Linear Extrapolation Calculator

This linear extrapolation calculator estimates a y value at an x that falls outside two known data points, by extending the straight line that runs through them. Extrapolation is a common way to make a quick forecast, whether you are projecting a trend in sales, growth or other related measurements, and the answer depends entirely on how well a straight line describes what happens beyond your data. You enter four numbers for your two known points, x1, y1, x2 and y2, plus the target x value you want to predict. The calculator works out the slope of the line, m = (y2 minus y1) divided by (x2 minus x1), then applies that slope to your target x, returning the predicted y value along with the slope so you can see the rate of change behind the forecast. With the default points (1, 2) and (3, 6) and a target x of 5, the slope comes out at 2 and the predicted y is 10, letting you check the tool before entering your own figures. Because extrapolation continues the existing trend rather than testing it against new data, it grows less reliable the further your target x sits from the original points, so treat the result as an indicative estimate rather than a guaranteed outcome, since real-world trends can curve, plateau or reverse outside the range you measured.

target x

Predicted y = 10

Slope2

Predicted y10

The formula

Find the slope m = (y2 minus y1) / (x2 minus x1), then predict y = y1 + m (x minus x1) at the target x. The same straight line is used whether x is inside or outside the two known points.

Worked example

With points (1, 2) and (3, 6), the slope is (6 minus 2)/(3 minus 1) = 2, so at x = 5, y = 2 + 2 times (5 minus 1) = 10. Enter 1, 2, 3, 6, 5 to confirm.

Frequently asked questions

What is extrapolation?

Estimating a value beyond the range of known data by extending an established trend, here a straight line.

How is it different from interpolation?

Interpolation estimates between known points; extrapolation estimates outside them. Both use the same line here.

Is extrapolation reliable?

Use it with care. It assumes the straight line trend continues, which may not hold far from the data.

Who this calculator is for

This calculator is for algebra students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard method is applied.
Results are rounded for display.

Formula and sources

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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