Calculator Form
Use one mode at a time. The layout stays in one page column, while fields adapt across large, medium, and mobile screens.
Example Data Table
| Scenario | Known Data | Formula Used | Output |
|---|---|---|---|
| Find y₂ | x₁ = 4, y₁ = 20, x₂ = 9 | k = y₁ / x₁ = 5, y₂ = 5 × 9 | y₂ = 45 |
| Find x | y = 36, k = 4.5 | x = y / k | x = 8 |
| Scale pair | (3, 18), factor = 2.5 | x₂ = fx₁, y₂ = fy₁ | (7.5, 45) |
| Verify | (2, 10) and (7, 35) | 10 / 2 = 35 / 7 | Yes, directly proportional |
Formula Used
Main relationship: y = kx
Constant of proportionality: k = y / x
Missing output: y₂ = (y₁ / x₁) × x₂
Missing input: x₂ = y₂ / (y₁ / x₁)
Verification: y₁ / x₁ = y₂ / x₂
Direct proportion means both quantities move together at a constant rate. When one quantity doubles, the other doubles too. The constant k stays the same for every valid pair in the relationship.
How to Use This Calculator
- Select the solving mode that fits your proportion problem.
- Enter the known values in the visible fields only.
- Choose decimal places and add a unit label if needed.
- Click Calculate to display the result above the form.
- Review the solved values, constant, and worked steps.
- Download the output as CSV or PDF whenever required.
Frequently Asked Questions
1. What does direct proportion mean?
Direct proportion means two quantities change at the same constant rate. Their ratio stays fixed, so one value increases or decreases in the same multiplier as the other.
2. When should I use pair mode?
Use pair mode when you already know one complete pair and one value from a second pair. Leave exactly one target field blank, and the solver finds the missing value.
3. What is the constant k?
The constant k is the proportional rate between y and x. It equals y divided by x, and every correct pair in the same proportion shares that constant.
4. Why can x not be zero in some modes?
The solver often computes k = y / x. If x equals zero, the ratio becomes undefined, so the constant cannot be derived reliably from that pair.
5. How does the verification mode work?
Verification mode computes the proportional constant for each pair separately. If both constants match within the selected precision, the pairs are treated as directly proportional.
6. What does the scale mode show?
Scale mode multiplies both values in a known pair by the same factor. This preserves the direct proportion and helps you build a new matching pair quickly.
7. What is included in the CSV and PDF downloads?
Both downloads include the result summary, key calculated values, formula reference, and worked steps. They are useful for homework records, audits, and quick reporting.
8. Can I use decimals and units?
Yes. The calculator accepts decimal entries, lets you control displayed precision, and adds an optional unit label to the relevant numeric results.