find the constant of proportionality?
Divide y by x for any paired values: if 4 notebooks cost $10, k = 10 ÷ 4 = 2.5 dollars per notebook, and the relationship is y = 2.5x. Check a second pair to confirm the relationship really is proportional — if 8 notebooks cost $18, k changed, and a straight ratio model doesn't apply.
How do I solve a proportion like 3/8 = x/56?
Cross-multiply: multiply 3 by 56 to get 168, then divide by 8, giving x = 21. The proportion 3/8 = 21/56 is true because both sides simplify to 0.375. The calculator solves this automatically: enter the three known values and it returns the missing one using the same cross-multiplication method.
How do I scale a drawing or recipe by a ratio?
Multiply every dimension or ingredient by the same scale factor. A floor plan at 1:50 means 1 cm on paper is 50 cm real, so a 6.4 cm wall is 3.2 m. Doubling a recipe is scale factor 2 across the board — scaling only some quantities is how proportions (and dinners) break.
What does the Ratio Calculator do?
Enter two or three numbers and this ratio calculator simplifies them to their lowest terms, converts the ratio to a fraction, percentage, and decimal, and can scale it up to find equivalent ratios. It also solves missing-value proportion problems — for. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
Is the Ratio Calculator free and private?
Yes — the Ratio Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Ratio Calculator?
Ratios are simplified exactly by dividing both terms by their greatest common factor, so 18:24 always becomes exactly 3:4 with no rounding. The fraction, percentage, and decimal conversions are computed to full precision from the simplified ratio. The only approximation is in the decimal display, which can be rounded for very long repeating values like 1:3.

Explore the full percentage & discount toolkit

Every CalcaTools percentage calculator — percent-of and percent-off math, stacked discounts, retail markup and margin, error and accuracy checks, plus year-over-year change and ratios — with the working shown on every result.

Core percentage math

Discounts & sale prices

Markup & margin

Change & comparison