Linear Interpolation Calculator

What this calculator does

You have two data points and you need a value that sits between them, one nobody actually measured. A reading at 10 and another at 20, but the one you want is at 14. Linear interpolation fills that gap by assuming a straight line runs between the two points you do have, and reading the value off it.

Enter the two known points and the x you are after, and it returns the matching y.

Using the calculator

1. Enter the first point, x1 and y1.
2. Enter the second point, x2 and y2.
3. Enter the x you want to interpolate at, and press Calculate.

The result is the interpolated y, along with the slope and intercept of the line.

What interpolation is

Interpolation means filling in a value between known data points. Linear interpolation does it the simplest way, by assuming the two points are joined by a straight line and reading off the y that sits at your chosen x on that line. It is how you estimate a figure that falls between the entries in a table or between two measured readings.

How it works

The tool finds the straight line through your two points, working out its slope and where it would cross the y-axis, then evaluates that line at the x you asked for. In effect, y = y1 + slope × (x − x1): start at the first point and climb along the line until you reach the target x.

Interpolation against extrapolation

A word of care. Interpolation estimates within the range of your two points, which is usually reliable. Estimating outside that range, called extrapolation, is riskier, because the straight-line assumption may not hold once you leave the stretch you actually know.

A worked example

Take the points (1, 10) and (5, 50), and find the value at x = 3.

1. The line has slope (50 − 10) ÷ (5 − 1) = 10.
2. y = 10 × (3 − 1) + 10 = 30.

Since 3 sits halfway between 1 and 5, the answer 30 sits halfway between 10 and 50, exactly as you would expect.

What it is for

Linear interpolation turns up everywhere data comes in tables, in engineering, science, finance, and computer graphics. Whenever you need a value between the ones you actually have, it is the quick and standard way to estimate it.

Questions people ask

What is linear interpolation?

Estimating a value between two known points by assuming a straight line joins them.

How does it work?

It finds the line through the two points and evaluates it at your chosen x.

What is the value at x = 3 between (1, 10) and (5, 50)?

30, the point halfway up the line, matching x = 3 halfway across.

How is it different from extrapolation?

Interpolation estimates within the known range; extrapolation estimates beyond it and is less reliable.

References

A note on the idea behind it. Linear interpolation estimates a value between two known points using the straight line that joins them, evaluated as y = y1 + slope × (x − x1). It is distinct from extrapolation, which estimates beyond the known range. For further reading, see Linear interpolation.

1. Linear interpolation, estimating a value between two points along the line connecting them.