Formula
y = y₁ + (x − x₁) × (y₂ − y₁) / (x₂ − x₁)
Draw a straight line through (x₁, y₁) and (x₂, y₂), then read y at your x.
Example
Known: 25 at x = 10, and 45 at x = 20. Find y at x = 14.
y = 25 + (14 − 10) × (45 − 25) / (20 − 10) = 25 + 4 × 2 = 33
Why it works
(y₂ − y₁)/(x₂ − x₁) is the slope of the line. Multiply it by how far you move from x₁ and add the result to y₁.
Equivalently, x = 14 is 40% of the way from 10 to 20, so y is 40% of the way from 25 to 45.
Interpolation vs. extrapolation
If x is between x₁ and x₂, you're interpolating, which is reliable for smooth data. If x is outside that range, you're extrapolating: the same formula applies, but you're assuming the trend continues.
Common uses
- Engineering tables (steam, refrigerant, material properties). For two inputs, use bilinear interpolation.
- Calibration curves and lab readings.
- Rates between two dates or maturities.
- Need x from y instead? Use inverse interpolation.
FAQ
Does the order of the points matter?
No. Swapping the two points gives the same result.
How do I do it in Excel?
With x₁, y₁ in A2:B2, x₂, y₂ in A3:B3 and x in D2: =B2+(D2-A2)*(B3-B2)/(A3-A2). Or use the free template.
How accurate is it?
Exact for straight-line data. For curved data, accuracy depends on how close the two points are. Use closer points or Lagrange interpolation.