Calculating your interpolated y is straightforward once you know the Linear Interpolation formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Linear Interpolation Calculator.
What is Linear Interpolation?
The Linear Interpolation calculation tells you your interpolated y from a few simple inputs. The figure you are solving for here is the interpolated y.
The Linear Interpolation formula
The core formula is:
Interpolated y = y1 + (x to interpolate - x1) × (y2 - y1) ÷ (x2 - x1)Here is what each input means:
- x1 — a number. Example: 0.
- y1 — a number. Example: 0.
- x2 — a number. Example: 10.
- y2 — a number. Example: 100.
- x to interpolate — a number. Example: 3.
How to calculate it step by step
- Write down the x1 (for example, 0).
- Write down the y1 (for example, 0).
- Write down the x2 (for example, 10).
- Write down the y2 (for example, 100).
- Write down the x to interpolate (for example, 3).
- Apply the formula above to get your interpolated y.
- Double-check the result with the Linear Interpolation Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| x1 | 0 |
| y1 | 0 |
| x2 | 10 |
| y2 | 100 |
| x to interpolate | 3 |
| Interpolated y | 30.0000 |
With x1 of 0, y1 of 0, x2 of 10 and y2 of 100, the interpolated y works out to 30.0000.
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Linear Interpolation Calculator does it instantly, for free, with the formula and a worked example built in.
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