Calculator Input
Formula Used
Primary Interpolation Formula
y(x) = y0 × (y1 / y0)^((x - x0) / (x1 - x0))
Equivalent Exponential Model
y = a × e^(k x)
k = ln(y1 / y0) / (x1 - x0)
a = y0 / e^(k x0)
Exponential interpolation assumes the rate of change is multiplicative rather than additive. That makes it useful when data behaves like growth, decay, compounding, population change, radioactive decrease, biological scaling, or other nonlinear trends.
How to Use This Calculator
- Enter the first known point as X0 and Y0.
- Enter the second known point as X1 and Y1.
- Add one or more target X values separated with commas.
- Choose the number of decimal places for displayed results.
- Set chart points for a smoother or lighter Plotly curve.
- Click Calculate Now to show results above the form.
- Review the table, curve, and growth metrics.
- Export the result table as CSV or PDF when needed.
Example Data Table
Example known points: (1, 50) and (5, 800). Example target X values: 2, 3, 4.
| X | Interpolated Y | Type |
|---|---|---|
| 2 | 100 | Interpolation |
| 3 | 200 | Interpolation |
| 4 | 400 | Interpolation |
Frequently Asked Questions
1) What is exponential interpolation?
It estimates an unknown value between two known points by assuming multiplicative change. Instead of a straight line, it follows an exponential curve.
2) When should I choose exponential interpolation over linear interpolation?
Use it when values grow or decay by ratios, percentages, or compounding effects. Linear interpolation is better when changes stay roughly additive.
3) Why must Y values be greater than zero?
The exponential model uses logarithms and ratios. Zero or negative Y values break that assumption, so the interpolation would not be valid.
4) Can I enter several target X values at once?
Yes. Add them as a comma separated list, such as 2, 2.5, 3, 4.75. The calculator returns a full result table.
5) Does the calculator also support extrapolation?
Yes. If a target X lies outside the known interval, the table labels it as extrapolation. That can be useful, but uncertainty usually increases.
6) What does the growth factor per unit mean?
It shows how much Y multiplies when X increases by one unit. A factor of 1.10 means 10% growth per unit.
7) What does the Plotly graph show?
The graph shows the exponential curve, both known points, and predicted target points. It helps you verify shape, direction, and scale visually.
8) Can I export my results?
Yes. Use the CSV button for spreadsheet work or the PDF button for reports, sharing, printing, and documentation.