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Arithmetic & Numbers

Ratio Calculator

Choose whether to simplify a ratio or solve a proportion. Decimals are cleared automatically, and proportions are solved by cross-multiplication with a check.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Try an example:
Answer2 : 3
  • Decimal ratio 0.666667
Step-by-step working 3 steps
  1. 1
    Write the ratio
    12 : 18
  2. 2
    Divide both by the GCF
    GCF(12, 18) = 6
12 ÷ 6 : 18 ÷ 6 = 2 : 3
  3. 3
    Other forms
    As a fraction: 2/3
As decimals: 1 : 1.5   or   0.666667 : 1

How to use the ratio calculator

  1. Choose simplify or solve.
  2. Enter a and b (and c for a proportion).
  3. Read the simplified ratio or the missing value.
  4. Use the check line to verify.

Ratios and proportions

a : b = (a ÷ g) : (b ÷ g), g = GCF(a, b)
a/b = c/x  ⇒  x = b × c ÷ a

Ratios compare quantities of the same kind; both terms must use the same unit.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

Simplify 12 : 18
Answer2 : 3
  • Decimal ratio 0.666667
Step-by-step working 3 steps
  1. 1
    Write the ratio
    12 : 18
  2. 2
    Divide both by the GCF
    GCF(12, 18) = 6
12 ÷ 6 : 18 ÷ 6 = 2 : 3
  3. 3
    Other forms
    As a fraction: 2/3
As decimals: 1 : 1.5   or   0.666667 : 1
Simplify 1.5 : 2.5
Answer3 : 5
  • Decimal ratio 0.6
Step-by-step working 4 steps
  1. 1
    Write the ratio
    1.5 : 2.5
  2. 2
    Clear the decimals
    × 10  →  15 : 25
  3. 3
    Divide both by the GCF
    GCF(15, 25) = 5
15 ÷ 5 : 25 ÷ 5 = 3 : 5
  4. 4
    Other forms
    As a fraction: 3/5
As decimals: 1 : 1.666667   or   0.6 : 1
2 : 3 = 10 : x
Answerx = 15
  • 2 : 3 = 10 : 15
Step-by-step working 4 steps
  1. 1
    Set up the proportion
    2 / 3 = 10 / x
  2. 2
    Cross-multiply
    2 × x = 3 × 10 = 30
  3. 3
    Divide
    x = 30 ÷ 2 = 15
  4. 4
    Check
    2 ÷ 3 = 0.666667   and   10 ÷ 15 = 0.666667

Common mistakes to avoid

Mixing units

30 minutes to 2 hours is 30 : 120 = 1 : 4, not 30 : 2.

Cross-multiplying the wrong way

In a/b = c/x, multiply a by x and b by c, then divide.

Forgetting to simplify

A ratio like 12 : 18 is usually expected as 2 : 3.

Frequently asked questions

How is a ratio different from a fraction?

A ratio compares two quantities part to part (2 : 3); a fraction is part of a whole (2/5 is 2 of 5 total parts).