Linear Interpolation Calculator
Estimate a value that falls between two known data points by assuming a straight line between them. Enter the two points and the x you are interested in to get the interpolated y, the slope and the equation of the line.
- Slope
- 3
- Type
- Interpolation (between the points)
- Line through the points
- y = 3x + 20
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter the first known point (x₁, y₁).
- Enter the second known point (x₂, y₂).
- Enter the x value where you want an estimate.
- Read the estimated y. The type line warns you if x lies outside the two points.
Worked examples
Between (10, 50) and (20, 80), at x = 14
- Estimated y
- 62
- Slope
- 3
- Line through the points
- y = 3x + 20
Between (1, 2) and (5, 10), at x = 3
- Estimated y
- 6
- Slope
- 2
- Line through the points
- y = 2x
A worked example
Between (10, 50) and (20, 80), at x = 14: the slope is (80 − 50) ÷ (20 − 10) = 3, so y = 50 + (14 − 10) × 3 = 62.
Another way to see it: 14 is 40% of the way from 10 to 20, so y is 40% of the way from 50 to 80.
When to trust it
Interpolation assumes the relationship is a straight line between the two points. That is a good approximation for closely spaced table entries — steam tables, tax tables, calibration charts — and a poor one for strongly curved data with widely spaced points.
Extrapolation, estimating outside the known points, uses the same formula but carries more risk, because nothing confirms the trend continues.
Questions people ask
What is y at x = 14 between (10, 50) and (20, 80)?
62.
What is y at x = 3 between (1, 2) and (5, 10)?
6. The slope is 2, so y = 2 + (3 − 1) × 2.
What is the difference between interpolation and extrapolation?
Interpolation estimates a value between two known points; extrapolation estimates one beyond them. Both use the same straight-line formula.