How to use the Linear Interpolation Calculator
Enter two known points, x1 with y1 and x2 with y2, then the x value you are interested in. The calculator returns the y value on the straight line between the two points.
Worked example
A table lists 50 at x = 10 and 80 at x = 20, and you need the value at 14. The line rises 30 over 10 steps, or 3 per step. You are 4 steps past 10, so the answer is 50 + 4 × 3 = 62.
Where it is used
Engineers read values between rows of steam and material tables, finance teams estimate interest rates between published terms, and analysts fill short gaps in data. It works well when the points are close together. Over wide gaps or curved data, the straight line can drift away from the real value.
The formula
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)
Examples
- Between (0, 0) and (4, 3) at x = 2
Interpolated value: 1.5
- Between (0, 10) and (10, 20) at x = 5
Interpolated value: 15
- Between (20, 68) and (30, 86) at x = 25
Interpolated value: 77
Limitations and assumptions
Assumes the values change in a straight line between the two points. Results outside the two points are extrapolation and less reliable.
Frequently asked questions
What is the formula?
y = y1 + (x − x1) × (y2 − y1) ÷ (x2 − x1).
Is it accurate?
It is exact for straight lines and a close estimate for smooth curves over short gaps.
Can I extrapolate?
Mathematically yes, but values outside the points are less reliable.
Where is it used?
Reading steam tables, tax tables and engineering charts.