Ratio Calculator
Simplify a ratio to its lowest terms and scale it to any size — both directions.
Simplify a ratio
Turn a decimal into a ratio
Find a missing value
How to use
- Enter the two numbers of your ratio (A and B). The simplified ratio and its decimal form appear instantly.
- To solve a proportion, type a new value for A — the matching B is calculated, and vice versa.
- Decimals work too: 2.5 : 1.5 simplifies to 5 : 3.
Examples
Simplify 1920:1080
Type 1920 and 1080 — the simplified ratio is 16 : 9, or 1.7778 : 1 as a decimal.
Recipe scaling
A recipe uses flour and sugar at 3 : 2. If you have 450 g of sugar (B), the proportion gives 675 g of flour (A).
Scaling a recipe
A recipe for four people scaled to seven is a proportion: 4 is to 7 as each ingredient is to its new amount. Multiply every quantity by 7 ÷ 4 = 1.75. Ratios keep the relationship exact where rounding each ingredient separately drifts, which shows up most in baking where the flour-to-liquid balance is what actually matters.
Splitting a bill or a payout
Three people contributing 300,000, 200,000 and 100,000 KRW share in the ratio 3:2:1, which is six parts. A 1,200,000 KRW return divides into 600,000, 400,000 and 200,000. Reducing to the simplest form first makes the arithmetic easy and makes the split easy to explain to everyone involved.
Mixing at a given concentration
Dilution instructions are ratios: 1:10 usually means one part concentrate to ten parts water, giving eleven parts total. Some products instead mean one part in ten total. The two readings differ by about 9% in final strength, so check which the label intends before scaling up.
Turning a decimal into a ratio
A decimal is just a ratio against one, so 0.4 is 0.4 : 1, which reduces to 2 : 5. The same step gives 1.25 as 5 : 4 and 0.125 as 1 : 8. This is the direction people usually need when a spec sheet gives a decimal and a form asks for whole numbers.
Reading a screen ratio from its decimal
A display described as 1.78 is 16 : 9, and 1.33 is 4 : 3. Converting the decimal back into whole numbers is how you match a measurement against the named format, since manufacturers quote the decimal and design tools expect the pair.
FAQ
How is a ratio simplified?
Both numbers are divided by their greatest common divisor (GCD). For 1920:1080 the GCD is 120, giving 16:9.
Can I use decimal numbers in a ratio?
Yes. Decimals are scaled up to whole numbers first (2.5:1.5 becomes 25:15), then simplified as usual to 5:3.
How does the missing-value (proportion) calculation work?
It solves A : B = newA : newB by cross-multiplying. Given 16:9 and a new A of 1280, newB = 1280 × 9 ÷ 16 = 720.
Why are zero or negative numbers rejected?
A ratio compares two positive quantities; with a zero or negative side the comparison (and division) stops being meaningful, so the tool asks for positive numbers.
Does 1:10 mean one in ten, or one to ten?
In standard notation a colon separates parts, so 1:10 is one part to ten parts and eleven parts in total — one eleventh of the mixture. Everyday usage is looser and some labels mean one in ten. When it matters, restate the ratio as a fraction of the whole to remove the ambiguity.
How do I convert a ratio to a percentage?
Divide the part by the total of all parts. In 3:2 the first share is 3 ÷ 5 = 60% and the second is 40%. The common mistake is dividing by the other part instead of the total, which turns 3:2 into 150% and produces shares that add to more than the whole.
Can a ratio have more than two terms?
Yes, and it works the same way. 2:3:5 has ten parts, so the shares are 20%, 30% and 50%. Simplification applies to all terms at once using their common divisor, so 4:6:10 reduces to 2:3:5. Reducing pairs separately breaks the relationship between the terms.
How do I convert a decimal to a ratio?
Treat the decimal as the first term against one and reduce. 0.4 becomes 0.4 : 1, multiply both sides until they are whole — 4 : 10 — then divide by the common factor to get 2 : 5. The tool does this directly: enter the decimal and it returns the reduced pair.
Why does 0.333 not become 1 : 3?
Because 0.333 is not one third. It reduces to 333 : 1000, which is correct for the number you typed. A repeating decimal has to be written as a fraction to stay exact, so if you mean one third, enter 1 and 3 in the two-term form instead of typing an approximation.