Calculator Inputs
Use direct or inverse proportion, solve either missing value, and tune graph precision.
Example Data Table
| Scenario | Type | Pair 1 | Known Pair 2 Input | Result |
|---|---|---|---|---|
| Recipe scaling | Direct | 4 cups flour → 20 cookies | 10 cups flour | 50 cookies |
| Travel speed | Direct | 2 hours → 120 km | 5 hours | 300 km |
| Workers and time | Inverse | 4 workers → 18 days | 6 workers | 12 days |
| Pumps and filling time | Inverse | 3 pumps → 24 minutes | 8 minutes | 9 pumps |
Formula Used
1) Direct Proportion
When two quantities increase or decrease together in the same ratio:
y = kx
Constant of proportionality:
k = y / x
2) Inverse Proportion
When one quantity increases while the other decreases so their product stays constant:
y = k / x
Constant of proportionality:
k = x × y
3) Missing Value Logic
Direct: If k is known, then y₂ = kx₂ or x₂ = y₂ / k.
Inverse: If k is known, then y₂ = k / x₂ or x₂ = k / y₂.
The calculator also reports ratio checks, products, scale factors, and percentage changes.
How to Use This Calculator
- Select Direct or Inverse proportion.
- Choose whether you want to solve the second Quantity A or second Quantity B.
- Enter the first known pair of proportional values.
- Enter the known second-pair value and leave the missing field empty.
- Pick precision, graph points, and optional graph limits, then press Calculate Proportion.
FAQs
What are proportional quantities?
Proportional quantities change in a predictable relationship. In direct proportion, their ratio stays constant. In inverse proportion, their product stays constant.
When should I use direct proportion?
Use direct proportion when one quantity grows or shrinks at the same rate as the other. Doubling one value doubles the other.
When should I use inverse proportion?
Use inverse proportion when increasing one quantity causes the other to decrease so that the product stays unchanged, such as workers and completion time.
What does the constant k mean?
k describes the fixed relationship between the variables. For direct proportion it is the common ratio. For inverse proportion it is the common product.
Why does the graph look different for direct and inverse types?
Direct proportion forms a straight line because y changes linearly with x. Inverse proportion creates a curve because y depends on dividing the constant by x.
Can I use decimals and negative values?
Yes. Decimals work for both models. Negative values can also work mathematically, though inverse graphs near zero require extra care because division by zero is undefined.
What do the CSV and PDF buttons export?
They export the current summary and generated point table. The PDF option also captures the visible result section for quick sharing or record keeping.
How can I verify my answer is correct?
Check the constant, scale factors, and the ratio or product shown in the summary table. Matching values confirm that the computed pair fits the selected proportion.