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Linear Interpolation — result sheet
Estimate y at an in-range x between two ordered points using a straight-line interpolation fraction.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: t = (x - x0)/(x1 - x0); y = (1 - t)y0 + ty1, for x0 < x1 and x0 <= x <= x1.
Linear interpolation uses the fraction of the horizontal interval reached by x and applies the same fraction between y0 and y1. Reversed or equal endpoints and out-of-range targets are rejected.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First x0 — The lower endpoint x coordinate.; minimum -1000000; maximum 1000000
- Second x1 — The upper endpoint x coordinate; it must exceed x0.; minimum -1000000; maximum 1000000
- First y0 — The y value paired with x0.; minimum -1000000; maximum 1000000
- Second y1 — The y value paired with x1.; minimum -1000000; maximum 1000000
- Target x — The target must lie from x0 through x1.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| First x0 | 0 |
| Second x1 | 10 |
| First y0 | 20 |
| Second y1 | 40 |
| Target x | 2.5 |
t = 0.25 and the interpolated y is 25.
Assumptions and limits
- The two endpoint x values are ordered with x0 less than x1, and x lies in the closed interval between them.
- The relationship between the endpoint pairs is modeled as a straight line; no curvature, uncertainty, or extrapolation is inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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