Linear Interpolation Calculator (Find y Between Two Points)
By Santaji GadepatilinUpdated November 4, 2026
Engineering tables only list values at fixed steps, so values in between are found by drawing a straight line between the two nearest points. This linear interpolation calculator does that for any table — steam tables, density charts or sensor calibration points, where the error depends on how well the curve follows a straight line, the sensor linearity.
How to use the linear interpolation calculator
Enter the two known points that bracket your value — (x₁, y₁) and (x₂, y₂) — and the x value you want. The calculator returns the interpolated y. To find x for a known y (inverse interpolation), clear x and enter y.
Linear interpolation formula
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)
Example
The density of water is 0.99821 g/cm³ at 20 °C and 0.99565 g/cm³ at 30 °C. At 25 °C:
- y = 0.99821 + (25 − 20) × (0.99565 − 0.99821) ÷ (30 − 20)
- y = 0.99821 + 5 × (−0.000256) = 0.99693 g/cm³
The tabulated value at 25 °C is 0.99705 g/cm³, so the straight-line estimate is off by 0.00012 g/cm³ — water density is slightly curved over this range.
Interpolated water density between 20 °C and 30 °C
| Temperature | Interpolated density |
|---|---|
| 20 °C | 0.99821 g/cm³ |
| 22 °C | 0.99770 g/cm³ |
| 24 °C | 0.99719 g/cm³ |
| 26 °C | 0.99667 g/cm³ |
| 28 °C | 0.99616 g/cm³ |
| 30 °C | 0.99565 g/cm³ |
Notes
- Always interpolate between the two closest table rows.
- A 4–20 mA signal is converted to engineering units with exactly this formula — see the 4–20 mA scaling calculator.
Frequently asked questions
What is the linear interpolation formula?
y = y₁ + (x − x₁)(y₂ − y₁) ÷ (x₂ − x₁). It assumes a straight line between the two known points (x₁, y₁) and (x₂, y₂).
What is the difference between interpolation and extrapolation?
Interpolation estimates a value between the known points; extrapolation extends the line beyond them. The same formula works for both, but extrapolation is much less reliable.
How accurate is linear interpolation?
It is exact for straight-line data. For curved data the error grows with the curvature and the spacing between table rows — use the closest bracketing rows, or a closer-spaced table.
How do I interpolate in a two-way table?
Use double (bilinear) interpolation — interpolate along one variable in two rows, then interpolate between those two results along the other variable.