a:b

Math calculator

Ratio Calculator

Simplify a ratio, scale it by a factor, or solve a missing term in a proportion a:b = c:d.

Simplified ratio2 : 3

FormulaSimplified ratio = (a ÷ gcd) : (b ÷ gcd)
Calculation steps
  1. Integer form: 8 : 12
  2. gcd = 4
  3. 8 ÷ 4 : 12 ÷ 4 = 2 : 3

On this device

History and favorites

History and favorites stay in this browser. They are not sent to KE Calculator. At most 20 history items are kept.

Recent results

Copy a result or share URL to save it here.

Favorite calculators

Save a calculator to open it quickly later.

How it works

How to use this ratio calculator

  1. Choose Simplify, Equivalent, or Missing term.
  2. Enter a and b. For an equivalent ratio also enter the scale factor. For a missing term enter the known third or fourth value.
  3. Read the reduced pair or the solved term and the substituted proportion.

Formula

The calculation formula

a : b = (a ÷ gcd) : (b ÷ gcd)
01

Write both terms with a shared integer scale when they have decimals.

02

Divide by their greatest common divisor to simplify.

03

For a proportion, use equal cross-products: a × d = b × c.

Worked examples

Example calculations

Simplify

8:12 has gcd 4, so the simplified ratio is 2:3. 1.5:2.5 becomes 3:5 after scaling to integers.

Missing fourth term

2:3 = 10:d. Then d = 3 × 10 ÷ 2 = 15, so 2:3 = 10:15.

When to use it

Common use cases

  • Reduce 8:12 to lowest terms
  • Scale a recipe or mix by a constant factor
  • Find the missing value in 2:3 = 10:x

Limits

Assumptions and limits

  • 0:0 is undefined. 0:n simplifies to 0:1.
  • Decimal terms are scaled to integers (up to 8 decimal places) before gcd.
  • Solving for the fourth term requires a ≠ 0. Solving for the third term requires b ≠ 0.

Questions

Frequently asked questions

How do you find a missing term in a ratio?

Keep the two ratios equal. If a:b = c:d and d is unknown, d = b × c ÷ a.

Is a simplified ratio the same as a fraction?

The reduced pair a:b matches the fraction a/b in lowest terms, but a ratio names a comparison, not a single quotient. Use the Fraction Calculator when you need arithmetic on those quotients.

Sources

Sources and review