Linear Interpolation Calculator

Find a value between two known points by linear interpolation (or beyond them by extrapolation).

x₁	10
y₁	50
x₂	20
y₂	80
x to find y at	14

x₁

y₁

x₂

y₂

x to find y at

40% of the way from point 1 to point 2.

Interpolation

1at (10, 50)Point at the chart, or Tab to it and use ← →

1: (10, 50)2: (20, 80)62: (14, 62)

How this was worked out

y = y₁ + (x − x₁)(y₂ − y₁) ÷ (x₂ − x₁)

y = 50 + (14 − 10)(80 − 50) ÷ (20 − 10) = 62

About the Linear Interpolation Calculator

Enter two known points (x₁, y₁) and (x₂, y₂) and the x where you want y. The calculator gives y, how far between the points it lies, and the working, and warns if you're extrapolating.

Linear interpolation assumes a straight line between two known points. It's used to read between rows of steam tables, tax tables, survey data and lookup charts.

The formula

y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)

Worked example

Points (10, 50) and (20, 80); find y at x = 14

x is 4 ÷ 10 = 40% of the way along
y = 50 + 0.4 × (80 − 50)
= 62

Questions people ask

What's extrapolation?

Using the same line beyond the known points; less reliable.

Can I interpolate a date?

Yes, convert dates to day numbers first.

How accurate is it?

Exact for straight-line data; for curves, the closer the two points, the smaller the error.