Calculator Inputs
Example Data Table
| Model | Initial Strength | Reference Distance | Target Distance | Exponent | Estimated Target Strength |
|---|---|---|---|---|---|
| Inverse Ratio | 120 units | 2 m | 6 m | 1 | 40 units |
| Inverse Square | 100 units | 1 m | 4 m | 2 | 6.25 units |
| Custom Power | 80 units | 3 m | 9 m | 1.5 | 15.40 units |
| Inverse Square | 250 units | 5 ft | 10 ft | 2 | 62.50 units |
| Custom Power | 60 units | 1 km | 2.5 km | 2.2 | 7.99 units |
Formula Used
- General model: S(d) = Sref × (dref / d)n
- Remaining ratio: S(d) / Sref = (dref / d)n
- Reference : target ratio: Sref / S(d)
- Decrease percent: ((Sref - S(d)) / Sref) × 100
- Inverse ratio model: n = 1
- Inverse square model: n = 2
- Custom model: n can be any positive value
How to Use This Calculator
- Choose a decay model that matches your problem.
- Enter the known strength at the reference distance.
- Type the reference distance and the target distance.
- Enter a custom exponent only when custom mode is selected.
- Add an optional comparison distance for extra analysis.
- Set chart range, point count, units, and decimal places.
- Press calculate to show the result above this form.
- Use the export buttons to save CSV and PDF copies.
Understanding Ratio Strength Decrease with Distance
Why Distance Changes Strength
Many systems weaken as distance grows. Light spreads. Sound spreads. Signals spread too. The same source energy covers a wider area. That lowers the measured strength. A ratio-based calculator helps you describe this change clearly. It shows how much remains. It also shows how much was lost between two distances.
How the Ratio Model Works
This page uses a power model. It starts with a known strength at one distance. Then it estimates strength at another distance. The exponent controls the speed of change. An exponent of one means a simple inverse ratio. An exponent of two means inverse square decay. Larger exponents create a steeper drop. Smaller exponents create a softer decline.
Why Ratios Matter
Ratios are easy to compare. A result of 4:1 means the reference point is four times stronger. That is often easier to read than a long decimal. Percentage values help too. They show the remaining share of the original strength. They also show the size of the decrease. These outputs help when you review spacing, performance, or coverage.
Using the Extra Options
The comparison distance adds another checkpoint. This helps when you test more than one location. The chart range lets you see the full curve. That is useful for reports and planning. Export buttons help you keep a record. CSV works well for spreadsheets. PDF is useful for sharing clean summaries. The example table also gives you a quick starting point.
Best Practice for Reliable Results
Use consistent units. Keep all distances in the same scale. Use a realistic exponent. If your model is unknown, test more than one value. Compare the graph shapes. Look at the remaining percentage and the ratio together. That gives a fuller picture. A single number can miss important context. A combined view is usually more useful.
Frequently Asked Questions
1. What does ratio strength decrease with distance mean?
It describes how a value becomes weaker as distance grows. The calculator shows the new strength, the remaining percent, and the ratio between reference and target points.
2. Which model should I choose?
Use inverse ratio for a simple 1/d pattern. Use inverse square for spread over area. Use custom power when your data follows a different decay rate.
3. Why does inverse square drop faster?
Because distance is squared in the denominator. When distance doubles, the remaining strength becomes one quarter of the starting reference value.
4. Can I use any distance unit?
Yes. You can use meters, feet, kilometers, centimeters, or any other unit. Just keep every distance entry in the same unit.
5. What is the remaining strength percentage?
It is the target strength divided by the reference strength, multiplied by one hundred. It shows how much of the original value still remains.
6. Why add a comparison distance?
It lets you inspect a second location without re-entering everything. This is useful when comparing candidate distances, layouts, or checkpoints in one calculation.
7. Can this calculator be used outside physics?
Yes. Any problem that follows distance-based weakening can use the same math. That includes abstract models, teaching examples, and simplified planning work.
8. What do the CSV and PDF options save?
CSV saves the result summary and plotted points in table form. PDF captures the result section, summary table, and graph for quick sharing.