Ratio Calculator
Enter three values to find the fourth — the unknown in the proportion.
Results
- x (the unknown)
- A : B in simplest form
- A ÷ B
- A as a percentage of B
- Share of A in the total
Proportions are the maths of everyday life: scaling a recipe for 3 up to 9, turning centimetres on a map into kilometres, or working out how long 8 workers need for a job that takes 4 workers 6 days.
In a direct proportion both values rise together; in an inverse proportion one falls as the other rises. The calculator solves both and reduces your ratio to its simplest form.
How to calculate Ratio
- Enter A and B — the ratio you know.
- Enter C — the value whose counterpart you want.
- Choose direct or inverse proportion and read x.
Ratio formula
Direct: A ÷ B = C ÷ x → x = B × C ÷ AInverse: A × B = C × x → x = A × B ÷ C
Ratio example
If 3 cups of flour make a recipe for 4, how many does 9 cups make? 3 : 4 = 9 : x, so x = 4 × 9 ÷ 3 = 12 servings.
Ratio: common questions
What is cross multiplication?
In A ÷ B = C ÷ x the cross products are equal: A × x = B × C. The unknown follows from that.
When do I use inverse proportion?
When one quantity falls as the other rises — more workers finish sooner; higher speed means a shorter journey.
How do I simplify a ratio?
Divide both numbers by their greatest common factor. 12 : 18 divided by 6 becomes 2 : 3.