Simple Linear Interpolation Calculator for Data & Graphs

Linear Interpolation Calculator with Step-by-Step Solution

A Linear Interpolation Calculator with Step-by-Step Solution estimates the value of a function at a point between two known data points by assuming the function varies linearly between them. It computes the interpolated value and shows each step so users can verify and learn the method.

What it does

• Accepts two known points (x0, y0) and (x1, y1) and a target x.
• Validates inputs (x0 ≠ x1, numeric values).
• Computes slope: m = (y1 − y0) / (x1 − x0).
• Computes interpolated y: y = y0 + m(x − x0).
• Displays the numeric substitution, intermediate values, and final result.
• Optionally shows a brief plot of the two points and the interpolation point.

Benefits

• Transparent: Users see each arithmetic step.
• Educational: Good for students learning interpolation.
• Quick: Produces results instantly for single-value estimates.
• Reusable: Works for evenly or unevenly spaced x-values.

Example (calculation steps)

Given (x0, y0) = (2, 4), (x1, y1) = (5, 10), target x = 3:

1. m = (10 − 4) / (5 − 2) = 6 / 3 = 2
2. y = 4 + 2 * (3 − 2) = 4 + 2 = 6
   Result: interpolated y = 6

Implementation notes

• Handle edge cases: x outside x0, x1, identical x0 and x1 (error).
• Provide optional rounding settings and units.
• For datasets with many points, use piecewise linear interpolation (find surrounding points first).