How to Calculate Linear Interpolation: Formula, Steps & Examples
Learn how to calculate Linear Interpolation — the formula explained step by step, with worked examples and a free calculator to check your answer.
Linear Interpolation Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
Interpolated y
30.0000
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Linear Interpolation Calculator
The Linear Interpolation Calculator works out your interpolated y in an instant. Enter x1, y1 and x2 and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the x1.
- Enter the y1.
- Enter the x2.
- Enter the y2.
- Enter the x to interpolate.
- Read off your interpolated y — the calculator updates automatically, with no button to press.
Formula
The Linear Interpolation Calculator uses the formula:
Interpolated y = y1 + (x to interpolate - x1) × (y2 - y1) ÷ (x2 - x1)
Worked example
For example, with x1 of 0, y1 of 0, x2 of 10 and y2 of 100 and the other inputs, the interpolated y is 30.0000.
| x1 | 0 |
|---|---|
| y1 | 0 |
| x2 | 10 |
| y2 | 100 |
| x to interpolate | 3 |
| Interpolated y | 30.0000 |
|---|
Results are estimates for educational use, not professional advice.
Frequently asked questions
It estimates a value between two known points by assuming a straight line between them. Between (0,0) and (10,100), x=3 gives y=30.
y = y1 + (x − x1) × (y2 − y1) ÷ (x2 − x1), which scales along the line between the two points.
Reading between table values, scaling measurements, and filling gaps in data series all use it.
Extrapolation uses the same line to estimate beyond the known points, which is less reliable than interpolating between them.
Enter the x1. Enter the y1. Enter the x2. Enter the y2. Enter the x to interpolate. Read off your interpolated y — the calculator updates automatically, with no button to press.