Situation
Example matching the default values: A = 120, B = 80 and target total = €1,000. The 120:80 ratio simplifies to 3:2; A represents 60%, or €600, and B represents 40%, or €400.
Ratio Calculator
The ratio calculator describes the relationship between two quantities and simplifies it for readability. It helps compare two volumes, split a total or translate a proportion into parts. It is not a rule of three: the main goal here is to understand the relationship between A and B, keep both sides visible and avoid turning every comparison into a single percentage too early.
Formula used
Simplified ratio = (A ÷ GCD(A,B)) : (B ÷ GCD(A,B))
The engine converts both values into comparable numbers, simplifies them with their greatest common divisor when possible, then calculates shares of the total. With A and B, A's share = A ÷ (A + B), and B's share = B ÷ (A + B).
Worked example and result reading
Interpretation
The simplified ratio shows how many parts of A correspond to how many parts of B. The percentages then show each side's place in the whole. For allocation, the target total is divided by these parts, not by reading the raw values separately.
Detailed calculation guide
Simplified relationship
Turning 120:80 into 3:2 helps reveal the real structure of the comparison. Simplifying does not change the proportion; it only makes it clearer.
Shares of a total
In a 3:2 ratio, there are 5 total parts. The first quantity receives 3 out of 5, or 60%, and the second receives 2 out of 5, or 40%.
Allocation
If a €1,000 budget follows a 3:2 ratio, it is split into €600 and €400. The target total turns the relationship into concrete amounts.
Ratio or percentage
A percentage converts a share to 100. A ratio keeps the relationship between two sides, which is often clearer for a recipe, allocation or technical comparison.
Decimal and inverse
The decimal A ÷ B shows how much A is worth compared with B. The inverse B ÷ A gives the opposite reading. Both can be useful depending on the question.
Units
Comparing kilograms with euros or kilometers with hours only makes sense if the context supports it. Otherwise, convert first or choose a more suitable indicator.
Key takeaways
- A ratio compares two quantities with each other.
- The simplified form makes the relationship easier to read.
- Shares of a total use A + B as the base.
- An inconsistent unit can make the ratio misleading.
Decision checklist
- Both values describe comparable quantities.
- The target total is the amount that should be allocated.
- The simplified ratio is read with both sides.
- Percentages use A + B as the base.
- The displayed unit or currency matches the real context.
Result checks before use
Identify the starting quantity
Before calculating, clearly define the base, unit, total or reference number. In practical math, many errors come from the wrong base, early rounding or confusion between change and final value. Writing the reference value first usually prevents the most common inversion mistakes.
Check the order of magnitude
After calculating, estimate whether the result is plausible. A percentage above 100%, an average outside the range, a simplified fraction or a probability should remain consistent with the starting values. This quick plausibility check catches many input errors before the result is reused.
Compare with an inverse method
When possible, verify the result in reverse: rebuild the total, return to the initial value, multiply after division or test cross multiplication. This quickly reveals inversions and unit errors.
Keep useful precision
Keep a few decimals during the calculation and round only at the end. This avoids accumulated gaps in percentages, ratios, probabilities, fractions and conversions used in an exercise or decision.
Scenarios to compare
Budget
A 3:2 ratio on €1,000 gives €600 for A and €400 for B.
Mix
2:1 means two parts of one ingredient for one part of the other.
Comparison
120 versus 80 reads as A being 1.5 times B.
Sharing
A total can be allocated by ratio parts instead of being split equally.
Common mistakes to avoid
- Reading 3:2 as 3% and 2%.
- Splitting the total without adding all ratio parts.
- Comparing values expressed in different units.
- Forgetting that a simplified ratio does not give the total volume.
- Confusing ratio, rule of three and average.
What to know before using the result
The result assumes the two quantities are comparable and positive in the studied context. A ratio does not prove causality, does not fix inconsistent units and does not replace a full statistical or financial analysis.
Frequently asked questions
How do you simplify a ratio?
Divide both values by their greatest common divisor when the values allow it.
What does a 3:2 ratio mean?
It means 3 parts on one side for 2 parts on the other, or 5 total parts.
How do you split a total using a ratio?
Add the parts, then multiply the total by each side's share.
How is this different from the rule of three?
A ratio describes a relationship; the rule of three uses a proportion to find a missing value.
Related calculators
Percentage Calculator
Quick and precise calculations for margins, changes, and ratios.
Rule of Three
Solve for variables through direct mathematical proportion.
Fraction Calculator
Add, subtract, multiply and divide fractions with a simplified result.
Unit Converter
Convert measurements between metric and imperial systems: length, mass, volume, temperature, area and speed.
Average Calculator
Calculate a simple or weighted average, inspect coefficients, median, spread, contribution and distribution charts.
Percentage Change Calculator
Calculate an increase, decrease, absolute delta, multiplier and target gap between an initial and final value.