Linear Interpolation Calculator
Linear interpolation calculator: estimate a value between two known points (x₁, y₁) and (x₂, y₂), or solve for any of the six values.
y = y₁ + (x − x₁) · y₂ − y₁x₂ − x₁
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
The straight line through both points gives y = y₁ + (x − x₁)(y₂ − y₁)/(x₂ − x₁). Useful for steam tables, tax brackets and other engineering data.
Formula
y = y₁ + (x − x₁) · y₂ − y₁x₂ − x₁
| Symbol | Quantity | Units |
|---|---|---|
| x₁ | x₁ | — |
| y₁ | y₁ | — |
| x₂ | x₂ | — |
| y₂ | y₂ | — |
| x | x (point to estimate) | — |
| y | y (interpolated value) | — |
Worked example
Given: x₁ = 10 · y₁ = 50 · x₂ = 20 · y₂ = 80 · x = 13
y = y₁ + (x − x₁) y₂ − y₁x₂ − x₁
Result: y = 59
y (interpolated value) for different values of x₁
| x₁ · x₁ | y · y (interpolated value) |
|---|---|
| 5 | 66 |
| 7.5 | 63.2 |
| 9 | 60.909 |
| 10 | 59 |
| 11 | 56.667 |
| 12.5 | 52 |
| 15 | 38 |
Other values as in the worked example.
Frequently asked questions
Between (10, 50) and (20, 80), what is y at x = 13?
59.
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