The formula this page uses
a : b = (a ÷ g) : (b ÷ g), where g = GCF(a, b) sharing a total T in a : b gives T × a/(a + b) and T × b/(a + b)
Simplify and scale ratios
Use the free ratio calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Ratio Calculator explained
The short version
- A ratio compares two amounts by division, so 18 : 24 and 3 : 4 say exactly the same thing.
- To share a total, add the parts first, work out what one part is worth, then multiply.
- Order matters: 3 : 4 and 4 : 3 describe two different mixes.
What each part means
SymbolWhat it means
a : b — The ratioTwo amounts of the same kind of thing, in the same unit. 20 cm : 5 m has to be fixed before use.
g — Greatest common factorWhat you divide both sides by to reach the simplest form.
a + b — Total partsHow many equal shares the whole gets cut into.
T — The totalThe amount being shared out, in grams, dollars, sweets or anything countable.
Show your work: a full example
- Simplify a ratio, then share with it18 : 24
- Find the greatest common factorGCF(18, 24) = 6
- Divide both sides18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18 : 24 = 3 : 4
- Now share 42 sweets in 3 : 43 + 4 = 7 parts
- Work out one part42 ÷ 7 = 6 sweets
- Multiply out each share3 × 6 = 18 and 4 × 6 = 24
- Check the total18 + 24 = 42
A second, different case
- A different case: the difference is given, not the totalconcrete is mixed cement : sand : gravel = 1 : 2 : 4
- Say gravel is 60 kg more than sandgravel − sand = 4 parts − 2 parts = 2 parts
- So two parts are worth 60 kgone part = 60 ÷ 2 = 30 kg
- Multiply each side outcement = 30 kg, sand = 60 kg, gravel = 120 kg
- Total the mix1 + 2 + 4 = 7 parts, so 7 × 30 = 210 kg
- Check the difference again120 − 60 = 60 kg
Copy-ready example
18 : 24
Simplify a ratio, then share with it
Questions about the Ratio Calculator
Is a ratio the same as a fraction?
Not quite. In a class with 2 : 3 boys to girls, the fraction of the class that is boys is 2/5, not 2/3. A ratio usually compares one part with another part, while a fraction compares a part with the whole. Read the words carefully to see which one is being asked for.
How do I simplify a ratio that has decimals in it, like 1.5 : 2?
Multiply both sides by the same power of ten until they are whole numbers, then reduce. Here 1.5 : 2 becomes 15 : 20, and dividing by 5 gives 3 : 4. Multiplying both sides by the same number never changes what a ratio means.
A recipe serves 4 and I need it for 10. What do I multiply by?
Divide the new number of servings by the old one: 10 ÷ 4 = 2.5. Every ingredient gets multiplied by 2.5, so 300 g of flour becomes 750 g. That single number is called the scale factor and it is the same for every line of the recipe.
Can a ratio have three or more numbers?
Yes, and it works the same way. In 1 : 2 : 4 you add all three to get 7 parts, then share out. The only rule that changes is simplifying: you have to divide by a number that goes into every side, so 2 : 4 : 5 will not reduce even though the first two would on their own.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.