What this calculator does
Are 3 : 4 and 9 : 12 the same ratio? Is 2 : 5 bigger than 3 : 7? This tool answers both by turning each ratio into a number (first ÷ second) and comparing, and by cross-multiplying so you can see the proof.
How to use it
- Type the first ratio in the first two boxes and the second ratio in the last two.
- Press Compare.
- Read the verdict and the working.
The method
Cross-multiply. For a : b and c : d, compare a × d with b × c.
- If they are equal, the ratios are equal.
- If a × d is larger, the first ratio is bigger.
- If b × c is larger, the second ratio is bigger.
3 : 4 vs 9 : 12 ⇒ 3 × 12 = 36 and 4 × 9 = 36 ⇒ equal
2 : 5 vs 3 : 7 ⇒ 2 × 7 = 14 and 5 × 3 = 15 ⇒ second is bigger
Examples you can try
| Ratios | Result |
|---|---|
| 3 : 4 and 9 : 12 | Equal |
| 2 : 5 and 3 : 7 | 3 : 7 is bigger (0.4286 vs 0.4) |
| 5 : 2 and 7 : 3 | 5 : 2 is bigger (2.5 vs 2.33) |
| 6 : 8 and 3 : 4 | Equal |
Where people use it
- Shopping: which pack has more protein per dollar?
- Sports and stats: compare shooting records such as 7 of 12 vs 5 of 8.
- School: check whether two fractions or ratios are equivalent.
Tips
- Compare in the same order: first part over second part in both ratios.
- If the ratios are equal, they simplify to the same form. Check with the simplify calculator.
Want to learn the method?
Ratio vs fraction: what is the difference?Read our short guide with worked examples you can follow on paper.
Frequently asked questions
How do you know if two ratios are equal?
Cross-multiply. If a × d equals b × c, the ratios are equal.
How do you compare which ratio is bigger?
Divide the first part by the second for each ratio and compare the results, or cross-multiply.
Are 3:4 and 9:12 equal?
Yes. Both equal 0.75 and both simplify to 3 : 4.
Can I compare ratios with decimals?
Yes.
Is this the same as comparing fractions?
Nearly. Comparing a : b with c : d works the same way as comparing a/b with c/d.