Keeping a usable Linear Interpolation record
Compute t=(x−x₁)/(x₂−x₁), then y=y₁+t(y₂−y₁). Check whether t lies from zero to one.
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
One set of Linear Interpolation inputs
From (10,40) to (20,70), x=16 lies 60% across. Applying 60% of the y-change 30 gives y=58.
The mathematical idea behind Linear Interpolation
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.
Using Linear Interpolation in later work
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.
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.
Confirming the Linear Interpolation setup
Substitute the Linear Interpolation solution into First x. This Linear Interpolation check rejects false Linear Interpolation branches and forbidden denominators.
Choose an easy First x value before running Linear Interpolation. Predict First y, then compare it with the Linear Interpolation output.
Start the Linear Interpolation cross-check with First x. Apply the original First y and recompute Interpolated value. Treat a different Second x as new Linear Interpolation data. That prevents its Interpolated value from being attributed to the earlier Linear Interpolation setup.
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.