Plot No. 57 · Education
Ratio Calculator (Simplify and Solve)
Simplify a ratio and solve a proportion in one place. To simplify A to B it divides both terms by their greatest common divisor. To solve A:B equals C:x it rearranges to x equals B times C divided by A, giving the missing term.
The simplifier divides both terms by their greatest common divisor. The proportion solver uses x equals B times C divided by A, so A:B and C:x describe the same ratio. Term A must not be zero to solve.
The link saves your inputs so you can bookmark or share this exact result.
How the ratio is simplified and solved
This does two jobs. To simplify a ratio A to B it finds the greatest common divisor of the two terms and divides both by it, leaving the ratio in its lowest whole-number terms. To solve a proportion, where A:B equals C:x, it cross multiplies and rearranges to x equals B times C divided by A, returning the missing fourth term.
The two halves share the A and B inputs, so a single pair of numbers both reduces and scales. Reducing tells you the simplest form of a ratio; solving tells you what a ratio becomes when one side is scaled up or down to a new first term.
How to use the ratio calculator
- Enter term A and term B, the ratio you want to simplify.
- Read the simplified ratio, both terms divided by their greatest common divisor.
- Enter term C to solve A:B = C:x, and read the missing value x.
Worked examples
A widescreen ratio
Inputs: A 16, B 9, C 32
Result: 16:9 stays 16:9 because 16 and 9 share no common factor above 1. Solving 16:9 = 32:x gives x = 18, since 9 times 32 divided by 16 is 18.
A ratio that reduces
Inputs: A 16, B 8, C 40
Result: 16:8 simplifies to 2:1 (both divide by 8). Solving 16:8 = 40:x gives x = 20.
Limitations and common mistakes
Edge cases and limitations
- Whole-number simplification only runs when both A and B are integers; decimal terms are shown side by side rather than reduced.
- The proportion solver needs term A to be non-zero, because dividing by zero has no answer.
Common mistakes
- Reading x as the simplified second term; x is the answer to the proportion A:B = C:x, not the reduced form of A:B.
- Entering the terms in the wrong order, which swaps the ratio. 16:9 and 9:16 are different ratios and give different results.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 16 to 9 the greatest common divisor is 1, so 16:9 is already in its lowest terms. For 16 to 8 the divisor is 8, which reduces the ratio to 2:1.
How do I solve a proportion like A:B = C:x?
Cross multiply and rearrange to x equals B times C divided by A. With A as 16, B as 9 and C as 32, x equals 9 times 32 divided by 16, which is 18. So 16:9 is the same ratio as 32:18.
Why does 16:9 stay 16:9?
Because 16 and 9 share no common factor greater than 1, their greatest common divisor is 1. A ratio only reduces when both terms can be divided by the same whole number, so 16:9 is already as simple as it gets.
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