Ratio Calculator
Simplify a ratio, find an equivalent ratio, divide a total in a ratio, or compare two two-part ratios.
Ratio formulas
A ratio a:b compares two quantities by division. To simplify an integer ratio, divide every term by their greatest common divisor (GCD):
a:b = (a ÷ GCD):(b ÷ GCD)
For an equivalent ratio, multiply every term by the same scale factor k. If one new term is known, k equals the new term divided by its original value.
To divide a total T in the ratio a:b:c, add the ratio terms S = a + b + c. Each part is T × term ÷ S.
Two positive two-part ratios a:b and c:d are equivalent when a × d = b × c.
Checked examples
| Calculation | Input | Result |
|---|---|---|
| Simplify | 8:12 | 2:3 |
| Simplify decimals | 1.5:2.25 | 2:3 |
| Equivalent ratio | 2:3; set term 2 to 12 | 8:12 |
| Divide a total | 100 in 2:3 | 40 and 60 |
| Divide three ways | 240 in 1:2:3 | 40, 80 and 120 |
| Compare | 3:4 and 9:12 | Equivalent |
| Compare | 3:4 and 2:3 | 3:4 is greater |
How to use the Ratio Calculator
- Choose simplification, equivalent ratio, total division or comparison.
- Enter the ratio with colons, commas, semicolons or spaces between the terms.
- Complete the additional field for the selected calculation.
- Select Calculate ratio and review the exact relationship and decimal shares.
Limits and interpretation
- Ratios may contain 2–20 positive terms. Zero and negative terms are not supported because their interpretation depends on context.
- Each term may contain up to six decimal places and must not exceed 1,000,000.
- The calculator treats terms as dimensionless. Convert quantities to the same unit before entering a ratio.
- Comparison uses positive two-part ratios only. Multi-part ratios can still be simplified, scaled and used to divide a total.
- Displayed decimal parts are rounded, but calculations retain full JavaScript numeric precision.
Frequently asked questions
How do I simplify a ratio with decimals?
Enter the decimals directly. The calculator first converts them to a common integer scale and then divides by the greatest common divisor.
How do I find a missing value in an equivalent ratio?
Choose “Find an equivalent ratio,” select the term whose new value is known, and enter that value. Every term is multiplied by the same factor.
How do I split money or a quantity in a ratio?
Choose “Divide a total in a ratio,” enter the total and the ratio. Each allocation equals the total multiplied by that term divided by the sum of all terms.
Is 2:3 the same as 4:6?
Yes. Both simplify to 2:3, and their cross-products are equal: 2 × 6 = 3 × 4.
Related calculators
Use the Fraction Calculator for arithmetic with fractions, the Percentage Calculator for percentage changes, or the Concrete Mix Ratio Calculator for construction mixtures.