Problems this can answer
It fills table gaps, estimates calibration values, and approximates a smooth relationship over a short interval. A related application of Linear Interpolation is endpoint slope.
Math calculator
Linear Interpolation Calculator
Estimate y between two known points by following their straight-line slope. Each submitted value produces interpolated value plus the intermediate reasoning.
Linear Interpolation inputs
Start with the given values
Seeing the method in action
From (10,40) to (20,70), x=16 lies 60% across. Applying 60% of the y-change 30 gives y=58.
The idea behind the result
Linear interpolation assumes constant change between two endpoints and takes the same fraction of the y-interval as the target occupies in the x-interval.
The calculation treats first x, first y, second x, second y and target x in the roles printed for Linear Interpolation, rather than as interchangeable entries in linear interpolation.
Before accepting the Linear Interpolation result
Equal x endpoints make the slope undefined. A target outside the interval is extrapolation and carries greater model risk.
An impossible interpolated value sign or magnitude should prompt a Linear Interpolation input review before rounding.
Reproducing the answer
Compute t=(x−x₁)/(x₂−x₁), then y=y₁+t(y₂−y₁). Check whether t lies from zero to one.
Using the result beyond this page
Start the linear interpolation setup by pairing every source number with first x, first y, second x, second y and target x. Convert unlike units before typing, and postpone rounding until the displayed interpolated value is ready to report.
Moving the target uniformly across x moves the estimate uniformly across y under the linear assumption. Use that direction of change to check the displayed interpolated value before copying it elsewhere.
When copying the result elsewhere, include its label and any squared, linear, angular, or percentage unit implied by the inputs. That record distinguishes a calculated interpolated value from an unlabeled number and makes later checking substantially easier.
Interpolation estimates between known points; a regression line fits a trend across a larger dataset. Keep that boundary in mind when interpreting the numerical result.
For later verification, record first x, first y, second x, second y and target x before rounding the interpolated value. The unrounded working value can feed subsequent steps while the rounded value serves presentation.
Interpreting the interpolation fraction
The parameter t is zero at the first endpoint, one at the second, and between them for interpolation. Values below zero or above one flag extrapolation automatically. Reporting t beside the estimate shows how far the target lies through—or beyond—the known x interval.
Questions about Linear Interpolation
What does t represent?
The target’s fractional position between the endpoints.
Can I extrapolate?
The formula can, but the assumption is less reliable outside the interval.
What if x₁=x₂?
Interpolation is undefined.
Does the real relationship have to be linear?
The estimate assumes it is locally linear.