Ratio calculator
Simplify a ratio or solve the missing side of a proportion with the scaling math shown step by step.
What this calculator covers
Use this ratio calculator to reduce a ratio into simplest form or to scale one known side into its matching partner.
The result keeps the simplified ratio and the unit-rate logic in view, which makes it easier to audit a proportion instead of treating it like a black box.
Frequently asked questions
- What does it mean to simplify a ratio?
- Simplifying a ratio means dividing both sides by their greatest common factor until no larger whole-number divisor exists. For example, 12:8 simplifies to 3:2. The relationship between the two quantities stays the same; only the numbers get smaller and easier to read.
- How do I solve for a missing side in a proportion?
- Enter the base ratio (A:B) and the known value for one side, then choose whether you want to solve for the other side. The calculator scales the known value by the unit rate — how much of the unknown side corresponds to one unit of the known side — to find the answer.
- Can I use decimals in the ratio fields?
- Yes. The calculator scales decimal inputs up to whole numbers before finding the greatest common divisor, so ratios like 1.5:2.5 are simplified correctly to 3:5.
- What is a unit rate?
- A unit rate expresses the ratio with one side set to 1, for example "1 A = 1.67 B." It shows how many units of one quantity correspond to a single unit of the other, which is the scaling factor used to solve a proportion.
Tool
Run the calculation
Result
RESULT · RATIO
â„–111
Primary result
20
Using the ratio 3:5, a A value of 12 gives B = 20.
- Simplified ratio
- 3:5
- Unit rate
- 1 A = 1.666667 B
- Solved B
- 20
Step-by-step solution
- 1.Simplify the starting ratio 3:5 to 3:5.
- 2.Turn the ratio into a unit rate so one known side can scale the other side proportionally.
- 3.Multiply the known value 12 by that unit rate to solve B = 20.
Walkthrough
Visual walkthrough
Proportion solving works by finding how many ratio-units fit inside the known side, then carrying that scale to the unknown side.
01
Reduce the base ratio
3:5
Using the simplest ratio makes the scaling relationship easier to read and explain.
02
Find the scale factor
1 A = 1.666667 B
The unit rate says how much of the unknown side belongs to one unit of the known side.
03
Scale to the unknown side
Multiply the known measurement by the unit rate to keep both sides in the same proportion.
B = 20