Case 1
- First term A
- 1
- Second term B
- 2
- Third term C
- 5
10.0000
Open with these valuesRatio Calculator
10.0000
Result: 10.0000Give three terms of a proportion and the fourth follows: D = (B × C) ÷ A. With 1 : 2 = 5 : D the answer is (2 × 5) ÷ 1 = 10. The table also shows A : B reduced to its lowest whole numbers, which changes nothing about the answer — only how the ratio reads.
The numbers at a glance
Held fixed: First term A 1.0000, Second term B 2.0000.
| Third term C | Result |
|---|---|
| 2.0000 | 4.0000 |
| 4.0000 | 8.0000 |
| 5.0000Your value | 10.0000 |
| 6.0000 | 12.0000 |
| 8.0000 | 16.0000 |
| 10.0000 | 20.0000 |
Worked examples
Case 2
- First term A
- 4
- Second term B
- 6
- Third term C
- 2
3.0000
Open with these valuesCase 3
- First term A
- 2.5
- Second term B
- 5
- Third term C
- 4
8.0000
Open with these valuesHow it's calculated
D = (B × C) ÷ A
- StepEnter A and B — the ratio you already know.
- StepEnter C, the first term of the second ratio.
- ResultRead D, the value that makes A : B equal C : D.
Reference table
| A, B, C | A : B reduced | Missing term D |
|---|---|---|
| 3, 9, 1 | 1 : 3 | 3 |
| 4, 6, 2 | 2 : 3 | 3 |
| 10, 15, 4 | 2 : 3 | 6 |
| 2.5, 5, 4 | 2.5 : 5, not reduced | 8 |
| 5, 4, 10 | 5 : 4 | 8 |
| 1, 2, 5 | 1 : 2 | 10 |
| 2, 3, 8 | 2 : 3 | 12 |
Questions
What is a ratio?
A ratio compares two quantities, written A : B — so 1 : 2 means the second quantity is twice the first. A proportion states that two ratios are equal, A : B = C : D. This calculator finds the missing term D.
How do I solve for the missing value?
Cross-multiply and divide: D = (B × C) ÷ A. For 1 : 2 = 5 : D that is (2 × 5) ÷ 1 = 10, so the proportion reads 1 : 2 = 5 : 10. The calculator does it as soon as the three known terms are in.
How is a ratio reduced?
Both terms of A : B are divided by their greatest common divisor. So 4 : 6 shares a divisor of 2 and reduces to 2 : 3, while 10 : 15 shares 5 and reduces to the same 2 : 3. Reducing only works on whole numbers; 2.5 : 5 is left as it stands.
Why must A be greater than zero?
Solving for D divides by A, and dividing by zero has no answer. A ratio also compares quantities, and a negative quantity has no meaning in that role. The first term therefore starts just above zero.
Does reducing the ratio change the answer?
No. 4 : 6 = 2 : 3 describes exactly the same relationship, so the missing term comes out the same whichever form you enter. Reducing only makes the ratio easier to read and compare.
Where are ratios used in practice?
Wherever quantities scale together: mixing paint, fuel or concrete, scaling a recipe up, reading a map scale, setting a screen aspect ratio, comparing odds. Solving the proportion keeps the mixture the same at any size.
Sources and last check
Information, not professional advice.