This ratio and proportion calculator is provided by Hesapstan to solve one unknown in A/B = C/D, simplify an A:B ratio, scale a ratio by a multiplier, and compare two ratios in one place.
What does this calculator do?
This calculator performs four common ratio and proportion operations: it solves one missing value in A/B = C/D, simplifies a two-part ratio, scales a ratio by a multiplier, and compares two ratios.
- Proportion solving: find the missing value in A/B = C/D.
- Ratio simplification: reduce a ratio such as 6:4 to 3:2.
- Ratio scaling: turn 2:3 into 10:15 by multiplying both parts by 5.
- Ratio comparison: decide whether 3:4 is equal to, greater than, or less than 6:7.
Ratio vs proportion
A ratio compares two values, while a proportion states that two ratios are equal. For example, 3:4 is a ratio, and 3/4 = 6/8 is a proportion.
This difference matters because simplifying a ratio and solving a proportion are different tasks. Simplifying rewrites one ratio in a cleaner equivalent form; solving a proportion finds a missing value in a four-term equality.
How does the proportion solver work?
The proportion solver works when exactly one value is missing in A/B = C/D. The calculator detects the blank field and solves it algebraically using cross-multiplication.
- If A is missing: A = (B × C) / D
- If B is missing: B = (A × D) / C
- If C is missing: C = (A × D) / B
- If D is missing: D = (B × C) / A
In proportion-solving mode, exactly one field must be left blank. If two or more values are missing, the calculator cannot determine a single result.
How does ratio simplification work?
Ratio simplification reduces an A:B ratio to an equivalent form with smaller terms. For example, 6:4 simplifies to 3:2.
Decimal inputs are supported. The calculator first scales decimal values into a suitable integer form, then reduces the ratio using a common-factor approach. This is not a percentage calculation; it is a way to express the same relationship more clearly.
What is ratio scaling?
Ratio scaling multiplies both parts of a ratio by the same number, keeping the relationship unchanged. For example, scaling 2:3 by 5 gives 10:15.
This is useful for recipes, mixtures, drawing scale, classroom examples, and other situations where the same relationship needs to be expressed with larger or smaller numbers.
How are two ratios compared?
Two ratios can be compared by cross-multiplication. For A:B and C:D, the calculator compares A × D with C × B to decide whether the ratios are equal or which one is greater.
The result also shows decimal equivalents so the comparison is easier to understand. Cross-multiplication helps avoid misleading conclusions from rounded decimal values.
Examples
Proportion example: if A = 3, B = 4, C = 6, and D is blank, the result is D = 8 because 3/4 = 6/8.
Simplification example: 12:8 reduces to 3:2. Scaling example: 2:3 scaled by 4 becomes 8:12. Comparison example: 3:4 is less than 6:7 because 0.75 is less than about 0.857.
What this calculator does not do
This calculator is for ratio and proportion operations. It is not designed for percentage increase, percentage decrease, discount rate, or percent-of-a-value calculations.
A ratio compares values with each other, while a percentage expresses a value out of 100. Use the Percentage Calculator when your question is about percentages rather than ratios.
Frequently Asked Questions
What does A/B = C/D calculate?
It represents a proportion. If exactly one of the four values is missing, the calculator uses the other three values to solve the unknown.
Why must there be exactly one blank value?
A single proportion equation can determine one unknown value. If two or more values are missing, there is not enough information for a unique result.
How do you simplify a ratio?
A ratio is simplified by dividing both parts by their common factor. For example, 6:4 simplifies to 3:2.
Can I simplify decimal ratios?
Yes. The calculator supports decimal inputs by scaling them into a suitable integer form before simplifying.
What is ratio scaling used for?
Ratio scaling is used when you want to keep the same relationship but express it with larger or smaller numbers, such as scaling a recipe or mixture.
Does scaling change the ratio?
No. Multiplying both parts by the same number keeps the ratio equivalent; it only changes the size of the terms.
How does ratio comparison work?
The calculator compares A:B and C:D by cross-multiplying A × D and C × B, then reports whether the ratios are equal or which one is greater.
Is this the same as a percentage calculator?
No. Ratios and percentages are related but different. Use a percentage calculator for percent increase, discount, or percent-of-a-value questions.