Ratio to Ratio Calculator
Find an equivalent ratio quickly. Enter an original ratio A:B, then provide one known value in the new ratio to solve the missing side.
What is a ratio-to-ratio conversion?
A ratio-to-ratio conversion means creating an equivalent ratio from a starting ratio. If two ratios are equivalent, they represent the same relationship, just scaled up or down by the same factor.
For example, 3:5 and 12:20 are equivalent because each term was multiplied by 4. This is the same idea used in proportions in math, science, recipes, construction, and business planning.
Formula used by the calculator
Given an original ratio A:B, the equivalent ratio A':B' is found using a scale factor k:
- A' = A × k
- B' = B × k
If you know A', then k = A' / A. If you know B', then k = B' / B.
Once the scale factor is known, the missing value is calculated by multiplying the other original term by k.
How to use this ratio to ratio calculator
- Enter the original ratio values A and B.
- Select whether your known value in the new ratio is the first term or the second term.
- Enter that known value.
- Click Calculate to see the equivalent ratio, scale factor, and simplified form.
Worked examples
Example 1: Scale up a ratio
Original ratio: 3:5. Known new first term: 12.
Scale factor is 12 ÷ 3 = 4. So the second term becomes 5 × 4 = 20. Equivalent ratio: 12:20.
Example 2: Scale down a ratio
Original ratio: 16:24. Known new second term: 6.
Scale factor is 6 ÷ 24 = 0.25. New first term is 16 × 0.25 = 4. Equivalent ratio: 4:6, which simplifies to 2:3.
Example 3: Decimal ratio conversion
Original ratio: 2.5:7.5. Known new first term: 10.
Scale factor is 10 ÷ 2.5 = 4. New second term is 7.5 × 4 = 30. Equivalent ratio: 10:30, simplified to 1:3.
Where ratio-to-ratio calculations are useful
- Cooking: Resize ingredient quantities while keeping flavor balance.
- Finance: Compare allocations (e.g., savings to spending) at different budget levels.
- Education: Teach proportions and equivalent ratios with clear steps.
- Engineering: Scale drawings, dimensions, or material mixes accurately.
- Data analysis: Keep category relationships consistent when normalizing data.
Common mistakes to avoid
- Multiplying only one side of the ratio instead of both sides.
- Mixing up which term in the new ratio corresponds to the known input.
- Ignoring decimal precision when exact values matter.
- Trying to solve a ratio from an undefined setup like 0:0.
Quick FAQ
Can I use decimals?
Yes. The calculator supports integer and decimal values.
Can ratios include zero?
Yes, but not every zero case yields a unique solution. For example, converting from a term that is zero to a non-zero known value is impossible.
Does the tool simplify ratios?
Yes. The result includes a simplified ratio form when possible.
Is this the same as solving a proportion?
Exactly. Ratio-to-ratio conversion is proportion solving with a clear scale factor.
Final note
This ratio to ratio calculator is built for fast, practical use. Whether you are scaling recipes, solving homework, or standardizing data, the key idea is the same: apply one consistent multiplier to both parts of the ratio.