Ratio Calculator
Adjust the inputs below. Results update as you type.
How it works
A ratio a:b is simplified by dividing both terms by GCF(a,b). Equivalent ratio: a:b = ka:kb for any k. To solve a:b = c:x, cross-multiply: x = bc/a. Ratios appear in scale models, cooking recipes, map scales, financial analysis (P/E ratio), and mixture problems. The golden ratio (≈1.618:1) appears in art, architecture, and nature.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
A ratio a:b compares quantities. Scale both sides by the same factor to keep it equal, or solve a proportion a:b = c:d by cross-multiplying ad = bc.
Worked example
Scaling 2:3 to a total of 25 parts: each 'part' is 25 ÷ 5 = 5, giving 10:15.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
How do I simplify a ratio?+
Divide both numbers by their greatest common divisor. 12:18 ÷ 6 = 2:3 in simplest form.
How do I solve a proportion?+
Cross-multiply: for a:b = c:d, set ad = bc and solve for the unknown.
How do I scale a recipe by ratio?+
Multiply every ingredient by the same factor. Doubling a 2:1 mix keeps it 2:1 but uses twice as much of each.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.