Ratio Calculator
Simplify a ratio, solve a proportion (A:B = C:?) or split a total in a given ratio — with the GCD, cross-multiplication and each part shown.
Ratio Calculator: with the default inputs, result is 2 : 3.
Used only when solving a proportion.
Used only when splitting a total.
- As 1 : n
- 1 : 1.5
- A ÷ B
- 0.6667
- A's share of the whole
- 40%
- B's share of the whole
- 60%
- Missing term
- —Only for the proportion mode.
Assumptions
- Decimal inputs are scaled by up to 10⁸ to reach whole numbers before simplifying.
- Negative terms are not accepted; a ratio compares magnitudes.
- A — 40%1240%
- B — 60%1860%
How this is worked out
The formula
Simplify: A : B = (A ÷ g) : (B ÷ g), where g = GCD(A, B) Proportion: A : B = C : D ⇒ A·D = B·C ⇒ D = B·C ÷ A Split a total T in A : B: share A = T × A ÷ (A + B), share B = T × B ÷ (A + B)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- What do you want to do?
- Choose one of 3 options.Simplify A : B · Solve the proportion A : B = C : ? · Split a total in the ratio A : B
- A
- A number.0 or more · defaults to 12
- B
- A number.0 or more · defaults to 18
- C (third term)
- Used only when solving a proportion.0 or more · defaults to 4
- Total to split
- Used only when splitting a total.0 or more · defaults to 100
What you get back
- Resultmain answer
- As 1 : n
- A ÷ B
- A's share of the whole
- B's share of the whole
- Missing term
- Only for the proportion mode.
What this assumes
- Decimal inputs are scaled by up to 10⁸ to reach whole numbers before simplifying.
- Negative terms are not accepted; a ratio compares magnitudes.
About this calculator
A ratio compares two quantities by division: 12 : 18 says "for every 12 of the first there are 18 of the second". Ratios don't care about the actual amounts, only the relationship, which is why 12 : 18, 2 : 3 and 0.5 : 0.75 are all the same ratio. This calculator handles the three jobs ratios do in real life.
Simplify a ratio
Divide both sides by their greatest common divisor, exactly like reducing a fraction. Decimal ratios are first scaled to whole numbers (1.5 : 2.5 → 15 : 25 → 3 : 5). The "1 : n" form is handy for comparisons — a 16 : 9 screen is 1 : 0.5625, a 3 : 2 mix is 1 : 0.667.
Solve a proportion
When two ratios are equal, A : B = C : D, cross-multiplying gives A·D = B·C. That one identity solves every missing-term problem: recipe scaling ("2 eggs for 3 cups; how many eggs for 8 cups?"), map scales, unit prices and similar triangles. Enter A, B and C; the calculator finds D and shows the cross-multiplication.
Split a total in a ratio
To share $100 in the ratio 2 : 3, count the parts (5), find the value of one part ($20) and multiply. Ratios are simplified first so the part count is as small as possible, but the answer is the same either way.
Ratios vs. fractions vs. percentages
A ratio of 2 : 3 does not mean 2/3 of the total — it means 2 parts out of 5, so the first share is 2/5 = 40%. The "share of the whole" outputs make that distinction explicit. It's the single most common ratio mistake.
Other things to watch
- Order matters: 2 : 3 and 3 : 2 are different ratios.
- Keep units consistent. 30 minutes : 2 hours is 30 : 120 = 1 : 4, not 30 : 2.
- A ratio with three or more terms (2 : 3 : 5) works the same way — simplify by the GCD of all terms and split totals over the sum of all parts.
Frequently asked questions
▸How do I simplify a ratio?
Divide both numbers by their greatest common divisor. 12 : 18 has GCD 6, so it simplifies to 2 : 3. If the numbers are decimals, multiply both by 10, 100, … until they are whole, then divide by the GCD.
▸How do I solve a proportion with a missing number?
Cross-multiply: if A : B = C : D then A × D = B × C. Solve for the unknown by dividing. For 3 : 2 = 8 : x, 3x = 16 so x = 5.33.
▸How do I divide an amount in a given ratio?
Add the ratio parts, divide the total by that sum to get one part, then multiply by each ratio number. $100 in 2 : 3 is 5 parts of $20, giving $40 and $60.
▸Is a ratio of 2 : 3 the same as 2/3?
No. 2 : 3 means 2 parts to 3 parts, so the first is 2/5 of the whole. 2/3 as a ratio is 2 : 3 only when comparing the parts to each other, not to the total.
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