Formula
x = x₁ + (y − y₁) × (x₂ − x₁) / (y₂ − y₁)
This is the linear interpolation formula solved for x.
Example
The reading is 2.5 at x = 100 and 3.7 at x = 150. At what x is it 3?
x = 100 + (0.5 / 1.2) × 50 ≈ 120.833
Typical uses
- Finding the temperature at which a property reaches a value in a steam table.
- Reading x off a calibration curve from a measurement.
- Finding when a quantity crosses a threshold.
FAQ
Why do I get an error when y₁ equals y₂?
The line between the points is flat, so every x gives the same y and there is no single answer.
Can I do this with a whole table?
Yes, if y always increases or always decreases. Put y in the first column and x in the second in the table calculator.