a⁄b : c⁄d = e⁄f : x
Proportion Calculator with Fractions
Solve a proportion where the terms are fractions or mixed numbers, with an exact fraction answer.
Open → Proportion Calculator with FractionsAll Proportion & Ratio Calculators
A complete set of 15 free calculators for proportions, ratios, rates and scale. Each one solves a specific question, shows its working step by step, and accepts fractions and decimals as well as whole numbers.
15 Calculators
3 Categories
Exact Fraction answers
Free No sign-up
Proportions
Solve, verify and model proportional relationships.
6 tools a × d = b × c
Cross Multiplication Calculator
Cross multiply two fractions to see both products, solve for x in any position, or test whether the ratios are equal.
Open → Cross Multiplication Calculator y = kx
Direct Proportion Calculator
Find the constant of proportionality k from one known pair, then predict any other value on the line y = kx.
Open → Direct Proportion Calculator x × y = k
Inverse Proportion Calculator
Work with quantities that move in opposite directions: find the constant k and solve x × y = k for any pair.
Open → Inverse Proportion Calculator x = √(a × b)
Mean Proportional Calculator
Find the geometric mean between two numbers, plus the third and fourth proportional, with exact surd form.
Open → Mean Proportional Calculator k = new ÷ original
Scale Factor Calculator
Find the scale factor between a model and the real thing, apply a 1:n scale to any dimension, and get area and volume factors.
Open → Scale Factor CalculatorRatios
Simplify, scale, share and compare ratios of any length.
5 tools A : B = C : D
Ratio Calculator
Solve A : B = C : D for any missing term, or scale a ratio up and down by a factor — with the decimal and percentage alongside.
Open → Ratio Calculator divide by GCD
Simplify Ratio Calculator
Reduce a ratio of 2 to 6 terms to its lowest whole numbers using the greatest common divisor — decimals and fractions accepted.
Open → Simplify Ratio Calculator a : b = na : nb
Equivalent Ratio Calculator
Generate a table of equivalent ratios from any starting ratio, or check whether two ratios are equivalent.
Open → Equivalent Ratio Calculator A : B : C
Ratio Calculator for 3 Numbers
Work with a three-part ratio A : B : C — simplify it, split a total between three shares, and see each part as a percentage.
Open → Ratio Calculator for 3 Numbers A : B : C : D …
Ratio Calculator for 4, 5 & 6 Numbers
Handle longer ratios with four, five or six terms: simplify, share out a total, scale by a factor and read off percentages.
Open → Ratio Calculator for 4, 5 & 6 NumbersConversions & Rates
Turn a ratio into a percentage, decimal, fraction or unit rate.
4 tools part ÷ total × 100
Ratio to Percentage Calculator
Convert a ratio of 2 to 6 parts into percentages of the whole, and express A : B as a percentage of B.
Open → Ratio to Percentage Calculator A : B → A ÷ B
Ratio to Decimal & Fraction Calculator
Turn a ratio into its decimal value, a simplified fraction, a mixed number and the 1 : n form — both directions.
Open → Ratio to Decimal & Fraction Calculator W : H
Width & Height Ratio Calculator
Get the aspect ratio from a width and height, or resize to a locked ratio such as 16:9 by entering just one dimension.
Open → Width & Height Ratio Calculator A : B → A⁄B : 1
Unit Ratio Calculator
Reduce a ratio to a per-one unit rate — cost per item, distance per hour, 1 : n form — and read both directions at once.
Open → Unit Ratio Calculator Start here
Which calculator do you need?
The tools overlap in maths but not in question. Match the shape of your problem to the row below.
| If your problem looks like… | Use this | Because |
|---|---|---|
| 3/4 = x/12 | Cross Multiplication | One unknown in a two-fraction proportion — solved by A × D = B × C. |
| (2/3) / (4/5) = x / (1 1/2) | Proportions with Fractions | The terms are fractions, so the answer should stay an exact fraction. |
| 4 kg costs $6, so 7 kg costs? | Direct Proportion | Both quantities rise together — find k, then scale. |
| 6 workers take 8 days, 4 workers take? | Inverse Proportion | One quantity falls as the other rises, so x × y stays constant. |
| x is the mean proportional of 4 and 9 | Mean Proportional | The unknown sits in both middle positions: x = √(ab). |
| A 1:50 model of a 12 m building | Scale Factor | Includes the area (k²) and volume (k³) factors most people forget. |
| Reduce 45 : 60 to lowest terms | Simplify Ratio | Divides every term by the greatest common divisor. |
| Split £450 in the ratio 2 : 3 : 4 | Ratio — 3 Numbers | Share-out problems need the total number of parts, not just the ratio. |
| Express 3 : 5 as a percentage | Ratio → Percentage | Gives each part as a share of the whole and A as a percentage of B. |
| 1920 × 1080 — what ratio is that? | Width & Height Ratio | Simplifies to 16 : 9 and resizes either dimension to a locked ratio. |
| $14.97 for 3 kg — price per kg? | Unit Ratio | Reduces the ratio to a per-one rate in both directions. |
Background
One idea, fifteen questions
Almost everything on this page comes back to a single statement: two ratios are equal.
Write that as A/B = C/D and you have a proportion. Cross-multiply it and
you get A × D = B × C, which is the one identity that makes every other
tool here work.
What changes from calculator to calculator is the question being asked of that identity. Sometimes one of the four terms is missing. Sometimes all four are known and you only want to check whether the equality actually holds. Sometimes the ratio has more than two parts, and the real question is how to divide a total between them. Sometimes you want the same relationship expressed differently — as a percentage, a decimal, a unit rate, or a scale on a drawing.
Splitting those questions into separate tools keeps each one short. You are not scrolling past four modes you do not need to reach the two fields you do, and the worked steps you get back are written for your specific case rather than a generic template.
Everything runs in your browser
There is no server round-trip and no account. The arithmetic happens in JavaScript on your device, which is why results appear as you type. It also means the numbers you enter never leave your machine — useful if you are working with figures from a spreadsheet you would rather not paste into a website.
Answers stay exact where they can
Most online calculators convert everything to decimals immediately, which turns
1/3 into 0.3333333 and compounds the error through the rest
of the calculation. These tools carry values as exact fractions internally and only
produce a decimal at the end, next to the exact form. Where a square root is
irrational, you get the surd — 4√3 — rather than only its approximation.
A / B = C / D
The proportion. Two ratios stated to be equal. Every calculator in this collection is a different question asked of this one line.
A × D = B × C
Cross multiplication. Clearing both denominators turns the proportion into a straight multiplication, which is what lets you solve for any single missing term.
Working, not just answers
Each result is followed by numbered steps and a verification line, so you can copy the method as well as the number.
Flexible input
Whole numbers, decimals, 3/4, 1 1/2 and 40%
are all accepted in any numeric field.