Math & Statistics
Ratio Calculator
Simplify two-part ratios, convert them to shares and percentages, solve an equivalent proportion, compare scale scenarios, visualize the composition, and export a professional PDF calculation record.
Simplified ratio-
A divided by B-
A share of total-
B share of total-
Equivalent term B-
Proportion analysis
Equivalent values at common scale factors
Composition of the entered ratioEach bar shows one term's share of the combined total
| Scale | Term A | Term B | Combined total | A share | B share |
|---|
Decision view
Part-to-part and part-to-whole ratio
A · 40%B · 60%
How to use Ratio Calculator
- Enter both ratio terms and a target value for the first term of an equivalent proportion.
- Check the simplified ratio, quotient, and each term's share of the combined total.
- Use the equivalent-value table to confirm both terms are multiplied by the same scale factor.
- Keep units consistent and distinguish a part-to-part ratio from a part-to-whole percentage.
Calculator guide
Understanding Ratio Calculator
A ratio compares quantities using a common scale. Simplifying exposes the smallest whole-number relationship, while shares and percentages show how each term contributes to the combined whole.
Calculation method
How the calculation works
Simplified ratio = each term divided by the greatest common divisor; equivalent terms share the same scale factor. Reduce integer terms by their greatest common divisor, divide one term by the other for relative scale, and divide each term by the combined total for composition percentages. Solve a missing equivalent term with cross multiplication.
Ratio structure
Simplification preserves proportion
A ratio changes appearance when both terms are divided or multiplied by the same nonzero factor, but its proportional relationship stays constant.
Worked example
From 24:36 to an equivalent recipe
Dividing both terms by 12 gives 2:3. If the first term becomes 20, multiplying both simplified terms by 10 makes the second term 30.
Worked situations
Practical examples
- Reduce 24:36 to the lowest whole-number ratio 2:3.
- Scale a 2:3 recipe so the first ingredient becomes 20 units.
- Convert both terms into their 40% and 60% shares of the combined total.
Better inputs
Useful tips
- Convert measurements to the same unit before comparing.
- Keep both ratio terms in the same order throughout the calculation.
- Use shares when the two terms are parts of one combined total.
Before relying on the result
Limitations and common mistakes
- Decimal terms are scaled before whole-number simplification and may be affected by entered precision.
- A zero denominator cannot form a finite quotient.
- A ratio describes relative size but not causation or statistical association.
Reference
Key terms
- Ratio
- Relative comparison between two quantities.
- Equivalent ratio
- Ratio with the same proportional relationship.
- Scale factor
- Multiplier applied to every term.
- Proportion
- Equation stating that two ratios are equal.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
How is a ratio simplified?
Divide both integer terms by their greatest common divisor.
Can a ratio contain decimals?
Yes. Scale the decimals to whole numbers before reducing when an exact finite representation is available.
Is 2:3 the same as 4:6?
Yes. Multiplying both terms by two preserves the relationship.
How are ratio percentages calculated?
Divide each term by the sum of both terms and multiply by 100.