Linear interpolation calculator

Enter two known points (x₁, y₁) and (x₂, y₂), then either an x to get y or a y to get x. The result comes with the slope, the line equation and a note when your value lies outside the two points.

Find

x₁

y₁

x₂

y₂

Known valueThe x when finding y, or the y when finding x.

y15

Slope: 5
y-intercept: 5
Line: y = 5x + 5
Type: Interpolation (between the two points)

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How to use it

Enter the two known points.
Choose whether you know x or y.
Type the known value and read the result.

How it works

The line through the points has slope m = (y₂ − y₁) / (x₂ − x₁). A value at x is y₁ + m × (x − x₁). Going the other way, x = x₁ + (y − y₁) / m, which this tool computes by swapping the roles of x and y.

Worked example

Points (1, 10) and (3, 20), x = 2: the slope is 10 / 2 = 5, so y = 10 + 5 × 1 = 15. Going backwards, y = 15 gives x = 2. The line is y = 5x + 5.

Tips

For table lookups, pick the two table rows that bracket your value.
A result marked as extrapolation deserves extra caution.

Frequently asked questions

What is the formula?

y = y₁ + (x − x₁) × (y₂ − y₁) / (x₂ − x₁). To find x from y the roles of x and y are swapped.

What is the difference between interpolation and extrapolation?

Interpolation estimates a value between the two known points, extrapolation beyond them. Extrapolation is less reliable because the true relationship may not stay straight.

When is linear interpolation accurate?

When the quantity changes roughly steadily between the two points, as in a table with close entries. For curved data, closer points give a better estimate.

Why is the line vertical error shown?

If both points have the same x, the slope would need a division by zero and y is not a function of x.

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All tools in this category: Math ·Updated November 3, 2026